Package 'multimark' reference manual

Title:	Capture-Mark-Recapture Analysis using Multiple Non-Invasive Marks
Description:	Traditional and spatial capture-mark-recapture analysis with multiple non-invasive marks. The models implemented in 'multimark' combine encounter history data arising from two different non-invasive "marks", such as images of left-sided and right-sided pelage patterns of bilaterally asymmetrical species, to estimate abundance and related demographic parameters while accounting for imperfect detection. Bayesian models are specified using simple formulae and fitted using Markov chain Monte Carlo. Addressing deficiencies in currently available software, 'multimark' also provides a user-friendly interface for performing Bayesian multimodel inference using non-spatial or spatial capture-recapture data consisting of a single conventional mark or multiple non-invasive marks. See McClintock (2015) <doi:10.1002/ece3.1676> and Maronde et al. (2020) <doi:10.1002/ece3.6990>.
Authors:	Brett T. McClintock [aut, cre], Acho Arnold [ctb, cph] (C original matrix library, https://github.com/najela/matrix.h), Barry Brown [ctb] (Fortran original ranlib library), James Lovato [ctb] (Fortran original ranlib library), John Burkardt [ctb] (C original ranlib library, http://people.sc.fsu.edu/~jburkardt/c_src/ranlib), Cleve Moler [ctb] (C original linpack library, http://www.kkant.net/geist/ranlib/), Arjun Gopalaswamy [ctb] (modified snippets of R package SPACECAP code)
Maintainer:	Brett T. McClintock <[email protected]>
License:	GPL-2
Version:	2.1.6
Built:	2024-11-21 04:20:29 UTC
Source:	https://github.com/bmcclintock/multimark

Bobcat data

Description

Example bobcat data for multimark package.

Format

The data are summarized in a 46x8 matrix containing observed encounter histories for 46 bobcats across 8 sampling occasions. Bobcats are bilaterially asymmetrical, and sampling was conducted using camera stations consisting of a single camera.

Because the left-side cannot be reconciled with the right-side, the two types of “marks” in this case are the pelage patterns on the left- and right-side of each individual. Encounter type 0 corresponds to non-detection, encounter type 1 corresponds to left-sided detection, encounter type 2 corresponds to right-sided detection.

Both-sided encounters were never observed in this dataset, hence the most appropriate multimark data type is data.type="never".

Source

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

Examples

data(bobcat)
data(bobcat)

Bobcat spatial capture-recapture data

Description

Example spatial bobcat data for multimark package.

Format

These spatial capture-recapture data with multiple mark types are summarized in a list of length 3 containing the following objects:

Enc.Mat is a 42 x (noccas*ntraps) matrix containing observed encounter histories for 42 bobcats across noccas=187 sampling occasions and ntraps=30 traps. The first 187 columns correspond to trap 1, the second 187 columns corresopond to trap 2, etc.

trapCoords is a matrix of dimension ntraps x (2 + noccas) indicating the Cartesian coordinates and operating occasions for the traps, where rows correspond to trap, the first column the x-coordinate, and the second column the y-coordinate. The last noccas columns indicate whether or not the trap was operating on each of the occasions, where ‘1’ indciates the trap was operating and ‘0’ indicates the trap was not operating.

studyArea is a 3-column matrix containing the coordinates for the centroids of the contiguous grid of 1023 cells that define the study area and available habitat. Each row corresponds to a grid cell. The first 2 columns indicate the Cartesian x- and y-coordinate for the centroid of each grid cell, and the third column indicates whether the cell is available habitat (=1) or not (=0). The grid cells are 0.65x0.65km resolution.

Bobcats are bilaterially asymmetrical, and sampling was conducted using camera stations consisting of a single camera. Because the left-side cannot be reconciled with the right-side, the two types of “marks” in this case are the pelage patterns on the left- and right-side of each individual. Encounter type 0 corresponds to non-detection, encounter type 1 corresponds to left-sided detection, encounter type 2 corresponds to right-sided detection.

Both-sided encounters were never observed in this dataset, hence the most appropriate multimark data type is data.type="never".

The first 15 rows of bobcatSCR$Enc.Mat correspond to individuals for which both the left and right sides were known because they were physically captured for telemetry deployments prior to sampling surveys. The encounter histories for these 15 individuals are therefore known with certainty and should be specified as such using the known argument in processdataSCR and/or multimarkClosedSCR (see example below).

These data were obtained from the R package SPIM (Augustine et al. 2017) and modified by projecting onto a regular rectangular grid consisting of square grid cells (as is required by the spatial capture-recapture models in multimark).

Details

We thank B. Augustine and co-authors for making these data publicly available in the SPIM package (Augustine et al. 2017).

Source

Augustine, B., Royle, J.A., Kelly, M., Satter, C., Alonso, R., Boydston, E. and Crooks, K. 2017. Spatial capture-recapture with partial identity: an application to camera traps. bioRxiv doi: https://doi.org/10.1101/056804

Examples

data(bobcatSCR)
#plot the traps and available habitat within the study area
plotSpatialData(trapCoords=bobcatSCR$trapCoords,studyArea=bobcatSCR$studyArea)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

# Fit spatial model to tiger data
Enc.Mat <- bobcatSCR$Enc.Mat
trapCoords <- bobcatSCR$trapCoords
studyArea <- bobcatSCR$studyArea

# specify known encounter histories
known <- c(rep(1,15),rep(0,nrow(Enc.Mat)-15))

# specify prior bounds for sigma2_scr
sig_bounds <- c(0.1,max(diff(range(studyArea[,"x"])),diff(range(studyArea[,"y"]))))

mmsSCR <- processdataSCR(Enc.Mat,trapCoords,studyArea,known=known)
bobcatSCR.dot.type <- multimarkClosedSCR(mms=mmsSCR,iter=200,adapt=100,burnin=100,
                                         sigma_bounds=sig_bounds)
summary(bobcatSCR.dot.type$mcmc)
data(bobcatSCR)
#plot the traps and available habitat within the study area
plotSpatialData(trapCoords=bobcatSCR$trapCoords,studyArea=bobcatSCR$studyArea)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

# Fit spatial model to tiger data
Enc.Mat <- bobcatSCR$Enc.Mat
trapCoords <- bobcatSCR$trapCoords
studyArea <- bobcatSCR$studyArea

# specify known encounter histories
known <- c(rep(1,15),rep(0,nrow(Enc.Mat)-15))

# specify prior bounds for sigma2_scr
sig_bounds <- c(0.1,max(diff(range(studyArea[,"x"])),diff(range(studyArea[,"y"]))))

mmsSCR <- processdataSCR(Enc.Mat,trapCoords,studyArea,known=known)
bobcatSCR.dot.type <- multimarkClosedSCR(mms=mmsSCR,iter=200,adapt=100,burnin=100,
                                         sigma_bounds=sig_bounds)
summary(bobcatSCR.dot.type$mcmc)

Calculate population density estimates

Description

This function calculates posterior population density estimates from multimarkClosedSCR output as D = N/A, where D is density, N is abundance, and A is the area of available habitat within the study area.

Usage

getdensityClosedSCR(out)
getdensityClosedSCR(out)

Arguments

out

List of output returned by multimarkClosedSCR.

Value

An object of class mcmc.list containing the following:

`D`	Posterior samples for density.

Author(s)

Brett T. McClintock

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run behavior model for simulated data with constant detection probability (i.e., mod.p=~c)
sim.data<-simdataClosedSCR()
Enc.Mat<-sim.data$Enc.Mat
trapCoords<-sim.data$spatialInputs$trapCoords
studyArea<-sim.data$spatialInputs$studyArea
example.dot <- multimarkClosedSCR(Enc.Mat,trapCoords,studyArea,mod.p=~1)
  
#Calculate capture and recapture probabilities
D <- getdensityClosedSCR(example.dot)
summary(D)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run behavior model for simulated data with constant detection probability (i.e., mod.p=~c)
sim.data<-simdataClosedSCR()
Enc.Mat<-sim.data$Enc.Mat
trapCoords<-sim.data$spatialInputs$trapCoords
studyArea<-sim.data$spatialInputs$studyArea
example.dot <- multimarkClosedSCR(Enc.Mat,trapCoords,studyArea,mod.p=~1)
  
#Calculate capture and recapture probabilities
D <- getdensityClosedSCR(example.dot)
summary(D)

Calculate posterior capture and survival probabilities

Description

This function calculates posterior capture ( $p$ ) and survival ( $\phi$ ) probabilities for each sampling occasion from multimarkCJS output.

Usage

getprobsCJS(out, link = "probit")
getprobsCJS(out, link = "probit")

Arguments

`out`	List of output returned by `multimarkCJS`
`link`	Link function for $p$ and $\phi$ . Must be "`probit`" or "`logit`". Note that `multimarkCJS` is currently implemented for the probit link only.

Value

An object of class mcmc.list containing the following:

`p`	Posterior samples for capture probability ( $p[c,t]$ ) for each release cohort ( $c=1,\ldots,T-1$ ) and sampling occasion ( $t=2,\ldots,T$ ).
`phi`	Posterior samples for survival probability ( $\phi[c,k]$ ) for each release cohort ( $c=1,\ldots,T-1$ ) and interval ( $k=1,\ldots,T-1$ ).

Author(s)

Brett T. McClintock

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Simulate open population data with temporal variation in survival
noccas <- 5
data <- simdataCJS(noccas=noccas, phibeta=rnorm(noccas-1,1.6,0.1))
 
#Fit open population model with temporal variation in survival
sim.time <- multimarkCJS(data$Enc.Mat,mod.phi=~time)
    
#Calculate capture and survival probabilities for each cohort and time
pphi <- getprobsCJS(sim.time)
summary(pphi)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Simulate open population data with temporal variation in survival
noccas <- 5
data <- simdataCJS(noccas=noccas, phibeta=rnorm(noccas-1,1.6,0.1))
 
#Fit open population model with temporal variation in survival
sim.time <- multimarkCJS(data$Enc.Mat,mod.phi=~time)
    
#Calculate capture and survival probabilities for each cohort and time
pphi <- getprobsCJS(sim.time)
summary(pphi)

Calculate posterior capture and recapture probabilities

Description

This function calculates posterior capture ( $p$ ) and recapture ( $c$ ) probabilities for each sampling occasion from multimarkClosed output.

Usage

getprobsClosed(out, link = "logit")
getprobsClosed(out, link = "logit")

Arguments

`out`	List of output returned by `multimarkClosed`.
`link`	Link function for detection probability. Must be "`logit`" or "`probit`". Note that `multimarkClosed` is currently implemented for the logit link only.

Value

An object of class mcmc.list containing the following:

`p`	Posterior samples for capture probability ( $p$ ) for each sampling occasion.
`c`	Posterior samples for recapture probability ( $c$ ) for each sampling occasion.

Author(s)

Brett T. McClintock

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run behavior model for bobcat data with constant detection probability (i.e., mod.p=~c)
bobcat.c <- multimarkClosed(bobcat,mod.p=~c)
  
#Calculate capture and recapture probabilities
pc <- getprobsClosed(bobcat.c)
summary(pc)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run behavior model for bobcat data with constant detection probability (i.e., mod.p=~c)
bobcat.c <- multimarkClosed(bobcat,mod.p=~c)
  
#Calculate capture and recapture probabilities
pc <- getprobsClosed(bobcat.c)
summary(pc)

Calculate posterior capture and recapture probabilities

Description

This function calculates posterior spatial capture ( $p$ ) and recapture ( $c$ ) probabilities (at zero distance from an activity center) for each sampling occasion from multimarkClosedSCR output.

Usage

getprobsClosedSCR(out, link = "cloglog")
getprobsClosedSCR(out, link = "cloglog")

Arguments

`out`	List of output returned by `multimarkClosedSCR`.
`link`	Link function for detection probability. Must be "`cloglog`". Note that `multimarkClosedSCR` is currently implemented for the cloglog link only.

Value

An object of class mcmc.list containing the following:

`p`	Posterior samples for capture probability ( $p$ ) for each sampling occasion (first index) and trap (second index).
`c`	Posterior samples for recapture probability ( $c$ ) for each sampling occasion (first index) and trap (second index).

Author(s)

Brett T. McClintock

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run behavior model for simulated data with constant detection probability (i.e., mod.p=~c)
sim.data<-simdataClosedSCR()
Enc.Mat<-sim.data$Enc.Mat
trapCoords<-sim.data$spatialInputs$trapCoords
studyArea<-sim.data$spatialInputs$studyArea
example.c <- multimarkClosedSCR(Enc.Mat,trapCoords,studyArea,mod.p=~c,
                                iter=1000,adapt=500,burnin=500)
  
#Calculate capture and recapture probabilities
pc <- getprobsClosedSCR(example.c)
summary(pc)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run behavior model for simulated data with constant detection probability (i.e., mod.p=~c)
sim.data<-simdataClosedSCR()
Enc.Mat<-sim.data$Enc.Mat
trapCoords<-sim.data$spatialInputs$trapCoords
studyArea<-sim.data$spatialInputs$studyArea
example.c <- multimarkClosedSCR(Enc.Mat,trapCoords,studyArea,mod.p=~c,
                                iter=1000,adapt=500,burnin=500)
  
#Calculate capture and recapture probabilities
pc <- getprobsClosedSCR(example.c)
summary(pc)

Fit open population survival models for “traditional” capture-mark-recapture data consisting of a single mark type

Description

This function fits Cormack-Jolly-Seber (CJS) open population models for survival probability ( $\phi$ ) and capture probability ( $p$ ) for “traditional” capture-mark-recapture data consisting of a single mark type. Using Bayesian analysis methods, Markov chain Monte Carlo (MCMC) is used to draw samples from the joint posterior distribution.

Usage

markCJS(
  Enc.Mat,
  covs = data.frame(),
  mod.p = ~1,
  mod.phi = ~1,
  parms = c("pbeta", "phibeta"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  propphibeta = 0.1,
  propzphi = 1,
  propsigmaphi = 1,
  pbeta0 = 0,
  pSigma0 = 1,
  phibeta0 = 0,
  phiSigma0 = 1,
  l0p = 1,
  d0p = 0.01,
  l0phi = 1,
  d0phi = 0.01,
  initial.values = NULL,
  link = "probit",
  printlog = FALSE,
  ...
)
markCJS(
  Enc.Mat,
  covs = data.frame(),
  mod.p = ~1,
  mod.phi = ~1,
  parms = c("pbeta", "phibeta"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  propphibeta = 0.1,
  propzphi = 1,
  propsigmaphi = 1,
  pbeta0 = 0,
  pSigma0 = 1,
  phibeta0 = 0,
  phiSigma0 = 1,
  l0p = 1,
  d0p = 0.01,
  l0phi = 1,
  d0phi = 0.01,
  initial.values = NULL,
  link = "probit",
  printlog = FALSE,
  ...
)

Arguments

`Enc.Mat`	A matrix of observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions. With a single mark type, encounter histories consist of only non-detections (0) and type 1 encounters (1).
`covs`	A data frame of temporal covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of sampling occasions. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`.
`mod.p`	Model formula for detection probability ( $p$ ). For example, `mod.p=~1` specifies no effects (i.e., intercept only), `mod.p~time` specifies temporal effects, `mod.p~age` specifies age effects, `mod.p~h` specifies individual heterogeneity, and `mod.p~time+age` specifies additive temporal and age effects.
`mod.phi`	Model formula for survival probability ( $\phi$ ). For example, `mod.phi=~1` specifies no effects (i.e., intercept only), `mod.phi~time` specifies temporal effects, `mod.phi~age` specifies age effects, `mod.phi~h` specifies individual heterogeneity, and `mod.phi~time+age` specifies additive temporal and age effects.
`parms`	A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are probit-scale detection probability parameters ("`pbeta`" for $p$ and "`phibeta`" for $\phi$ ), probit-scale individual heterogeneity variance terms ("`sigma2_zp`" for $p$ and "`sigma2_zphi`" for $\phi$ ), and probit-scale individual effects ("`zp`" and "`zphi`"). Latent variable indicators for whether each individual was alive (1) or dead (0) during each sampling occasion ("`q`") and the log likelihood ("`loglike`") may also be monitored. Setting `parms="all"` monitors all possible parameters and latent variables.
`nchains`	The number of parallel MCMC chains for the model.
`iter`	The number of MCMC iterations.
`adapt`	Ignored; no adaptive phase is needed for "probit" link.
`bin`	Ignored; no adaptive phase is needed for "probit" link.
`thin`	Thinning interval for monitored parameters.
`burnin`	Number of burn-in iterations (`0 <= burnin < iter`).
`taccept`	Ignored; no adaptive phase is needed for "probit" link.
`tuneadjust`	Ignored; no adaptive phase is needed for "probit" link.
`proppbeta`	Ignored; no adaptive phase is needed for "probit" link.
`propzp`	Ignored; no adaptive phase is needed for "probit" link.
`propsigmap`	Ignored; no adaptive phase is needed for "probit" link.
`propphibeta`	Ignored; no adaptive phase is needed for "probit" link.
`propzphi`	Ignored; no adaptive phase is needed for "probit" link.
`propsigmaphi`	Ignored; no adaptive phase is needed for "probit" link.
`pbeta0`	Scaler or vector (of length k) specifying mean of pbeta ~ multivariateNormal(pbeta0, pSigma0) prior. If `pbeta0` is a scaler, then this value is used for all j = 1, ..., k. Default is `pbeta0 = 0`.
`pSigma0`	Scaler or k x k matrix specifying covariance matrix of pbeta ~ multivariateNormal(pbeta0, pSigma0) prior. If `pSigma0` is a scaler, then this value is used for all pSigma0[j,j] for j = 1, ..., k (with pSigma[j,l] = 0 for all $j \ne l$ ). Default is `pSigma0 = 1`.
`phibeta0`	Scaler or vector (of length k) specifying mean of phibeta ~ multivariateNormal(phibeta0, phiSigma0) prior. If `phibeta0` is a scaler, then this value is used for all j = 1, ..., k. Default is `phibeta0 = 0`.
`phiSigma0`	Scaler or k x k matrix specifying covariance matrix of phibeta ~ multivariateNormal(phibeta0, phiSigma0) prior. If `phiSigma0` is a scaler, then this value is used for all phiSigma0[j,j] for j = 1, ..., k (with phiSigma[j,l] = 0 for all $j \ne l$ ). Default is `phiSigma0 = 1`.
`l0p`	Specifies "shape" parameter for [sigma2_zp] ~ invGamma(l0p,d0p) prior. Default is `l0p = 1`.
`d0p`	Specifies "scale" parameter for [sigma2_zp] ~ invGamma(l0p,d0p) prior. Default is `d0p = 0.01`.
`l0phi`	Specifies "shape" parameter for [sigma2_zphi] ~ invGamma(l0phi,d0phi) prior. Default is `l0phi = 1`.
`d0phi`	Specifies "scale" parameter for [sigma2_zphi] ~ invGamma(l0phi,d0phi) prior. Default is `d0phi = 0.01`.
`initial.values`	OOptional list of `nchain` list(s) specifying initial values for "`pbeta`", "`phibeta`", "`sigma2_zp`", "`sigma2_zphi`", "`zp`", "`zphi`", and "`q`". Default is `initial.values = NULL`, which causes initial values to be generated automatically.
`link`	Link function for survival and capture probabilities. Only probit link is currently implemented.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.
`...`	Additional "`parameters`" arguments for specifying `mod.p` and `mod.phi`. See `RMark::make.design.data`.

Details

The first time markCJS (or markClosed) is called, it will likely produce a firewall warning alerting users that R has requested the ability to accept incoming network connections. Incoming network connections are required to use parallel processing as implemented in multimarkCJS. Note that setting parms="all" is required for any markCJS model output to be used in multimodelCJS.

Value

A list containing the following:

`mcmc`	Markov chain Monte Carlo object of class `mcmc.list`.
`mod.p`	Model formula for detection probability (as specified by `mod.p` above).
`mod.phi`	Model formula for survival probability (as specified by `mod.phi` above).
`mod.delta`	Formula always `NULL`; only for internal use in `multimodelCJS`.
`DM`	A list of design matrices for detection and survival probability respectively generated by `mod.p` and `mod.phi`, where DM$p is the design matrix for capture probability ( $p$ ) and DM$phi is the design matrix for survival probability ( $\phi$ ).
`initial.values`	A list containing the parameter and latent variable values at iteration `iter` for each chain. Values are provided for "`pbeta`", "`phibeta`", "`sigma2_zp`", "`sigma2_zphi`", "`zp`", "`zphi`", and "`q`".
`mms`	An object of class `multimarksetup`

Author(s)

Brett T. McClintock

Examples


# These examples are excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Simulate open population data using defaults
data <- simdataCJS(delta_1=1,delta_2=0)$Enc.Mat

#Fit default open population model
sim.dot <- markCJS(data)

#Posterior summary for monitored parameters
summary(sim.dot$mcmc)
plot(sim.dot$mcmc)

#Fit ``age'' model with 2 age classes (e.g., juvenile and adult) for survival
#using 'parameters' and 'right' arguments from RMark::make.design.data
sim.age <- markCJS(data,mod.phi=~age,
           parameters=list(Phi=list(age.bins=c(0,1,4))),right=FALSE)
summary(getprobsCJS(sim.age))

# These examples are excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Simulate open population data using defaults
data <- simdataCJS(delta_1=1,delta_2=0)$Enc.Mat

#Fit default open population model
sim.dot <- markCJS(data)

#Posterior summary for monitored parameters
summary(sim.dot$mcmc)
plot(sim.dot$mcmc)

#Fit ``age'' model with 2 age classes (e.g., juvenile and adult) for survival
#using 'parameters' and 'right' arguments from RMark::make.design.data
sim.age <- markCJS(data,mod.phi=~age,
           parameters=list(Phi=list(age.bins=c(0,1,4))),right=FALSE)
summary(getprobsCJS(sim.age))

Fit closed population abundance models for “traditional” capture-mark-recapture data consisting of a single mark type

Description

This function fits closed population abundance models for “traditional” capture-mark-recapture data consisting of a single mark type using Bayesian analysis methods. Markov chain Monte Carlo (MCMC) is used to draw samples from the joint posterior distribution.

Usage

markClosed(
  Enc.Mat,
  covs = data.frame(),
  mod.p = ~1,
  parms = c("pbeta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  npoints = 500,
  a = 25,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  initial.values = NULL,
  printlog = FALSE,
  ...
)
markClosed(
  Enc.Mat,
  covs = data.frame(),
  mod.p = ~1,
  parms = c("pbeta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  npoints = 500,
  a = 25,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  initial.values = NULL,
  printlog = FALSE,
  ...
)

Arguments

`Enc.Mat`	A matrix of observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions. With a single mark type, encounter histories consist of only non-detections (0) and type 1 encounters (1).
`covs`	A data frame of temporal covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of sampling occasions. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`.
`mod.p`	Model formula for detection probability. For example, `mod.p=~1` specifies no effects (i.e., intercept only), `mod.p~time` specifies temporal effects, `mod.p~c` specifies behavioral reponse (i.e., trap "happy" or "shy"), `mod.p~h` specifies individual heterogeneity, and `mod.p~time+c` specifies additive temporal and behavioral effects.
`parms`	A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are logit-scale detection probability parameters ("`pbeta`"), population abundance ("`N`"), logit-scale individual heterogeneity variance term ("`sigma2_zp`"), and logit-scale individual effects ("`zp`"). The log posterior density ("`logPosterior`") may also be monitored. Setting `parms="all"` monitors all possible parameters and latent variables.
`nchains`	The number of parallel MCMC chains for the model.
`iter`	The number of MCMC iterations.
`adapt`	The number of iterations for proposal distribution adaptation. If `adapt = 0` then no adaptation occurs.
`bin`	Bin length for calculating acceptance rates during adaptive phase (`0 < bin <= iter`).
`thin`	Thinning interval for monitored parameters.
`burnin`	Number of burn-in iterations (`0 <= burnin < iter`).
`taccept`	Target acceptance rate during adaptive phase (`0 < taccept <= 1`). Acceptance rate is monitored every `bin` iterations. Default is `taccept = 0.44`.
`tuneadjust`	Adjustment term during adaptive phase (`0 < tuneadjust <= 1`). If acceptance rate is less than `taccept`, then proposal term (`proppbeta`, `propzp`, or `propsigmap`) is multiplied by `tuneadjust`. If acceptance rate is greater than or equal to `taccept`, then proposal term is divided by `tuneadjust`. Default is `tuneadjust = 0.95`.
`proppbeta`	Scaler or vector (of length k) specifying the initial standard deviation of the Normal(pbeta[j], proppbeta[j]) proposal distribution. If `proppbeta` is a scaler, then this value is used for all j = 1, ..., k. Default is `proppbeta = 0.1`.
`propzp`	Scaler or vector (of length M) specifying the initial standard deviation of the Normal(zp[i], propzp[i]) proposal distribution. If `propzp` is a scaler, then this value is used for all i = 1, ..., M individuals. Default is `propzp = 1`.
`propsigmap`	Scaler specifying the initial Gamma(shape = 1/`propsigmap`, scale = sigma_zp * `propsigmap`) proposal distribution for sigma_zp = sqrt(sigma2_zp). Default is `propsigmap=1`.
`npoints`	Number of Gauss-Hermite quadrature points to use for numerical integration. Accuracy increases with number of points, but so does computation time.
`a`	Scale parameter for [sigma_z] ~ half-Cauchy(a) prior for the individual hetegeneity term sigma_zp = sqrt(sigma2_zp). Default is “uninformative” `a = 25`.
`mu0`	Scaler or vector (of length k) specifying mean of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `mu0 = 0`.
`sigma2_mu0`	Scaler or vector (of length k) specifying variance of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `sigma2_mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `sigma2_mu0 = 1.75`.
`initial.values`	Optional list of `nchain` list(s) specifying initial values for "`pbeta`", "`zp`", "`sigma2_zp`", and "`N`". Default is `initial.values = NULL`, which causes initial values to be generated automatically.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.
`...`	Additional "`parameters`" arguments for specifying `mod.p`. See `make.design.data`.

Details

The first time markClosed (or markCJS) is called, it will likely produce a firewall warning alerting users that R has requested the ability to accept incoming network connections. Incoming network connections are required to use parallel processing as implemented in markClosed. Note that setting parms="all" is required for any markClosed model output to be used in multimodelClosed.

Value

A list containing the following:

`mcmc`	Markov chain Monte Carlo object of class `mcmc.list`.
`mod.p`	Model formula for detection probability (as specified by `mod.p` above).
`mod.delta`	Formula always `NULL`; only for internal use in `multimodelClosed`.
`DM`	A list of design matrices for detection probability generated for model `mod.p`, where DM$p is the design matrix for initial capture probability (p) and DM$c is the design matrix for recapture probability (c).
`initial.values`	A list containing the parameter and latent variable values at iteration `iter` for each chain. Values are provided for "`pbeta`", "`zp`", "`sigma2_zp`", and "`N`".
`mms`	An object of class `multimarksetup`

Author(s)

Brett T. McClintock

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run single chain using the default model for simulated ``traditional'' data
data<-simdataClosed(delta_1=1,delta_2=0)$Enc.Mat
sim.dot<-markClosed(data)

#Posterior summary for monitored parameters
summary(sim.dot$mcmc)
plot(sim.dot$mcmc)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run single chain using the default model for simulated ``traditional'' data
data<-simdataClosed(delta_1=1,delta_2=0)$Enc.Mat
sim.dot<-markClosed(data)

#Posterior summary for monitored parameters
summary(sim.dot$mcmc)
plot(sim.dot$mcmc)

Fit spatial population abundance models for “traditional” capture-mark-recapture data consisting of a single mark type

Description

This function fits spatial population abundance models for “traditional” capture-mark-recapture data consisting of a single mark type using Bayesian analysis methods. Markov chain Monte Carlo (MCMC) is used to draw samples from the joint posterior distribution.

Usage

markClosedSCR(
  Enc.Mat,
  trapCoords,
  studyArea = NULL,
  buffer = NULL,
  ncells = 1024,
  covs = data.frame(),
  mod.p = ~1,
  detection = "half-normal",
  parms = c("pbeta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propsigma = 1,
  propcenter = NULL,
  sigma_bounds = NULL,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  initial.values = NULL,
  scalemax = 10,
  printlog = FALSE,
  ...
)
markClosedSCR(
  Enc.Mat,
  trapCoords,
  studyArea = NULL,
  buffer = NULL,
  ncells = 1024,
  covs = data.frame(),
  mod.p = ~1,
  detection = "half-normal",
  parms = c("pbeta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propsigma = 1,
  propcenter = NULL,
  sigma_bounds = NULL,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  initial.values = NULL,
  scalemax = 10,
  printlog = FALSE,
  ...
)

Arguments

`Enc.Mat`	A matrix containing the observed encounter histories with rows corresponding to individuals and (`ntraps`*`noccas`) columns corresponding to traps and sampling occasions. The first `noccas` columns correspond to trap 1, the second `noccas` columns corresopond to trap 2, etc.
`trapCoords`	A matrix of dimension `ntraps` x (2 + `noccas`) indicating the Cartesian coordinates and operating occasions for the traps, where rows correspond to trap, the first column the x-coordinate (“x”), and the second column the y-coordinate (“y”). The last `noccas` columns indicate whether or not the trap was operating on each of the occasions, where ‘1’ indciates the trap was operating and ‘0’ indicates the trap was not operating. Ignored unless `mms=NULL`.
`studyArea`	is a 3-column matrix containing the coordinates for the centroids a contiguous grid of cells that define the study area and available habitat. Each row corresponds to a grid cell. The first 2 columns (“x” and “y”) indicate the Cartesian x- and y-coordinate for the centroid of each grid cell, and the third column (“avail”) indicates whether the cell is available habitat (=1) or not (=0). All cells must have the same resolution. If `studyArea=NULL` (the default) and `mms=NULL`, then a square study area grid composed of `ncells` cells of available habitat is drawn around the bounding box of `trapCoords` based on `buffer`. Ignored unless `mms=NULL`. Note that rows should be ordered by raster cell order (raster cell numbers start at 1 in the upper left corner, and increase from left to right, and then from top to bottom).
`buffer`	A scaler in same units as `trapCoords` indicating the buffer around the bounding box of `trapCoords` for defining the study area when `studyArea=NULL`. Ignored unless `studyArea=NULL`.
`ncells`	The number of grid cells in the study area when `studyArea=NULL`. The square root of `ncells` must be a whole number. Default is `ncells=1024`. Ignored unless `studyArea=NULL` and `mms=NULL`.
`covs`	A data frame of time- and/or trap-dependent covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of traps times the number of sampling occasions (`ntraps*noccas`), where the first `noccas` rows correspond to trap 1, the `noccas` rows correspond to trap 2, etc. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`.
`mod.p`	Model formula for detection probability. For example, `mod.p=~1` specifies no effects (i.e., intercept only), `mod.p~time` specifies temporal effects, `mod.p~c` specifies behavioral reponse (i.e., trap "happy" or "shy"), `mod.p~trap` specifies trap effects, and `mod.p~time+c` specifies additive temporal and behavioral effects.
`detection`	Model for detection probability as a function of distance from activity centers . Must be "`half-normal`" (of the form $\exp{(-d^2 / (2*\sigma^2))}$ , where $d$ is distance) or "`exponential`" (of the form $\exp{(-d / \lambda)}$ ).
`parms`	A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are cloglog-scale detection probability parameters ("`pbeta`"), population abundance ("`N`"), and cloglog-scale distance term for the detection function ("`sigma2_scr`" when detection=``half-normal'' or "`lambda`" when detection=``exponential''). Individual activity centers ("`centers`") and the log posterior density ("`logPosterior`") may also be monitored. Setting `parms="all"` monitors all possible parameters and latent variables.
`nchains`	The number of parallel MCMC chains for the model.
`iter`	The number of MCMC iterations.
`adapt`	The number of iterations for proposal distribution adaptation. If `adapt = 0` then no adaptation occurs.
`bin`	Bin length for calculating acceptance rates during adaptive phase (`0 < bin <= iter`).
`thin`	Thinning interval for monitored parameters.
`burnin`	Number of burn-in iterations (`0 <= burnin < iter`).
`taccept`	Target acceptance rate during adaptive phase (`0 < taccept <= 1`). Acceptance rate is monitored every `bin` iterations. Default is `taccept = 0.44`.
`tuneadjust`	Adjustment term during adaptive phase (`0 < tuneadjust <= 1`). If acceptance rate is less than `taccept`, then proposal term (`proppbeta` or `propsigma`) is multiplied by `tuneadjust`. If acceptance rate is greater than or equal to `taccept`, then proposal term is divided by `tuneadjust`. Default is `tuneadjust = 0.95`.
`proppbeta`	Scaler or vector (of length k) specifying the initial standard deviation of the Normal(pbeta[j], proppbeta[j]) proposal distribution. If `proppbeta` is a scaler, then this value is used for all j = 1, ..., k. Default is `proppbeta = 0.1`.
`propsigma`	Scaler specifying the initial Gamma(shape = 1/`propsigma`, scale = sigma_scr * `propsigma`) proposal distribution for sigma_scr = sqrt(sigma2_scr). Default is `propsigma=1`.
`propcenter`	Scaler specifying the neighborhood distance when proposing updates to activity centers. When `propcenter=NULL` (the default), then propcenter = a*10, where a is the cell size for the study area grid, and each cell has (at most) approximately 300 neighbors.
`sigma_bounds`	Positive vector of length 2 for the lower and upper bounds for the [sigma_scr] ~ Uniform(sigma_bounds[1], sigma_bounds[2]) (or [sqrt(lambda)] when detection=``exponential'') prior for the detection function term sigma_scr = sqrt(sigma2_scr) (or sqrt(lambda)). When `sigma_bounds = NULL` (the default), then `sigma_bounds = c(1.e-6,max(diff(range(studyArea[,"x"])),diff(range(studyArea[,"y"]))))`.
`mu0`	Scaler or vector (of length k) specifying mean of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `mu0 = 0`.
`sigma2_mu0`	Scaler or vector (of length k) specifying variance of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `sigma2_mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `sigma2_mu0 = 1.75`.
`initial.values`	Optional list of `nchain` list(s) specifying initial values for "`pbeta`", "`N`", "`sigma2_scr`", and "`centers`". Default is `initial.values = NULL`, which causes initial values to be generated automatically.
`scalemax`	Upper bound for internal re-scaling of grid cell centroid coordinates. Default is `scalemax=10`, which re-scales the centroids to be between 0 and 10. Re-scaling is done internally to avoid numerical overflows during model fitting.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.
`...`	Additional "`parameters`" arguments for specifying `mod.p`. See `make.design.data`.

Details

The first time markClosedSCR is called, it will likely produce a firewall warning alerting users that R has requested the ability to accept incoming network connections. Incoming network connections are required to use parallel processing as implemented in markClosed. Note that setting parms="all" is required for any markClosed model output to be used in multimodelClosed.

Value

A list containing the following:

`mcmc`	Markov chain Monte Carlo object of class `mcmc.list`.
`mod.p`	Model formula for detection probability (as specified by `mod.p` above).
`mod.delta`	Formula always `NULL`; only for internal use in `multimodelClosedSCR`.
`mod.det`	Model formula for detection function (as specified by `detection` above).
`DM`	A list of design matrices for detection probability generated for model `mod.p`, where DM$p is the design matrix for initial capture probability (p) and DM$c is the design matrix for recapture probability (c).
`initial.values`	A list containing the parameter and latent variable values at iteration `iter` for each chain. Values are provided for "`pbeta`", "`N`", "`sigma2_scr`", and "`centers`".
`mms`	An object of class `multimarkSCRsetup`

Author(s)

Brett T. McClintock

References

Gopalaswamy, A.M., Royle, J.A., Hines, J.E., Singh, P., Jathanna, D., Kumar, N. and Karanth, K.U. 2012. Program SPACECAP: software for estimating animal density using spatially explicit capture-recapture models. Methods in Ecology and Evolution 3:1067-1072.

King, R., McClintock, B. T., Kidney, D., and Borchers, D. L. 2016. Capture-recapture abundance estimation using a semi-complete data likelihood approach. The Annals of Applied Statistics 10: 264-285

Royle, J.A., Karanth, K.U., Gopalaswamy, A.M. and Kumar, N.S. 2009. Bayesian inference in camera trapping studies for a class of spatial capture-recapture models. Ecology 90: 3233-3244.

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run single chain using the default model for ``traditional'' tiger data of Royle et al (2009)
Enc.Mat<-tiger$Enc.Mat
trapCoords<-tiger$trapCoords
studyArea<-tiger$studyArea
tiger.dot<-markClosedSCR(Enc.Mat,trapCoords,studyArea,iter=100,adapt=50,burnin=50)

#Posterior summary for monitored parameters
summary(tiger.dot$mcmc)
plot(tiger.dot$mcmc)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run single chain using the default model for ``traditional'' tiger data of Royle et al (2009)
Enc.Mat<-tiger$Enc.Mat
trapCoords<-tiger$trapCoords
studyArea<-tiger$studyArea
tiger.dot<-markClosedSCR(Enc.Mat,trapCoords,studyArea,iter=100,adapt=50,burnin=50)

#Posterior summary for monitored parameters
summary(tiger.dot$mcmc)
plot(tiger.dot$mcmc)

Fit open population survival models for capture-mark-recapture data consisting of multiple non-invasive marks

Description

This function fits Cormack-Jolly-Seber (CJS) open population models for survival probability ( $\phi$ ) and capture probability ( $p$ ) from capture-mark-recapture data consisting of multiple non-invasive marks. Using Bayesian analysis methods, Markov chain Monte Carlo (MCMC) is used to draw samples from the joint posterior distribution.

Usage

multimarkCJS(
  Enc.Mat,
  data.type = "never",
  covs = data.frame(),
  mms = NULL,
  mod.p = ~1,
  mod.phi = ~1,
  mod.delta = ~type,
  parms = c("pbeta", "phibeta", "delta"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  propphibeta = 0.1,
  propzphi = 1,
  propsigmaphi = 1,
  maxnumbasis = 1,
  pbeta0 = 0,
  pSigma0 = 1,
  phibeta0 = 0,
  phiSigma0 = 1,
  l0p = 1,
  d0p = 0.01,
  l0phi = 1,
  d0phi = 0.01,
  a0delta = 1,
  a0alpha = 1,
  b0alpha = 1,
  a0psi = 1,
  b0psi = 1,
  initial.values = NULL,
  known = integer(),
  link = "probit",
  printlog = FALSE,
  ...
)
multimarkCJS(
  Enc.Mat,
  data.type = "never",
  covs = data.frame(),
  mms = NULL,
  mod.p = ~1,
  mod.phi = ~1,
  mod.delta = ~type,
  parms = c("pbeta", "phibeta", "delta"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  propphibeta = 0.1,
  propzphi = 1,
  propsigmaphi = 1,
  maxnumbasis = 1,
  pbeta0 = 0,
  pSigma0 = 1,
  phibeta0 = 0,
  phiSigma0 = 1,
  l0p = 1,
  d0p = 0.01,
  l0phi = 1,
  d0phi = 0.01,
  a0delta = 1,
  a0alpha = 1,
  b0alpha = 1,
  a0psi = 1,
  b0psi = 1,
  initial.values = NULL,
  known = integer(),
  link = "probit",
  printlog = FALSE,
  ...
)

Arguments

`Enc.Mat`	A matrix of observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions (ignored unless `mms=NULL`).
`data.type`	Specifies the encounter history data type. All data types include non-detections (type 0 encounter), type 1 encounter (e.g., left-side), and type 2 encounters (e.g., right-side). When both type 1 and type 2 encounters occur for the same individual within a sampling occasion, these can either be "non-simultaneous" (type 3 encounter) or "simultaneous" (type 4 encounter). Three data types are currently permitted: `data.type="never"` indicates both type 1 and type 2 encounters are never observed for the same individual within a sampling occasion, and observed encounter histories therefore include only type 1 or type 2 encounters (e.g., only left- and right-sided photographs were collected). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), and type 2 encounters (2). See `bobcat`. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 3 encounters (3). `data.type="sometimes"` indicates both type 1 and type 2 encounters are sometimes observed (e.g., both-sided photographs are sometimes obtained, but not necessarily for all individuals). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). Type 3 encounters can only be observed when an individual has at least one type 4 encounter. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). `data.type="always"` indicates both type 1 and type 2 encounters are always observed, but some encounter histories may still include only type 1 or type 2 encounters. Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4). Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4).
`covs`	A data frame of temporal covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of sampling occasions. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`.
`mms`	An optional object of class `multimarksetup-class`; if `NULL` it is created. See `processdata`.
`mod.p`	Model formula for detection probability ( $p$ ). For example, `mod.p=~1` specifies no effects (i.e., intercept only), `mod.p~time` specifies temporal effects, `mod.p~age` specifies age effects, `mod.p~h` specifies individual heterogeneity, and `mod.p~time+age` specifies additive temporal and age effects.
`mod.phi`	Model formula for survival probability ( $\phi$ ). For example, `mod.phi=~1` specifies no effects (i.e., intercept only), `mod.phi~time` specifies temporal effects, `mod.phi~age` specifies age effects, `mod.phi~h` specifies individual heterogeneity, and `mod.phi~time+age` specifies additive temporal and age effects.
`mod.delta`	Model formula for conditional probabilities of type 1 (delta_1) and type 2 (delta_2) encounters, given detection. Currently only `mod.delta=~1` (i.e., $\delta_1 = \delta_2$ ) and `mod.delta=~type` (i.e., $\delta_1 \ne \delta_2$ ) are implemented.
`parms`	A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are probit-scale detection probability parameters ("`pbeta`" for $p$ and "`phibeta`" for $\phi$ ), conditional probability of type 1 or type 2 encounter, given detection ("`delta`)", probability of simultaneous type 1 and type 2 detection, given both types encountered ("`alpha`"), probit-scale individual heterogeneity variance terms ("`sigma2_zp`" for $p$ and "`sigma2_zphi`" for $\phi$ ), probit-scale individual effects ("`zp`" and "`zphi`"), and the probability that a randomly selected individual from the `M = nrow(Enc.Mat)` observed individuals belongs to the $n$ unique individuals encountered at least once ("`psi`"). Individual encounter history indices ("`H`"), latent variable indicators for whether each individual was alive (1) or dead (0) during each sampling occasion ("`q`"), and the log likelihood ("`loglike`") may also be monitored. Setting `parms="all"` monitors all possible parameters and latent variables.
`nchains`	The number of parallel MCMC chains for the model.
`iter`	The number of MCMC iterations.
`adapt`	Ignored; no adaptive phase is needed for "probit" link.
`bin`	Ignored; no adaptive phase is needed for "probit" link.
`thin`	Thinning interval for monitored parameters.
`burnin`	Number of burn-in iterations (`0 <= burnin < iter`).
`taccept`	Ignored; no adaptive phase is needed for "probit" link.
`tuneadjust`	Ignored; no adaptive phase is needed for "probit" link.
`proppbeta`	Ignored; no adaptive phase is needed for "probit" link.
`propzp`	Ignored; no adaptive phase is needed for "probit" link.
`propsigmap`	Ignored; no adaptive phase is needed for "probit" link.
`propphibeta`	Ignored; no adaptive phase is needed for "probit" link.
`propzphi`	Ignored; no adaptive phase is needed for "probit" link.
`propsigmaphi`	Ignored; no adaptive phase is needed for "probit" link.
`maxnumbasis`	Maximum number of basis vectors to use when proposing latent history frequency updates. Default is `maxnumbasis = 1`, but higher values can potentially improve mixing.
`pbeta0`	Scaler or vector (of length k) specifying mean of pbeta ~ multivariateNormal(pbeta0, pSigma0) prior. If `pbeta0` is a scaler, then this value is used for all j = 1, ..., k. Default is `pbeta0 = 0`.
`pSigma0`	Scaler or k x k matrix specifying covariance matrix of pbeta ~ multivariateNormal(pbeta0, pSigma0) prior. If `pSigma0` is a scaler, then this value is used for all pSigma0[j,j] for j = 1, ..., k (with pSigma[j,l] = 0 for all $j \ne l$ ). Default is `pSigma0 = 1`.
`phibeta0`	Scaler or vector (of length k) specifying mean of phibeta ~ multivariateNormal(phibeta0, phiSigma0) prior. If `phibeta0` is a scaler, then this value is used for all j = 1, ..., k. Default is `phibeta0 = 0`.
`phiSigma0`	Scaler or k x k matrix specifying covariance matrix of phibeta ~ multivariateNormal(phibeta0, phiSigma0) prior. If `phiSigma0` is a scaler, then this value is used for all phiSigma0[j,j] for j = 1, ..., k (with phiSigma[j,l] = 0 for all $j \ne l$ ). Default is `phiSigma0 = 1`.
`l0p`	Specifies "shape" parameter for [sigma2_zp] ~ invGamma(l0p,d0p) prior. Default is `l0p = 1`.
`d0p`	Specifies "scale" parameter for [sigma2_zp] ~ invGamma(l0p,d0p) prior. Default is `d0p = 0.01`.
`l0phi`	Specifies "shape" parameter for [sigma2_zphi] ~ invGamma(l0phi,d0phi) prior. Default is `l0phi = 1`.
`d0phi`	Specifies "scale" parameter for [sigma2_zphi] ~ invGamma(l0phi,d0phi) prior. Default is `d0phi = 0.01`.
`a0delta`	Scaler or vector (of length d) specifying the prior for the conditional (on detection) probability of type 1 (delta_1), type 2 (delta_2), and both type 1 and type 2 encounters (1-delta_1-delta_2). If `a0delta` is a scaler, then this value is used for all a0delta[j] for j = 1, ..., d. For `mod.delta=~type`, d=3 with [delta_1, delta_2, 1-delta_1-delta_2] ~ Dirichlet(a0delta) prior. For `mod.delta=~1`, d=2 with [tau] ~ Beta(a0delta[1],a0delta[2]) prior, where (delta_1,delta_2,1-delta_1-delta_2) = (tau/2,tau/2,1-tau). See McClintock et al. (2013) for more details.
`a0alpha`	Specifies "shape1" parameter for [alpha] ~ Beta(a0alpha, b0alpha) prior. Only applicable when `data.type = "sometimes"`. Default is `a0alpha = 1`. Note that when `a0alpha = 1` and `b0alpha = 1`, then [alpha] ~ Unif(0,1).
`b0alpha`	Specifies "shape2" parameter for [alpha] ~ Beta(a0alpha, b0alpha) prior. Only applicable when `data.type = "sometimes"`. Default is `b0alpha = 1`. Note that when `a0alpha = 1` and `b0alpha = 1`, then [alpha] ~ Unif(0,1).
`a0psi`	Specifies "shape1" parameter for [psi] ~ Beta(a0psi,b0psi) prior. Default is `a0psi = 1`.
`b0psi`	Specifies "shape2" parameter for [psi] ~ Beta(a0psi,b0psi) prior. Default is `b0psi = 1`.
`initial.values`	Optional list of `nchain` list(s) specifying initial values for parameters and latent variables. Default is `initial.values = NULL`, which causes initial values to be generated automatically. In addition to the parameters ("`pbeta`", "`phibeta`", "`delta_1`", "`delta_2`", "`alpha`", "`sigma2_zp`", "`sigma2_zphi`", "`zp`", "`zphi`", and "`psi`"), initial values can be specified for the initial latent history frequencies ("`x`"), initial individual encounter history indices ("`H`"), and initial latent variable indicators for whether each individual was alive (1) or dead (0) during each sampling occasion ("`q`").
`known`	Optional integer vector indicating whether the encounter history of an individual is known with certainty (i.e., the observed encounter history is the true encounter history). Encounter histories with at least one type 4 encounter are automatically assumed to be known, and `known` does not need to be specified unless there exist encounter histories that do not contain a type 4 encounter that happen to be known with certainty (e.g., from independent telemetry studies). If specified, `known = c(v_1,v_2,...,v_M)` must be a vector of length `M = nrow(Enc.Mat)` where `v_i = 1` if the encounter history for individual `i` is known (`v_i = 0` otherwise). Note that known all-zero encounter histories (e.g., ‘000’) are ignored.
`link`	Link function for survival and capture probabilities. Only probit link is currently implemented.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.
`...`	Additional "`parameters`" arguments for specifying `mod.p` and `mod.phi`. See `RMark::make.design.data`.

Details

The first time multimarkCJS (or multimarkClosed) is called, it will likely produce a firewall warning alerting users that R has requested the ability to accept incoming network connections. Incoming network connections are required to use parallel processing as implemented in multimarkCJS. Note that setting parms="all" is required for any multimarkCJS model output to be used in multimodelCJS.

Value

A list containing the following:

`mcmc`	Markov chain Monte Carlo object of class `mcmc.list`.
`mod.p`	Model formula for detection probability (as specified by `mod.p` above).
`mod.phi`	Model formula for survival probability (as specified by `mod.phi` above).
`mod.delta`	Formula always `NULL`; only for internal use in `multimodelCJS`.
`DM`	A list of design matrices for detection and survival probability respectively generated by `mod.p` and `mod.phi`, where DM$p is the design matrix for capture probability ( $p$ ) and DM$phi is the design matrix for survival probability ( $\phi$ ).
`initial.values`	A list containing the parameter and latent variable values at iteration `iter` for each chain. Values are provided for "`pbeta`", "`phibeta`", "`delta_1`", "`delta_2`", "`alpha`", "`sigma2_zp`" "`sigma2_zphi`", "`zp`", "`zphi`", "`psi`", "`x`", "`H`", and "`q`".
`mms`	An object of class `multimarksetup`

Author(s)

Brett T. McClintock

References

Bonner, S. J., and Holmberg J. 2013. Mark-recapture with multiple, non-invasive marks. Biometrics 69: 766-775.

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

McClintock, B. T., Bailey, L. L., Dreher, B. P., and Link, W. A. 2014. Probit models for capture-recapture data subject to imperfect detection, individual heterogeneity and misidentification. The Annals of Applied Statistics 8: 2461-2484.

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Simulate open population data using defaults
data <- simdataCJS()

#Fit default open population model
sim.dot <- multimarkCJS(data$Enc.Mat)

#Posterior summary for monitored parameters
summary(sim.dot$mcmc)
plot(sim.dot$mcmc)

#' #Fit ``age'' model with 2 age classes (e.g., juvenile and adult) for survival
#using 'parameters' and 'right' arguments from RMark::make.design.data
sim.age <- multimarkCJS(data$Enc.Mat,mod.phi=~age,
           parameters=list(Phi=list(age.bins=c(0,1,4))),right=FALSE)
summary(getprobsCJS(sim.age))

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Simulate open population data using defaults
data <- simdataCJS()

#Fit default open population model
sim.dot <- multimarkCJS(data$Enc.Mat)

#Posterior summary for monitored parameters
summary(sim.dot$mcmc)
plot(sim.dot$mcmc)

#' #Fit ``age'' model with 2 age classes (e.g., juvenile and adult) for survival
#using 'parameters' and 'right' arguments from RMark::make.design.data
sim.age <- multimarkCJS(data$Enc.Mat,mod.phi=~age,
           parameters=list(Phi=list(age.bins=c(0,1,4))),right=FALSE)
summary(getprobsCJS(sim.age))

Fit closed population abundance models for capture-mark-recapture data consisting of multiple non-invasive marks

Description

This function fits closed population abundance models for capture-mark-recapture data consisting of multiple non-invasive marks using Bayesian analysis methods. Markov chain Monte Carlo (MCMC) is used to draw samples from the joint posterior distribution.

Usage

multimarkClosed(
  Enc.Mat,
  data.type = "never",
  covs = data.frame(),
  mms = NULL,
  mod.p = ~1,
  mod.delta = ~type,
  parms = c("pbeta", "delta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  npoints = 500,
  maxnumbasis = 1,
  a0delta = 1,
  a0alpha = 1,
  b0alpha = 1,
  a = 25,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  a0psi = 1,
  b0psi = 1,
  initial.values = NULL,
  known = integer(),
  printlog = FALSE,
  ...
)
multimarkClosed(
  Enc.Mat,
  data.type = "never",
  covs = data.frame(),
  mms = NULL,
  mod.p = ~1,
  mod.delta = ~type,
  parms = c("pbeta", "delta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propzp = 1,
  propsigmap = 1,
  npoints = 500,
  maxnumbasis = 1,
  a0delta = 1,
  a0alpha = 1,
  b0alpha = 1,
  a = 25,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  a0psi = 1,
  b0psi = 1,
  initial.values = NULL,
  known = integer(),
  printlog = FALSE,
  ...
)

Arguments

`Enc.Mat`	A matrix of observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions (ignored unless `mms=NULL`).
`data.type`	Specifies the encounter history data type. All data types include non-detections (type 0 encounter), type 1 encounter (e.g., left-side), and type 2 encounters (e.g., right-side). When both type 1 and type 2 encounters occur for the same individual within a sampling occasion, these can either be "non-simultaneous" (type 3 encounter) or "simultaneous" (type 4 encounter). Three data types are currently permitted: `data.type="never"` indicates both type 1 and type 2 encounters are never observed for the same individual within a sampling occasion, and observed encounter histories therefore include only type 1 or type 2 encounters (e.g., only left- and right-sided photographs were collected). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), and type 2 encounters (2). See `bobcat`. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 3 encounters (3). `data.type="sometimes"` indicates both type 1 and type 2 encounters are sometimes observed (e.g., both-sided photographs are sometimes obtained, but not necessarily for all individuals). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). Type 3 encounters can only be observed when an individual has at least one type 4 encounter. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). `data.type="always"` indicates both type 1 and type 2 encounters are always observed, but some encounter histories may still include only type 1 or type 2 encounters. Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4). Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4).
`covs`	A data frame of temporal covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of sampling occasions. Covariate names cannot be "time", "c", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`.
`mms`	An optional object of class `multimarksetup-class`; if `NULL` it is created. See `processdata`.
`mod.p`	Model formula for detection probability. For example, `mod.p=~1` specifies no effects (i.e., intercept only), `mod.p~time` specifies temporal effects, `mod.p~c` specifies behavioral reponse (i.e., trap "happy" or "shy"), `mod.p~h` specifies individual heterogeneity, and `mod.p~time+c` specifies additive temporal and behavioral effects.
`mod.delta`	Model formula for conditional probabilities of type 1 (delta_1) and type 2 (delta_2) encounters, given detection. Currently only `mod.delta=~1` (i.e., $\delta_1 = \delta_2$ ) and `mod.delta=~type` (i.e., $\delta_1 \ne \delta_2$ ) are implemented.
`parms`	A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are logit-scale detection probability parameters ("`pbeta`"), population abundance ("`N`"), conditional probability of type 1 or type 2 encounter, given detection ("`delta`)", probability of simultaneous type 1 and type 2 detection, given both types encountered ("`alpha`"), logit-scale individual heterogeneity variance term ("`sigma2_zp`"), logit-scale individual effects ("`zp`"), and the probability that a randomly selected individual from the `M = nrow(Enc.Mat)` observed individuals belongs to the $n$ unique individuals encountered at least once ("`psi`"). Individual encounter history indices ("`H`") and the log posterior density ("`logPosterior`") may also be monitored. Setting `parms="all"` monitors all possible parameters and latent variables.
`nchains`	The number of parallel MCMC chains for the model.
`iter`	The number of MCMC iterations.
`adapt`	The number of iterations for proposal distribution adaptation. If `adapt = 0` then no adaptation occurs.
`bin`	Bin length for calculating acceptance rates during adaptive phase (`0 < bin <= iter`).
`thin`	Thinning interval for monitored parameters.
`burnin`	Number of burn-in iterations (`0 <= burnin < iter`).
`taccept`	Target acceptance rate during adaptive phase (`0 < taccept <= 1`). Acceptance rate is monitored every `bin` iterations. Default is `taccept = 0.44`.
`tuneadjust`	Adjustment term during adaptive phase (`0 < tuneadjust <= 1`). If acceptance rate is less than `taccept`, then proposal term (`proppbeta`, `propzp`, or `propsigmap`) is multiplied by `tuneadjust`. If acceptance rate is greater than or equal to `taccept`, then proposal term is divided by `tuneadjust`. Default is `tuneadjust = 0.95`.
`proppbeta`	Scaler or vector (of length k) specifying the initial standard deviation of the Normal(pbeta[j], proppbeta[j]) proposal distribution. If `proppbeta` is a scaler, then this value is used for all j = 1, ..., k. Default is `proppbeta = 0.1`.
`propzp`	Scaler or vector (of length M) specifying the initial standard deviation of the Normal(zp[i], propzp[i]) proposal distribution. If `propzp` is a scaler, then this value is used for all i = 1, ..., M individuals. Default is `propzp = 1`.
`propsigmap`	Scaler specifying the initial Gamma(shape = 1/`propsigmap`, scale = sigma_zp * `propsigmap`) proposal distribution for sigma_zp = sqrt(sigma2_zp). Default is `propsigmap=1`.
`npoints`	Number of Gauss-Hermite quadrature points to use for numerical integration. Accuracy increases with number of points, but so does computation time.
`maxnumbasis`	Maximum number of basis vectors to use when proposing latent history frequency updates. Default is `maxnumbasis = 1`, but higher values can potentially improve mixing.
`a0delta`	Scaler or vector (of length d) specifying the prior for the conditional (on detection) probability of type 1 (delta_1), type 2 (delta_2), and both type 1 and type 2 encounters (1-delta_1-delta_2). If `a0delta` is a scaler, then this value is used for all a0delta[j] for j = 1, ..., d. For `mod.delta=~type`, d=3 with [delta_1, delta_2, 1-delta_1-delta_2] ~ Dirichlet(a0delta) prior. For `mod.delta=~1`, d=2 with [tau] ~ Beta(a0delta[1],a0delta[2]) prior, where (delta_1,delta_2,1-delta_1-delta_2) = (tau/2,tau/2,1-tau). See McClintock et al. (2013) for more details.
`a0alpha`	Specifies "shape1" parameter for [alpha] ~ Beta(a0alpha, b0alpha) prior. Only applicable when `data.type = "sometimes"`. Default is `a0alpha = 1`. Note that when `a0alpha = 1` and `b0alpha = 1`, then [alpha] ~ Unif(0,1).
`b0alpha`	Specifies "shape2" parameter for [alpha] ~ Beta(a0alpha, b0alpha) prior. Only applicable when `data.type = "sometimes"`. Default is `b0alpha = 1`. Note that when `a0alpha = 1` and `b0alpha = 1`, then [alpha] ~ Unif(0,1).
`a`	Scale parameter for [sigma_z] ~ half-Cauchy(a) prior for the individual hetegeneity term sigma_zp = sqrt(sigma2_zp). Default is “uninformative” `a = 25`.
`mu0`	Scaler or vector (of length k) specifying mean of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `mu0 = 0`.
`sigma2_mu0`	Scaler or vector (of length k) specifying variance of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `sigma2_mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `sigma2_mu0 = 1.75`.
`a0psi`	Specifies "shape1" parameter for [psi] ~ Beta(a0psi,b0psi) prior. Default is `a0psi = 1`.
`b0psi`	Specifies "shape2" parameter for [psi] ~ Beta(a0psi,b0psi) prior. Default is `b0psi = 1`.
`initial.values`	Optional list of `nchain` list(s) specifying initial values for parameters and latent variables. Default is `initial.values = NULL`, which causes initial values to be generated automatically. In addition to the parameters ("`pbeta`", "`N`", "`delta_1`", "`delta_2`", "`alpha`", "`sigma2_zp`", "`zp`", and "`psi`"), initial values can be specified for the initial latent history frequencies ("`x`") and initial individual encounter history indices ("`H`").
`known`	Optional integer vector indicating whether the encounter history of an individual is known with certainty (i.e., the observed encounter history is the true encounter history). Encounter histories with at least one type 4 encounter are automatically assumed to be known, and `known` does not need to be specified unless there exist encounter histories that do not contain a type 4 encounter that happen to be known with certainty (e.g., from independent telemetry studies). If specified, `known = c(v_1,v_2,...,v_M)` must be a vector of length `M = nrow(Enc.Mat)` where `v_i = 1` if the encounter history for individual `i` is known (`v_i = 0` otherwise). Note that known all-zero encounter histories (e.g., ‘000’) are ignored.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.
`...`	Additional "`parameters`" arguments for specifying `mod.p`. See `make.design.data`.

Details

The first time multimarkClosed (or multimarkCJS) is called, it will likely produce a firewall warning alerting users that R has requested the ability to accept incoming network connections. Incoming network connections are required to use parallel processing as implemented in multimarkClosed. Note that setting parms="all" is required for any multimarkClosed model output to be used in multimodelClosed.

Value

A list containing the following:

`mcmc`	Markov chain Monte Carlo object of class `mcmc.list`.
`mod.p`	Model formula for detection probability (as specified by `mod.p` above).
`mod.delta`	Model formula for conditional probability of type 1 or type 2 encounter, given detection (as specified by `mod.delta` above).
`DM`	A list of design matrices for detection probability generated for model `mod.p`, where DM$p is the design matrix for initial capture probability (p) and DM$c is the design matrix for recapture probability (c).
`initial.values`	A list containing the parameter and latent variable values at iteration `iter` for each chain. Values are provided for "`pbeta`", "`N`", "`delta_1`", "`delta_2`", "`alpha`", "`sigma2_zp`", "`zp`", "`psi`", "`x`", and "`H`".
`mms`	An object of class `multimarksetup`

Author(s)

Brett T. McClintock

References

Bonner, S. J., and Holmberg J. 2013. Mark-recapture with multiple, non-invasive marks. Biometrics 69: 766-775.

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run single chain using the default model for bobcat data
bobcat.dot<-multimarkClosed(bobcat)

#Posterior summary for monitored parameters
summary(bobcat.dot$mcmc)
plot(bobcat.dot$mcmc)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Run single chain using the default model for bobcat data
bobcat.dot<-multimarkClosed(bobcat)

#Posterior summary for monitored parameters
summary(bobcat.dot$mcmc)
plot(bobcat.dot$mcmc)

Fit spatially-explicit population abundance models for capture-mark-recapture data consisting of multiple non-invasive marks

Description

This function fits spatially-explicit population abundance models for capture-mark-recapture data consisting of multiple non-invasive marks using Bayesian analysis methods. Markov chain Monte Carlo (MCMC) is used to draw samples from the joint posterior distribution.

Usage

multimarkClosedSCR(
  Enc.Mat,
  trapCoords,
  studyArea = NULL,
  buffer = NULL,
  ncells = 1024,
  data.type = "never",
  covs = data.frame(),
  mms = NULL,
  mod.p = ~1,
  mod.delta = ~type,
  detection = "half-normal",
  parms = c("pbeta", "delta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propsigma = 1,
  propcenter = NULL,
  maxnumbasis = 1,
  a0delta = 1,
  a0alpha = 1,
  b0alpha = 1,
  sigma_bounds = NULL,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  a0psi = 1,
  b0psi = 1,
  initial.values = NULL,
  known = integer(),
  scalemax = 10,
  printlog = FALSE,
  ...
)
multimarkClosedSCR(
  Enc.Mat,
  trapCoords,
  studyArea = NULL,
  buffer = NULL,
  ncells = 1024,
  data.type = "never",
  covs = data.frame(),
  mms = NULL,
  mod.p = ~1,
  mod.delta = ~type,
  detection = "half-normal",
  parms = c("pbeta", "delta", "N"),
  nchains = 1,
  iter = 12000,
  adapt = 1000,
  bin = 50,
  thin = 1,
  burnin = 2000,
  taccept = 0.44,
  tuneadjust = 0.95,
  proppbeta = 0.1,
  propsigma = 1,
  propcenter = NULL,
  maxnumbasis = 1,
  a0delta = 1,
  a0alpha = 1,
  b0alpha = 1,
  sigma_bounds = NULL,
  mu0 = 0,
  sigma2_mu0 = 1.75,
  a0psi = 1,
  b0psi = 1,
  initial.values = NULL,
  known = integer(),
  scalemax = 10,
  printlog = FALSE,
  ...
)

Arguments

`Enc.Mat`	A matrix containing the observed encounter histories with rows corresponding to individuals and (`ntraps`*`noccas`) columns corresponding to traps and sampling occasions. The first `noccas` columns correspond to trap 1, the second `noccas` columns corresopond to trap 2, etc. Ignored unless `mms=NULL`.
`trapCoords`	A matrix of dimension `ntraps` x (2 + `noccas`) indicating the Cartesian coordinates and operating occasions for the traps, where rows correspond to trap, the first column the x-coordinate (“x”), and the second column the y-coordinate (“y”). The last `noccas` columns indicate whether or not the trap was operating on each of the occasions, where ‘1’ indciates the trap was operating and ‘0’ indicates the trap was not operating. Ignored unless `mms=NULL`.
`studyArea`	is a 3-column matrix containing the coordinates for the centroids of a contiguous grid of cells that define the study area and available habitat. Each row corresponds to a grid cell. The first 2 columns (“x” and “y”) indicate the Cartesian x- and y-coordinate for the centroid of each grid cell, and the third column (“avail”) indicates whether the cell is available habitat (=1) or not (=0). All cells must be square and have the same resolution. If `studyArea=NULL` (the default) and `mms=NULL`, then a square study area grid composed of `ncells` cells of available habitat is drawn around the bounding box of `trapCoords` based on `buffer`. Ignored unless `mms=NULL`. Note that rows should be ordered in raster cell order (raster cell numbers start at 1 in the upper left corner, and increase from left to right, and then from top to bottom).
`buffer`	A scaler in same units as `trapCoords` indicating the buffer around the bounding box of `trapCoords` for defining the study area when `studyArea=NULL`. Ignored unless `studyArea=NULL` and `mms=NULL`.
`ncells`	The number of grid cells in the study area when `studyArea=NULL`. The square root of `ncells` must be a whole number. Default is `ncells=1024`. Ignored unless `studyArea=NULL` and `mms=NULL`.
`data.type`	Specifies the encounter history data type. All data types include non-detections (type 0 encounter), type 1 encounter (e.g., left-side), and type 2 encounters (e.g., right-side). When both type 1 and type 2 encounters occur for the same individual within a sampling occasion, these can either be "non-simultaneous" (type 3 encounter) or "simultaneous" (type 4 encounter). Three data types are currently permitted: `data.type="never"` indicates both type 1 and type 2 encounters are never observed for the same individual within a sampling occasion, and observed encounter histories therefore include only type 1 or type 2 encounters (e.g., only left- and right-sided photographs were collected). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), and type 2 encounters (2). See `bobcat`. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 3 encounters (3). `data.type="sometimes"` indicates both type 1 and type 2 encounters are sometimes observed (e.g., both-sided photographs are sometimes obtained, but not necessarily for all individuals). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). Type 3 encounters can only be observed when an individual has at least one type 4 encounter. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). `data.type="always"` indicates both type 1 and type 2 encounters are always observed, but some encounter histories may still include only type 1 or type 2 encounters. Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4). Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4).
`covs`	A data frame of time- and/or trap-dependent covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of traps times the number of sampling occasions (`ntraps*noccas`), where the first `noccas` rows correspond to trap 1, the second `noccas` rows correspond to trap 2, etc. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`.
`mms`	An optional object of class `multimarkSCRsetup-class`; if `NULL` it is created. See `processdataSCR`.
`mod.p`	Model formula for detection probability as a function of distance from activity centers. For example, `mod.p=~1` specifies no effects (i.e., intercept only) other than distance, `mod.p~time` specifies temporal effects, `mod.p~c` specifies behavioral reponse (i.e., trap "happy" or "shy"), `mod.p~trap` specifies trap effects, and `mod.p~time+c` specifies additive temporal and behavioral effects.
`mod.delta`	Model formula for conditional probabilities of type 1 (delta_1) and type 2 (delta_2) encounters, given detection. Currently only `mod.delta=~1` (i.e., $\delta_1 = \delta_2$ ) and `mod.delta=~type` (i.e., $\delta_1 \ne \delta_2$ ) are implemented.
`detection`	Model for detection probability as a function of distance from activity centers . Must be "`half-normal`" (of the form $\exp{(-d^2 / (2*\sigma^2))}$ , where $d$ is distance) or "`exponential`" (of the form $\exp{(-d / \lambda)}$ ).
`parms`	A character vector giving the names of the parameters and latent variables to monitor. Possible parameters are cloglog-scale detection probability parameters ("`pbeta`"), population abundance ("`N`"), conditional probability of type 1 or type 2 encounter, given detection ("`delta`)", probability of simultaneous type 1 and type 2 detection, given both types encountered ("`alpha`"), cloglog-scale distance term for the detection function ("`sigma2_scr`" when detection=``half-normal'' or "`lambda`" when detection=``exponential''), and the probability that a randomly selected individual from the `M = nrow(Enc.Mat)` observed individuals belongs to the $n$ unique individuals encountered at least once ("`psi`"). Individual activity centers ("`centers`"), encounter history indices ("`H`"), and the log posterior density ("`logPosterior`") may also be monitored. Setting `parms="all"` monitors all possible parameters and latent variables.
`nchains`	The number of parallel MCMC chains for the model.
`iter`	The number of MCMC iterations.
`adapt`	The number of iterations for proposal distribution adaptation. If `adapt = 0` then no adaptation occurs.
`bin`	Bin length for calculating acceptance rates during adaptive phase (`0 < bin <= iter`).
`thin`	Thinning interval for monitored parameters.
`burnin`	Number of burn-in iterations (`0 <= burnin < iter`).
`taccept`	Target acceptance rate during adaptive phase (`0 < taccept <= 1`). Acceptance rate is monitored every `bin` iterations. Default is `taccept = 0.44`.
`tuneadjust`	Adjustment term during adaptive phase (`0 < tuneadjust <= 1`). If acceptance rate is less than `taccept`, then proposal term (`proppbeta` or `propsigma`) is multiplied by `tuneadjust`. If acceptance rate is greater than or equal to `taccept`, then proposal term is divided by `tuneadjust`. Default is `tuneadjust = 0.95`.
`proppbeta`	Scaler or vector (of length k) specifying the initial standard deviation of the Normal(pbeta[j], proppbeta[j]) proposal distribution. If `proppbeta` is a scaler, then this value is used for all j = 1, ..., k. Default is `proppbeta = 0.1`.
`propsigma`	Scaler specifying the initial Gamma(shape = 1/`propsigma`, scale = sigma_scr * `propsigma`) proposal distribution for sigma_scr = sqrt(sigma2_scr) (or sqrt(lambda) = lambda if detection=``exponential''). Default is `propsigma=1`.
`propcenter`	Scaler specifying the neighborhood distance when proposing updates to activity centers. When `propcenter=NULL` (the default), then propcenter = a*10, where a is the cell size for the study area grid, and each cell has (at most) approximately 300 neighbors.
`maxnumbasis`	Maximum number of basis vectors to use when proposing latent history frequency updates. Default is `maxnumbasis = 1`, but higher values can potentially improve mixing.
`a0delta`	Scaler or vector (of length d) specifying the prior for the conditional (on detection) probability of type 1 (delta_1), type 2 (delta_2), and both type 1 and type 2 encounters (1-delta_1-delta_2). If `a0delta` is a scaler, then this value is used for all a0delta[j] for j = 1, ..., d. For `mod.delta=~type`, d=3 with [delta_1, delta_2, 1-delta_1-delta_2] ~ Dirichlet(a0delta) prior. For `mod.delta=~1`, d=2 with [tau] ~ Beta(a0delta[1],a0delta[2]) prior, where (delta_1,delta_2,1-delta_1-delta_2) = (tau/2,tau/2,1-tau). See McClintock et al. (2013) for more details.
`a0alpha`	Specifies "shape1" parameter for [alpha] ~ Beta(a0alpha, b0alpha) prior. Only applicable when `data.type = "sometimes"`. Default is `a0alpha = 1`. Note that when `a0alpha = 1` and `b0alpha = 1`, then [alpha] ~ Unif(0,1).
`b0alpha`	Specifies "shape2" parameter for [alpha] ~ Beta(a0alpha, b0alpha) prior. Only applicable when `data.type = "sometimes"`. Default is `b0alpha = 1`. Note that when `a0alpha = 1` and `b0alpha = 1`, then [alpha] ~ Unif(0,1).
`sigma_bounds`	Positive vector of length 2 for the lower and upper bounds for the [sigma_scr] ~ Uniform(sigma_bounds[1], sigma_bounds[2]) (or [sqrt(lambda)] when detection=``exponential'') prior for the detection function term sigma_scr = sqrt(sigma2_scr) (or sqrt(lambda)). When `sigma_bounds = NULL` (the default), then `sigma_bounds = c(1.e-6,max(diff(range(studyArea[,"x"])),diff(range(studyArea[,"y"]))))`.
`mu0`	Scaler or vector (of length k) specifying mean of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `mu0 = 0`.
`sigma2_mu0`	Scaler or vector (of length k) specifying variance of pbeta[j] ~ Normal(mu0[j], sigma2_mu0[j]) prior. If `sigma2_mu0` is a scaler, then this value is used for all j = 1, ..., k. Default is `sigma2_mu0 = 1.75`.
`a0psi`	Specifies "shape1" parameter for [psi] ~ Beta(a0psi,b0psi) prior. Default is `a0psi = 1`.
`b0psi`	Specifies "shape2" parameter for [psi] ~ Beta(a0psi,b0psi) prior. Default is `b0psi = 1`.
`initial.values`	Optional list of `nchain` list(s) specifying initial values for parameters and latent variables. Default is `initial.values = NULL`, which causes initial values to be generated automatically. In addition to the parameters ("`pbeta`", "`N`", "`delta_1`", "`delta_2`", "`alpha`", "`sigma2_scr`", "`centers`", and "`psi`"), initial values can be specified for the initial latent history frequencies ("`x`") and initial individual encounter history indices ("`H`").
`known`	Optional integer vector indicating whether the encounter history of an individual is known with certainty (i.e., the observed encounter history is the true encounter history). Encounter histories with at least one type 4 encounter are automatically assumed to be known, and `known` does not need to be specified unless there exist encounter histories that do not contain a type 4 encounter that happen to be known with certainty (e.g., from independent telemetry studies). If specified, `known = c(v_1,v_2,...,v_M)` must be a vector of length `M = nrow(Enc.Mat)` where `v_i = 1` if the encounter history for individual `i` is known (`v_i = 0` otherwise). Note that known all-zero encounter histories (e.g., ‘000’) are ignored.
`scalemax`	Upper bound for internal re-scaling of grid cell centroid coordinates. Default is `scalemax=10`, which re-scales the centroids to be between 0 and 10. Re-scaling is done internally to avoid numerical overflows during model fitting. Ignored unless `mms=NULL`.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.
`...`	Additional "`parameters`" arguments for specifying `mod.p`. See `make.design.data`.

Details

The first time multimarkSCRClosed is called, it will likely produce a firewall warning alerting users that R has requested the ability to accept incoming network connections. Incoming network connections are required to use parallel processing as implemented in multimarkClosed. Note that setting parms="all" is required for any multimarkClosed model output to be used in multimodelClosed.

Value

A list containing the following:

`mcmc`	Markov chain Monte Carlo object of class `mcmc.list`.
`mod.p`	Model formula for detection probability (as specified by `mod.p` above).
`mod.delta`	Model formula for conditional probability of type 1 or type 2 encounter, given detection (as specified by `mod.delta` above).
`mod.det`	Model formula for detection function (as specified by `detection` above).
`DM`	A list of design matrices for detection probability generated for model `mod.p`, where DM$p is the design matrix for initial capture probability (p) and DM$c is the design matrix for recapture probability (c).
`initial.values`	A list containing the parameter and latent variable values at iteration `iter` for each chain. Values are provided for "`pbeta`", "`N`", "`delta_1`", "`delta_2`", "`alpha`", "`sigma2_scr`", "`centers`", "`psi`", "`x`", and "`H`".
`mms`	An object of class `multimarkSCRsetup`

Author(s)

Brett T. McClintock

References

Bonner, S. J., and Holmberg J. 2013. Mark-recapture with multiple, non-invasive marks. Biometrics 69: 766-775.

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

Royle, J.A., Karanth, K.U., Gopalaswamy, A.M. and Kumar, N.S. 2009. Bayesian inference in camera trapping studies for a class of spatial capture-recapture models. Ecology 90: 3233-3244.

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarkSCRsetup" from simulated data
sim.data<-simdataClosedSCR()
Enc.Mat <- sim.data$Enc.Mat
trapCoords <- sim.data$spatialInputs$trapCoords
studyArea <- sim.data$spatialInputs$studyArea

#Run single chain using the default model for simulated data
example.dot<-multimarkClosedSCR(Enc.Mat,trapCoords,studyArea)

#Posterior summary for monitored parameters
summary(example.dot$mcmc)
plot(example.dot$mcmc)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarkSCRsetup" from simulated data
sim.data<-simdataClosedSCR()
Enc.Mat <- sim.data$Enc.Mat
trapCoords <- sim.data$spatialInputs$trapCoords
studyArea <- sim.data$spatialInputs$studyArea

#Run single chain using the default model for simulated data
example.dot<-multimarkClosedSCR(Enc.Mat,trapCoords,studyArea)

#Posterior summary for monitored parameters
summary(example.dot$mcmc)
plot(example.dot$mcmc)

Class `"multimarkSCRsetup"`

Description

A class of spatial 'mulitmark' model inputs

Slots

Enc.Mat: Object of class "matrix". The observed encounter histories (with rows corresponding to individuals and columns corresponding to sampling occasions).
data.type: Object of class "character". The encounter history data type ("never", "sometimes", or "always").
vAll.hists: Object of class "integer". An ordered vector containing all possible encounter histories in sequence.
Aprime: Object of class "sparseMatrix". Transpose of the A matrix mapping latent encounter histories to observed histories.
indBasis: Object of class "numeric".An ordered vector of the indices of the three encounter histories updated by each basis vector.
ncolbasis: Object of class "integer". The number of needed basis vectors.
knownx: Object of class "integer". Frequencies of known encounter histories.
C: Object of class "integer". Sampling occasion of first capture for each encounter history.
L: Object of class "integer". Sampling occasion of last capture for each encounter history.
naivex: Object of class "integer". “Naive” latent history frequencies assuming a one-to-one mapping with Enc.Mat.
covs: Object of class "data.frame". Temporal covariates for detection probability (the number of rows in the data frame must equal the number of sampling occasions).
spatialInputs: Object of class "list". List is of length 4 containing trapCoords and studyArea after re-scaling coordinates based on maxscale, as well as the original (not re-scaled) grid cell resolution (origCellRes) and re-scaling range (Srange).

Objects from the Class

Objects can be created by calls of the form processdata(Enc.Mat, ...) or new("multimarkSCRsetup", ...).

Methods

No methods defined with class "multimarkSCRsetup".

Author(s)

Brett T. McClintock

Examples

showClass("multimarkSCRsetup")
showClass("multimarkSCRsetup")

Class `"multimarksetup"`

Description

A class of 'mulitmark' model inputs

Slots

Enc.Mat: Object of class "matrix". The observed encounter histories (with rows corresponding to individuals and columns corresponding to sampling occasions).
data.type: Object of class "character". The encounter history data type ("never", "sometimes", or "always").
vAll.hists: Object of class "integer". An ordered vector containing all possible encounter histories in sequence.
Aprime: Object of class "sparseMatrix". Transpose of the A matrix mapping latent encounter histories to observed histories.
indBasis: Object of class "numeric".An ordered vector of the indices of the three encounter histories updated by each basis vector.
ncolbasis: Object of class "integer". The number of needed basis vectors.
knownx: Object of class "integer". Frequencies of known encounter histories.
C: Object of class "integer". Sampling occasion of first capture for each encounter history.
L: Object of class "integer". Sampling occasion of last capture for each encounter history.
naivex: Object of class "integer". “Naive” latent history frequencies assuming a one-to-one mapping with Enc.Mat.
covs: Object of class "data.frame". Temporal covariates for detection probability (the number of rows in the data frame must equal the number of sampling occasions).

Objects from the Class

Objects can be created by calls of the form processdata(Enc.Mat, ...) or new("multimarksetup", ...).

Methods

No methods defined with class "multimarksetup".

Author(s)

Brett T. McClintock

Examples

showClass("multimarksetup")
showClass("multimarksetup")

Multimodel inference for 'multimark' open population survival models

Description

This function performs Bayesian multimodel inference for a set of 'multimark' open population survival (i.e., Cormack-Jolly-Seber) models using the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm proposed by Barker & Link (2013).

Usage

multimodelCJS(
  modlist,
  modprior = rep(1/length(modlist), length(modlist)),
  monparms = "phi",
  miter = NULL,
  mburnin = 0,
  mthin = 1,
  M1 = NULL,
  pbetapropsd = 1,
  zppropsd = NULL,
  phibetapropsd = 1,
  zphipropsd = NULL,
  sigppropshape = 1,
  sigppropscale = 0.01,
  sigphipropshape = 1,
  sigphipropscale = 0.01,
  printlog = FALSE
)
multimodelCJS(
  modlist,
  modprior = rep(1/length(modlist), length(modlist)),
  monparms = "phi",
  miter = NULL,
  mburnin = 0,
  mthin = 1,
  M1 = NULL,
  pbetapropsd = 1,
  zppropsd = NULL,
  phibetapropsd = 1,
  zphipropsd = NULL,
  sigppropshape = 1,
  sigppropscale = 0.01,
  sigphipropshape = 1,
  sigphipropscale = 0.01,
  printlog = FALSE
)

Arguments

`modlist`	A list of individual model output lists returned by `multimarkCJS`. The models must have the same number of chains and MCMC iterations.
`modprior`	Vector of length `length(modlist)` containing prior model probabilities. Default is `modprior = rep(1/length(modlist), length(modlist))`.
`monparms`	Parameters to monitor. Only parameters common to all models can be monitored (e.g., "`pbeta[(Intercept)]`", "`phibeta[(Intercept)]`", "`psi`"), but derived survival ("`phi`") and capture ("`p`") probabilities can also be monitored. Default is `monparms = "phi"`.
`miter`	The number of RJMCMC iterations per chain. If `NULL`, then the number of MCMC iterations for each individual model chain is used.
`mburnin`	Number of burn-in iterations (`0 <= mburnin < miter`).
`mthin`	Thinning interval for monitored parameters.
`M1`	Integer vector indicating the initial model for each chain, where `M1_j=i` initializes the RJMCMC algorithm for chain j in the model corresponding to `modlist[[i]]` for i=1,..., `length(modlist)`. If `NULL`, the algorithm for all chains is initialized in the most general model. Default is `M1=NULL`.
`pbetapropsd`	Scaler specifying the standard deviation of the Normal(0, pbetapropsd) proposal distribution for "`pbeta`" parameters. Default is `pbetapropsd=1`. See Barker & Link (2013) for more details.
`zppropsd`	Scaler specifying the standard deviation of the Normal(0, zppropsd) proposal distribution for "`zp`" parameters. Only applies if at least one (but not all) model(s) include individual hetergeneity in detection probability. If `NULL`, zppropsd = sqrt(sigma2_zp) is used. Default is `zppropsd=NULL`. See Barker & Link (2013) for more details.
`phibetapropsd`	Scaler specifying the standard deviation of the Normal(0, phibetapropsd) proposal distribution for "`phibeta`" parameters. Default is `phibetapropsd=1`. See Barker & Link (2013) for more details.
`zphipropsd`	Scaler specifying the standard deviation of the Normal(0, zphipropsd) proposal distribution for "`zphi`" parameters. Only applies if at least one (but not all) model(s) include individual hetergeneity in survival probability. If `NULL`, zphipropsd = sqrt(sigma2_zphi) is used. Default is `zphipropsd=NULL`. See Barker & Link (2013) for more details.
`sigppropshape`	Scaler specifying the shape parameter of the invGamma(shape = sigppropshape, scale = sigppropscale) proposal distribution for "`sigma2_zp`". Only applies if at least one (but not all) model(s) include individual hetergeneity in detection probability. Default is `sigppropshape=1`. See Barker & Link (2013) for more details.
`sigppropscale`	Scaler specifying the scale parameter of the invGamma(shape = sigppropshape, scale = sigppropscale) proposal distribution for "`sigma2_zp`". Only applies if at least one (but not all) model(s) include individual hetergeneity in detection probability. Default is `sigppropscale=0.01`. See Barker & Link (2013) for more details.
`sigphipropshape`	Scaler specifying the shape parameter of the invGamma(shape = sigphipropshape, scale = sigphipropscale) proposal distribution for "`sigma2_zphi`". Only applies if at least one (but not all) model(s) include individual hetergeneity in survival probability. Default is `sigphipropshape=1`. See Barker & Link (2013) for more details.
`sigphipropscale`	Scaler specifying the scale parameter of the invGamma(shape = sigphipropshape, scale = sigphipropscale) proposal distribution for "`sigma_zphi`". Only applies if at least one (but not all) model(s) include individual hetergeneity in survival probability. Default is `sigphipropscale=0.01`. See Barker & Link (2013) for more details.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.

Details

Note that setting parms="all" is required when fitting individual multimarkCJS models to be included in modlist.

Value

A list containing the following:

`rjmcmc`	Reversible jump Markov chain Monte Carlo object of class `mcmc.list`. Includes RJMCMC output for monitored parameters and the current model at each iteration ("`M`").
`pos.prob`	A list of calculated posterior model probabilities for each chain, including the overall posterior model probabilities across all chains.

Author(s)

Brett T. McClintock

References

Barker, R. J. and Link. W. A. 2013. Bayesian multimodel inference by RJMCMC: a Gibbs sampling approach. The American Statistician 67: 150-156.

Examples



# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarksetup" from simulated data
data_type = "always"
noccas <- 5
phibetaTime <- seq(2,0,length=noccas-1) # declining trend in survival
data <- simdataCJS(noccas=5,phibeta=phibetaTime,data.type=data_type)
setup <- processdata(data$Enc.Mat,data.type=data_type)

#Run single chain using the default model. Note parms="all".
sim.pdot.phidot <- multimarkCJS(mms=setup,parms="all",iter=1000,adapt=500,burnin=500)

#Run single chain with temporal trend for phi. Note parms="all".
sim.pdot.phiTime <- multimarkCJS(mms=setup,mod.phi=~Time,parms="all",iter=1000,adapt=500,burnin=500)

#Perform RJMCMC using defaults
modlist <- list(mod1=sim.pdot.phidot,mod2=sim.pdot.phiTime)
sim.M <- multimodelCJS(modlist=modlist)

#Posterior model probabilities
sim.M$pos.prob

#multimodel posterior summary for survival (display first cohort only)
summary(sim.M$rjmcmc[,paste0("phi[1,",1:(noccas-1),"]")])

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarksetup" from simulated data
data_type = "always"
noccas <- 5
phibetaTime <- seq(2,0,length=noccas-1) # declining trend in survival
data <- simdataCJS(noccas=5,phibeta=phibetaTime,data.type=data_type)
setup <- processdata(data$Enc.Mat,data.type=data_type)

#Run single chain using the default model. Note parms="all".
sim.pdot.phidot <- multimarkCJS(mms=setup,parms="all",iter=1000,adapt=500,burnin=500)

#Run single chain with temporal trend for phi. Note parms="all".
sim.pdot.phiTime <- multimarkCJS(mms=setup,mod.phi=~Time,parms="all",iter=1000,adapt=500,burnin=500)

#Perform RJMCMC using defaults
modlist <- list(mod1=sim.pdot.phidot,mod2=sim.pdot.phiTime)
sim.M <- multimodelCJS(modlist=modlist)

#Posterior model probabilities
sim.M$pos.prob

#multimodel posterior summary for survival (display first cohort only)
summary(sim.M$rjmcmc[,paste0("phi[1,",1:(noccas-1),"]")])

Multimodel inference for 'multimark' closed population abundance models

Description

This function performs Bayesian multimodel inference for a set of 'multimark' closed population abundance models using the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm proposed by Barker & Link (2013).

Usage

multimodelClosed(
  modlist,
  modprior = rep(1/length(modlist), length(modlist)),
  monparms = "N",
  miter = NULL,
  mburnin = 0,
  mthin = 1,
  M1 = NULL,
  pbetapropsd = 1,
  zppropsd = NULL,
  sigppropshape = 6,
  sigppropscale = 4,
  printlog = FALSE
)
multimodelClosed(
  modlist,
  modprior = rep(1/length(modlist), length(modlist)),
  monparms = "N",
  miter = NULL,
  mburnin = 0,
  mthin = 1,
  M1 = NULL,
  pbetapropsd = 1,
  zppropsd = NULL,
  sigppropshape = 6,
  sigppropscale = 4,
  printlog = FALSE
)

Arguments

`modlist`	A list of individual model output lists returned by `multimarkClosed` or `markClosed`. The models must have the same number of chains and MCMC iterations.
`modprior`	Vector of length `length(modlist)` containing prior model probabilities. Default is `modprior = rep(1/length(modlist), length(modlist))`.
`monparms`	Parameters to monitor. Only parameters common to all models can be monitored (e.g., "`pbeta[(Intercept)]`", "`N`"), but derived capture ("`p`") and recapture ("`c`") probabilities can also be monitored. Default is `monparms = "N"`.
`miter`	The number of RJMCMC iterations per chain. If `NULL`, then the number of MCMC iterations for each individual model chain is used.
`mburnin`	Number of burn-in iterations (`0 <= mburnin < miter`).
`mthin`	Thinning interval for monitored parameters.
`M1`	Integer vector indicating the initial model for each chain, where `M1_j=i` initializes the RJMCMC algorithm for chain j in the model corresponding to `modlist[[i]]` for i=1,..., `length(modlist)`. If `NULL`, the algorithm for all chains is initialized in the most general model. Default is `M1=NULL`.
`pbetapropsd`	Scaler specifying the standard deviation of the Normal(0, pbetapropsd) proposal distribution for "`pbeta`" parameters. Default is `pbetapropsd=1`. See Barker & Link (2013) for more details.
`zppropsd`	Scaler specifying the standard deviation of the Normal(0, zppropsd) proposal distribution for "`zp`" parameters. Only applies if at least one (but not all) model(s) include individual hetergeneity in detection probability. If `NULL`, zppropsd = sqrt(sigma2_zp) is used. Default is `zppropsd=NULL`. See Barker & Link (2013) for more details.
`sigppropshape`	Scaler specifying the shape parameter of the invGamma(shape = sigppropshape, scale = sigppropscale) proposal distribution for `sigma_zp`. Only applies if at least one (but not all) model(s) include individual hetergeneity in detection probability. Default is `sigppropshape=6`. See Barker & Link (2013) for more details.
`sigppropscale`	Scaler specifying the scale parameter of the invGamma(shape = sigppropshape, scale = sigppropscale) proposal distribution for `sigma_zp`. Only applies if at least one (but not all) model(s) include individual hetergeneity in detection probability. Default is `sigppropscale=4`. See Barker & Link (2013) for more details.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.

Details

Note that setting parms="all" is required when fitting individual multimarkClosed or markClosed models to be included in modlist.

Value

A list containing the following:

`rjmcmc`	Reversible jump Markov chain Monte Carlo object of class `mcmc.list`. Includes RJMCMC output for monitored parameters and the current model at each iteration ("`M`").
`pos.prob`	A list of calculated posterior model probabilities for each chain, including the overall posterior model probabilities across all chains.

Author(s)

Brett T. McClintock

References

Barker, R. J. and Link. W. A. 2013. Bayesian multimodel inference by RJMCMC: a Gibbs sampling approach. The American Statistician 67: 150-156.

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarksetup"
setup <- processdata(bobcat)
 
#Run single chain using the default model for bobcat data. Note parms="all".
bobcat.dot <- multimarkClosed(mms=setup,parms="all",iter=1000,adapt=500,burnin=500)

#Run single chain for bobcat data with time effects. Note parms="all".
bobcat.time <- multimarkClosed(mms=setup,mod.p=~time,parms="all",iter=1000,adapt=500,burnin=500)

#Perform RJMCMC using defaults
modlist <- list(mod1=bobcat.dot,mod2=bobcat.time)
bobcat.M <- multimodelClosed(modlist=modlist,monparms=c("N","p"))

#Posterior model probabilities
bobcat.M$pos.prob
 
#multimodel posterior summary for abundance
summary(bobcat.M$rjmcmc[,"N"])

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarksetup"
setup <- processdata(bobcat)
 
#Run single chain using the default model for bobcat data. Note parms="all".
bobcat.dot <- multimarkClosed(mms=setup,parms="all",iter=1000,adapt=500,burnin=500)

#Run single chain for bobcat data with time effects. Note parms="all".
bobcat.time <- multimarkClosed(mms=setup,mod.p=~time,parms="all",iter=1000,adapt=500,burnin=500)

#Perform RJMCMC using defaults
modlist <- list(mod1=bobcat.dot,mod2=bobcat.time)
bobcat.M <- multimodelClosed(modlist=modlist,monparms=c("N","p"))

#Posterior model probabilities
bobcat.M$pos.prob
 
#multimodel posterior summary for abundance
summary(bobcat.M$rjmcmc[,"N"])

Multimodel inference for 'multimark' spatial population abundance models

Description

This function performs Bayesian multimodel inference for a set of 'multimark' spatial population abundance models using the reversible jump Markov chain Monte Carlo (RJMCMC) algorithm proposed by Barker & Link (2013).

Usage

multimodelClosedSCR(
  modlist,
  modprior = rep(1/length(modlist), length(modlist)),
  monparms = "N",
  miter = NULL,
  mburnin = 0,
  mthin = 1,
  M1 = NULL,
  pbetapropsd = 1,
  sigpropmean = 0.8,
  sigpropsd = 0.4,
  printlog = FALSE
)
multimodelClosedSCR(
  modlist,
  modprior = rep(1/length(modlist), length(modlist)),
  monparms = "N",
  miter = NULL,
  mburnin = 0,
  mthin = 1,
  M1 = NULL,
  pbetapropsd = 1,
  sigpropmean = 0.8,
  sigpropsd = 0.4,
  printlog = FALSE
)

Arguments

`modlist`	A list of individual model output lists returned by `multimarkClosedSCR` or `markClosedSCR`. The models must have the same number of chains and MCMC iterations.
`modprior`	Vector of length `length(modlist)` containing prior model probabilities. Default is `modprior = rep(1/length(modlist), length(modlist))`.
`monparms`	Parameters to monitor. Only parameters common to all models can be monitored (e.g., "`pbeta[(Intercept)]`", "`N`", "`sigma2_scr`"), but derived density ("`D`") as well as capture ("`p`") and recapture ("`c`") probabilities (at distance zero from activity centers) can also be monitored. Default is `monparms = "N"`.
`miter`	The number of RJMCMC iterations per chain. If `NULL`, then the number of MCMC iterations for each individual model chain is used.
`mburnin`	Number of burn-in iterations (`0 <= mburnin < miter`).
`mthin`	Thinning interval for monitored parameters.
`M1`	Integer vector indicating the initial model for each chain, where `M1_j=i` initializes the RJMCMC algorithm for chain j in the model corresponding to `modlist[[i]]` for i=1,..., `length(modlist)`. If `NULL`, the algorithm for all chains is initialized in the most general model. Default is `M1=NULL`.
`pbetapropsd`	Scaler specifying the standard deviation of the Normal(0, pbetapropsd) proposal distribution for "`pbeta`" parameters. Default is `pbetapropsd=1`. See Barker & Link (2013) for more details.
`sigpropmean`	Scaler specifying the mean of the inverse Gamma proposal distribution for `sigma2_scr` (or `lambda` if detection=``exponential''). Only applies if models do not have the same detection function (i.e., “half-normal” or “exponential”). Default is `sigpropmean=0.8`. See Barker & Link (2013) for more details.
`sigpropsd`	Scaler specifying the standard deviation of the inverse Gamma proposal distribution for `sigma2_scr` (or `lambda` if detection=``exponential''). Only applies if models do not have the same detection function (i.e., “half-normal” or “exponential”). Default is `sigpropsd=0.4`. See Barker & Link (2013) for more details.
`printlog`	Logical indicating whether to print the progress of chains and any errors to a log file in the working directory. Ignored when `nchains=1`. Updates are printed to log file as 1% increments of `iter` of each chain are completed. With >1 chains, setting `printlog=TRUE` is probably most useful for Windows users because progress and errors are automatically printed to the R console for "Unix-like" machines (i.e., Mac and Linux) when `printlog=FALSE`. Default is `printlog=FALSE`.

Details

Note that setting parms="all" is required when fitting individual multimarkClosedSCR or markClosedSCR models to be included in modlist.

Value

A list containing the following:

`rjmcmc`	Reversible jump Markov chain Monte Carlo object of class `mcmc.list`. Includes RJMCMC output for monitored parameters and the current model at each iteration ("`M`").
`pos.prob`	A list of calculated posterior model probabilities for each chain, including the overall posterior model probabilities across all chains.

Author(s)

Brett T. McClintock

References

Barker, R. J. and Link. W. A. 2013. Bayesian multimodel inference by RJMCMC: a Gibbs sampling approach. The American Statistician 67: 150-156.

Examples


# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarkSCRsetup"
sim.data<-simdataClosedSCR()
Enc.Mat<-sim.data$Enc.Mat
trapCoords<-sim.data$spatialInputs$trapCoords
studyArea<-sim.data$spatialInputs$studyArea
setup<-processdataSCR(Enc.Mat,trapCoords,studyArea)
 
#Run single chain using the default model for simulated data. Note parms="all".
example.dot <- multimarkClosedSCR(mms=setup,parms="all",iter=1000,adapt=500,burnin=500)

#Run single chain for simulated data with behavior effects. Note parms="all".
example.c <- multimarkClosedSCR(mms=setup,mod.p=~c,parms="all",iter=1000,adapt=500,burnin=500)

#Perform RJMCMC using defaults
modlist <- list(mod1=example.dot,mod2=example.c)
example.M <- multimodelClosedSCR(modlist=modlist,monparms=c("N","D","sigma2_scr"))

#Posterior model probabilities
example.M$pos.prob
 
#multimodel posterior summary for abundance and density
summary(example.M$rjmcmc[,c("N","D")])

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarkSCRsetup"
sim.data<-simdataClosedSCR()
Enc.Mat<-sim.data$Enc.Mat
trapCoords<-sim.data$spatialInputs$trapCoords
studyArea<-sim.data$spatialInputs$studyArea
setup<-processdataSCR(Enc.Mat,trapCoords,studyArea)
 
#Run single chain using the default model for simulated data. Note parms="all".
example.dot <- multimarkClosedSCR(mms=setup,parms="all",iter=1000,adapt=500,burnin=500)

#Run single chain for simulated data with behavior effects. Note parms="all".
example.c <- multimarkClosedSCR(mms=setup,mod.p=~c,parms="all",iter=1000,adapt=500,burnin=500)

#Perform RJMCMC using defaults
modlist <- list(mod1=example.dot,mod2=example.c)
example.M <- multimodelClosedSCR(modlist=modlist,monparms=c("N","D","sigma2_scr"))

#Posterior model probabilities
example.M$pos.prob
 
#multimodel posterior summary for abundance and density
summary(example.M$rjmcmc[,c("N","D")])

Plot spatial capture-mark-recapture data

Description

This function plots the study area grid, available habitat, and trap coordinates for spatial capture-recapture studies. Activity centers and capture locations can also be plotted.

Usage

plotSpatialData(
  mms = NULL,
  trapCoords,
  studyArea,
  centers = NULL,
  trapLines = FALSE
)
plotSpatialData(
  mms = NULL,
  trapCoords,
  studyArea,
  centers = NULL,
  trapLines = FALSE
)

Arguments

`mms`	An optional object of class `multimarkSCRsetup-class` from which the (re-scaled) study area and trap coordinates are plotted.
`trapCoords`	A matrix of dimension `ntraps` x (2 + `noccas`) indicating the Cartesian coordinates and operating occasions for the traps, where rows correspond to trap, the first column the x-coordinate, and the second column the y-coordinate. The last `noccas` columns indicate whether or not the trap was operating on each of the occasions, where ‘1’ indciates the trap was operating and ‘0’ indicates the trap was not operating. Ignored unless `mms=NULL`.
`studyArea`	A 3-column matrix defining the study area and available habitat. Each row corresponds to a grid cell. The first 2 columns indicate the Cartesian x- and y-coordinate for the centroid of each grid cell, and the third column indicates whether the cell is available habitat (=1) or not (=0). All cells must have the same resolution. Ignored unless `mms=NULL`. Note that rows should be ordered in raster cell order (raster cell numbers start at 1 in the upper left corner, and increase from left to right, and then from top to bottom).
`centers`	An optional vector indicating the grid cell (i.e., the row of `studyArea`) that contains the true (latent) activity centers for each individual. If `mms` is provided, then `centers` must be of length `nrow(Enc.Mat)` (i.e., a center must be provided for each observed individual).
`trapLines`	Logical indicating whether to draw lines from activity centers to respective traps at which each individual was captured. Default is `trapLines=FALSE`. Ignored when `mms=NULL` or `centers=NULL`.

Author(s)

Brett T. McClintock

Examples

#Plot the tiger example data
plotSpatialData(trapCoords=tiger$trapCoords,studyArea=tiger$studyArea)

#Plot the tiger example data
plotSpatialData(trapCoords=tiger$trapCoords,studyArea=tiger$studyArea)

Generate model inputs for fitting 'multimark' models

Description

This function generates an object of class multimarksetup that is required to fit ‘multimark’ models.

Usage

processdata(
  Enc.Mat,
  data.type = "never",
  covs = data.frame(),
  known = integer()
)
processdata(
  Enc.Mat,
  data.type = "never",
  covs = data.frame(),
  known = integer()
)

Arguments

`Enc.Mat`	A matrix of observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions (ignored unless `mms=NULL`).
`data.type`	Specifies the encounter history data type. All data types include non-detections (type 0 encounter), type 1 encounter (e.g., left-side), and type 2 encounters (e.g., right-side). When both type 1 and type 2 encounters occur for the same individual within a sampling occasion, these can either be "non-simultaneous" (type 3 encounter) or "simultaneous" (type 4 encounter). Three data types are currently permitted: `data.type="never"` indicates both type 1 and type 2 encounters are never observed for the same individual within a sampling occasion, and observed encounter histories therefore include only type 1 or type 2 encounters (e.g., only left- and right-sided photographs were collected). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), and type 2 encounters (2). See `bobcat`. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 3 encounters (3). `data.type="sometimes"` indicates both type 1 and type 2 encounters are sometimes observed (e.g., both-sided photographs are sometimes obtained, but not necessarily for all individuals). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). Type 3 encounters can only be observed when an individual has at least one type 4 encounter. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). `data.type="always"` indicates both type 1 and type 2 encounters are always observed, but some encounter histories may still include only type 1 or type 2 encounters. Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4). Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4).
`covs`	A data frame of temporal covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of sampling occasions. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`.
`known`	Optional integer vector indicating whether the encounter history of an individual is known with certainty (i.e., the observed encounter history is the true encounter history). Encounter histories with at least one type 4 encounter are automatically assumed to be known, and `known` does not need to be specified unless there exist encounter histories that do not contain a type 4 encounter that happen to be known with certainty (e.g., from independent telemetry studies). If specified, `known = c(v_1,v_2,...,v_M)` must be a vector of length `M = nrow(Enc.Mat)` where `v_i = 1` if the encounter history for individual `i` is known (`v_i = 0` otherwise). Note that known all-zero encounter histories (e.g., ‘000’) are ignored.

Value

An object of class multimarksetup.

Author(s)

Brett T. McClintock

References

Bonner, S. J., and Holmberg J. 2013. Mark-recapture with multiple, non-invasive marks. Biometrics 69: 766-775.

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

Examples



# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarksetup"
setup <- processdata(bobcat)

#Run single chain using the default model for bobcat data
bobcat.dot<-multimarkClosed(mms=setup)

#Run single chain for bobcat data with temporal effects (i.e., mod.p=~time)
bobcat.time <- multimarkClosed(mms=setup,mod.p=~time)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarksetup"
setup <- processdata(bobcat)

#Run single chain using the default model for bobcat data
bobcat.dot<-multimarkClosed(mms=setup)

#Run single chain for bobcat data with temporal effects (i.e., mod.p=~time)
bobcat.time <- multimarkClosed(mms=setup,mod.p=~time)

Generate model inputs for fitting spatial 'multimark' models

Description

This function generates an object of class multimarkSCRsetup that is required to fit spatial ‘multimark’ models.

Usage

processdataSCR(
  Enc.Mat,
  trapCoords,
  studyArea = NULL,
  buffer = NULL,
  ncells = NULL,
  data.type = "never",
  covs = data.frame(),
  known = integer(),
  scalemax = 10
)
processdataSCR(
  Enc.Mat,
  trapCoords,
  studyArea = NULL,
  buffer = NULL,
  ncells = NULL,
  data.type = "never",
  covs = data.frame(),
  known = integer(),
  scalemax = 10
)

Arguments

`Enc.Mat`	A matrix containing the observed encounter histories with rows corresponding to individuals and (`ntraps`*`noccas`) columns corresponding to traps and sampling occasions. The first `noccas` columns correspond to trap 1, the second `noccas` columns corresopond to trap 2, etc. Ignored unless `mms=NULL`.
`trapCoords`	A matrix of dimension `ntraps` x (2 + `noccas`) indicating the Cartesian coordinates and operating occasions for the traps, where rows correspond to trap, the first column the x-coordinate, and the second column the y-coordinate. The last `noccas` columns indicate whether or not the trap was operating on each of the occasions, where ‘1’ indciates the trap was operating and ‘0’ indicates the trap was not operating.
`studyArea`	is a 3-column matrix containing the coordinates for the centroids of a contiguous grid of cells that define the study area and available habitat. Each row corresponds to a grid cell. The first 2 columns indicate the Cartesian x- and y-coordinate for the centroid of each grid cell, and the third column indicates whether the cell is available habitat (=1) or not (=0). All cells must be square and have the same resolution. If `studyArea=NULL` (the default), then a square study area grid composed of `ncells` cells of available habitat is drawn around the bounding box of `trapCoords` based on `buffer`. Note that rows should be ordered in raster cell order (raster cell numbers start at 1 in the upper left corner, and increase from left to right, and then from top to bottom).
`buffer`	A scaler in same units as `trapCoords` indicating the buffer around the bounding box of `trapCoords` for defining the study area when `studyArea=NULL`. Ignored unless `studyArea=NULL`.
`ncells`	The number of grid cells in the study area when `studyArea=NULL`. The square root of `ncells` must be a whole number. Default is `ncells=1024`. Ignored unless `studyArea=NULL`.
`data.type`	Specifies the encounter history data type. All data types include non-detections (type 0 encounter), type 1 encounter (e.g., left-side), and type 2 encounters (e.g., right-side). When both type 1 and type 2 encounters occur for the same individual within a sampling occasion, these can either be "non-simultaneous" (type 3 encounter) or "simultaneous" (type 4 encounter). Three data types are currently permitted: `data.type="never"` indicates both type 1 and type 2 encounters are never observed for the same individual within a sampling occasion, and observed encounter histories therefore include only type 1 or type 2 encounters (e.g., only left- and right-sided photographs were collected). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), and type 2 encounters (2). See `bobcat`. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 3 encounters (3). `data.type="sometimes"` indicates both type 1 and type 2 encounters are sometimes observed (e.g., both-sided photographs are sometimes obtained, but not necessarily for all individuals). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). Type 3 encounters can only be observed when an individual has at least one type 4 encounter. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). `data.type="always"` indicates both type 1 and type 2 encounters are always observed, but some encounter histories may still include only type 1 or type 2 encounters. Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4). Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4).
`covs`	A data frame of time- and/or trap-dependent covariates for detection probabilities (ignored unless `mms=NULL`). The number of rows in the data frame must equal the number of traps times the number of sampling occasions (`ntraps*noccas`), where the first `noccas` rows correspond to trap 1, the second `noccas` rows correspond to trap 2, etc. Covariate names cannot be "time", "age", or "h"; these names are reserved for temporal, behavioral, and individual effects when specifying `mod.p` and `mod.phi`.
`known`	Optional integer vector indicating whether the encounter history of an individual is known with certainty (i.e., the observed encounter history is the true encounter history). Encounter histories with at least one type 4 encounter are automatically assumed to be known, and `known` does not need to be specified unless there exist encounter histories that do not contain a type 4 encounter that happen to be known with certainty (e.g., from independent telemetry studies). If specified, `known = c(v_1,v_2,...,v_M)` must be a vector of length `M = nrow(Enc.Mat)` where `v_i = 1` if the encounter history for individual `i` is known (`v_i = 0` otherwise). Note that known all-zero encounter histories (e.g., ‘000’) are ignored.
`scalemax`	Upper bound for internal re-scaling of grid cell centroid coordinates. Default is `scalemax=10`, which re-scales the centroids to be between 0 and 10. Re-scaling is done internally to avoid numerical overflows during model fitting.

Value

An object of class multimarkSCRsetup.

Author(s)

Brett T. McClintock

References

Bonner, S. J., and Holmberg J. 2013. Mark-recapture with multiple, non-invasive marks. Biometrics 69: 766-775.

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

Royle, J.A., Karanth, K.U., Gopalaswamy, A.M. and Kumar, N.S. 2009. Bayesian inference in camera trapping studies for a class of spatial capture-recapture models. Ecology 90: 3233-3244.

Examples



# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarksetup" from simulated data
sim.data<-simdataClosedSCR()
Enc.Mat <- sim.data$Enc.Mat
trapCoords <- sim.data$spatialInputs$trapCoords
studyArea <- sim.data$spatialInputs$studyArea
setup <- processdataSCR(Enc.Mat,trapCoords,studyArea)

#Run single chain using the default model for simulated data
example.dot<-multimarkClosedSCR(mms=setup)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

#Generate object of class "multimarksetup" from simulated data
sim.data<-simdataClosedSCR()
Enc.Mat <- sim.data$Enc.Mat
trapCoords <- sim.data$spatialInputs$trapCoords
studyArea <- sim.data$spatialInputs$studyArea
setup <- processdataSCR(Enc.Mat,trapCoords,studyArea)

#Run single chain using the default model for simulated data
example.dot<-multimarkClosedSCR(mms=setup)

Simulate open population capture-mark-recapture data arising from multiple non-invasive marks

Description

This function generates encounter histories from simulated open population capture-mark-recapture data consisting of multiple non-invasive marks.

Usage

simdataCJS(
  N = 100,
  noccas = 5,
  pbeta = -0.25,
  sigma2_zp = 0,
  phibeta = 1.6,
  sigma2_zphi = 0,
  delta_1 = 0.4,
  delta_2 = 0.4,
  alpha = 0.5,
  data.type = "never",
  link = "probit"
)
simdataCJS(
  N = 100,
  noccas = 5,
  pbeta = -0.25,
  sigma2_zp = 0,
  phibeta = 1.6,
  sigma2_zphi = 0,
  delta_1 = 0.4,
  delta_2 = 0.4,
  alpha = 0.5,
  data.type = "never",
  link = "probit"
)

Arguments

`N`	Number of individuals.
`noccas`	Number of sampling occasions. `floor(N/noccas)` individuals are first encountered on each occasion.
`pbeta`	Logit- or probit-scale intercept term(s) for capture probability (p). Must be a scaler or vector of length `noccas`.
`sigma2_zp`	Logit- or probit-scale individual heterogeneity variance term for capture probability (p).
`phibeta`	Logit- or probit-scale intercept term(s) for survival probability ( $\phi$ ). Must be a scaler or vector of length `noccas`.
`sigma2_zphi`	Logit- or probit-scale individual heterogeneity variance term for survival probability ( $\phi$ ).
`delta_1`	Conditional probability of type 1 encounter, given detection.
`delta_2`	Conditional probability of type 2 encounter, given detection.
`alpha`	Conditional probability of simultaneous type 1 and type 2 detection, given both types encountered. Only applies when `data.type="sometimes"`.
`data.type`	Specifies the encounter history data type. All data types include non-detections (type 0 encounter), type 1 encounter (e.g., left-side), and type 2 encounters (e.g., right-side). When both type 1 and type 2 encounters occur for the same individual within a sampling occasion, these can either be "non-simultaneous" (type 3 encounter) or "simultaneous" (type 4 encounter). Three data types are currently permitted: `data.type="never"` indicates both type 1 and type 2 encounters are never observed for the same individual within a sampling occasion, and observed encounter histories therefore include only type 1 or type 2 encounters (e.g., only left- and right-sided photographs were collected). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), and type 2 encounters (2). See `bobcat`. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 3 encounters (3). `data.type="sometimes"` indicates both type 1 and type 2 encounters are sometimes observed (e.g., both-sided photographs are sometimes obtained, but not necessarily for all individuals). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). Type 3 encounters can only be observed when an individual has at least one type 4 encounter. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). `data.type="always"` indicates both type 1 and type 2 encounters are always observed, but some encounter histories may still include only type 1 or type 2 encounters. Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4). Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4).
`link`	Link function for detection probability. Must be "`logit`" or "`probit`". Note that `multimarkCJS` is currently implemented for the probit link only.

Value

A list containing the following:

`Enc.Mat`	A matrix containing the observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions.
`trueEnc.Mat`	A matrix containing the true (latent) encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions.

Author(s)

Brett T. McClintock

References

Bonner, S. J., and Holmberg J. 2013. Mark-recapture with multiple, non-invasive marks. Biometrics 69: 766-775.

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

Examples

#simulate data for data.type="sometimes" using defaults
data<-simdataCJS(data.type="sometimes")

#simulate data for data.type="sometimes" using defaults
data<-simdataCJS(data.type="sometimes")

Simulate closed population capture-mark-recapture data arising from multiple non-invasive marks

Description

This function generates encounter histories from simulated closed population capture-mark-recapture data consisting of multiple non-invasive marks.

Usage

simdataClosed(
  N = 100,
  noccas = 5,
  pbeta = -0.4,
  tau = 0,
  sigma2_zp = 0,
  delta_1 = 0.4,
  delta_2 = 0.4,
  alpha = 0.5,
  data.type = "never",
  link = "logit"
)
simdataClosed(
  N = 100,
  noccas = 5,
  pbeta = -0.4,
  tau = 0,
  sigma2_zp = 0,
  delta_1 = 0.4,
  delta_2 = 0.4,
  alpha = 0.5,
  data.type = "never",
  link = "logit"
)

Arguments

`N`	True population size or abundance.
`noccas`	The number of sampling occasions.
`pbeta`	Logit- or probit-scale intercept term(s) for capture probability (p). Must be a scaler or vector of length `noccas`.
`tau`	Additive logit- or probit-scale behavioral effect term for recapture probability (c).
`sigma2_zp`	Logit- or probit-scale individual heterogeneity variance term.
`delta_1`	Conditional probability of type 1 encounter, given detection.
`delta_2`	Conditional probability of type 2 encounter, given detection.
`alpha`	Conditional probability of simultaneous type 1 and type 2 detection, given both types encountered. Only applies when `data.type="sometimes"`.
`data.type`	Specifies the encounter history data type. All data types include non-detections (type 0 encounter), type 1 encounter (e.g., left-side), and type 2 encounters (e.g., right-side). When both type 1 and type 2 encounters occur for the same individual within a sampling occasion, these can either be "non-simultaneous" (type 3 encounter) or "simultaneous" (type 4 encounter). Three data types are currently permitted: `data.type="never"` indicates both type 1 and type 2 encounters are never observed for the same individual within a sampling occasion, and observed encounter histories therefore include only type 1 or type 2 encounters (e.g., only left- and right-sided photographs were collected). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), and type 2 encounters (2). See `bobcat`. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 3 encounters (3). `data.type="sometimes"` indicates both type 1 and type 2 encounters are sometimes observed (e.g., both-sided photographs are sometimes obtained, but not necessarily for all individuals). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). Type 3 encounters can only be observed when an individual has at least one type 4 encounter. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). `data.type="always"` indicates both type 1 and type 2 encounters are always observed, but some encounter histories may still include only type 1 or type 2 encounters. Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4). Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4).
`link`	Link function for detection probability. Must be "`logit`" or "`probit`". Note that `multimarkClosed` is currently implemented for the logit link only.

Value

A list containing the following:

`Enc.Mat`	A matrix containing the observed encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions.
`trueEnc.Mat`	A matrix containing the true (latent) encounter histories with rows corresponding to individuals and columns corresponding to sampling occasions.

Author(s)

Brett T. McClintock

References

Bonner, S. J., and Holmberg J. 2013. Mark-recapture with multiple, non-invasive marks. Biometrics 69: 766-775.

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

Examples

#simulate data for data.type="sometimes" using defaults
data<-simdataClosed(data.type="sometimes")

#simulate data for data.type="sometimes" using defaults
data<-simdataClosed(data.type="sometimes")

Simulate spatially-explicit capture-mark-recapture data from a (demographically) closed population with multiple non-invasive marks

Description

This function generates encounter histories from spatially-explicit capture-mark-recapture data consisting of multiple non-invasive marks.

Usage

simdataClosedSCR(
  N = 30,
  ntraps = 9,
  noccas = 5,
  pbeta = 0.25,
  tau = 0,
  sigma2_scr = 0.75,
  lambda = 0.75,
  delta_1 = 0.4,
  delta_2 = 0.4,
  alpha = 0.5,
  data.type = "never",
  detection = "half-normal",
  spatialInputs = NULL,
  buffer = 3 * sqrt(sigma2_scr),
  ncells = 1024,
  scalemax = 10,
  plot = TRUE
)
simdataClosedSCR(
  N = 30,
  ntraps = 9,
  noccas = 5,
  pbeta = 0.25,
  tau = 0,
  sigma2_scr = 0.75,
  lambda = 0.75,
  delta_1 = 0.4,
  delta_2 = 0.4,
  alpha = 0.5,
  data.type = "never",
  detection = "half-normal",
  spatialInputs = NULL,
  buffer = 3 * sqrt(sigma2_scr),
  ncells = 1024,
  scalemax = 10,
  plot = TRUE
)

Arguments

`N`	True population size or abundance.
`ntraps`	The number of traps. If `trapCoords=NULL`, the square root of `ntraps` must be a whole number in order to create a regular grid of trap coordinates on a square.
`noccas`	Scaler indicating the number of sampling occasions per trap.
`pbeta`	Complementary loglog-scale intercept term for detection probability (p). Must be a scaler or vector of length `noccas`.
`tau`	Additive complementary loglog-scale behavioral effect term for recapture probability (c).
`sigma2_scr`	Complementary loglog-scale term for effect of distance in the “half-normal” detection function. Ignored unless detection=``half-normal''.
`lambda`	Complementary loglog-scale term for effect of distance in the “exponential” detection function. Ignored unless detection=``exponential''.
`delta_1`	Conditional probability of type 1 encounter, given detection.
`delta_2`	Conditional probability of type 2 encounter, given detection.
`alpha`	Conditional probability of simultaneous type 1 and type 2 detection, given both types encountered. Only applies when `data.type="sometimes"`.
`data.type`	Specifies the encounter history data type. All data types include non-detections (type 0 encounter), type 1 encounter (e.g., left-side), and type 2 encounters (e.g., right-side). When both type 1 and type 2 encounters occur for the same individual within a sampling occasion, these can either be "non-simultaneous" (type 3 encounter) or "simultaneous" (type 4 encounter). Three data types are currently permitted: `data.type="never"` indicates both type 1 and type 2 encounters are never observed for the same individual within a sampling occasion, and observed encounter histories therefore include only type 1 or type 2 encounters (e.g., only left- and right-sided photographs were collected). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), and type 2 encounters (2). See `bobcat`. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 3 encounters (3). `data.type="sometimes"` indicates both type 1 and type 2 encounters are sometimes observed (e.g., both-sided photographs are sometimes obtained, but not necessarily for all individuals). Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). Type 3 encounters can only be observed when an individual has at least one type 4 encounter. Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), type 3 encounters (3), and type 4 encounters (4). `data.type="always"` indicates both type 1 and type 2 encounters are always observed, but some encounter histories may still include only type 1 or type 2 encounters. Observed encounter histories can consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4). Latent encounter histories consist of non-detections (0), type 1 encounters (1), type 2 encounters (2), and type 4 encounters (4).
`detection`	Model for detection probability as a function of distance from activity centers. Must be "`half-normal`" (of the form $\exp{(-d^2 / (2*\sigma^2))}$ , where $d$ is distance) or "`exponential`" (of the form $\exp{(-d / \lambda)}$ ).
`spatialInputs`	A list of length 3 composed of objects named `trapCoords`, `studyArea`, and `centers`: `trapCoords` is a matrix of dimension `ntraps` x (2 + `noccas`) indicating the Cartesian coordinates and operating occasions for the traps, where rows correspond to trap, the first column the x-coordinate (“x”), and the second column the y-coordinate (“y”). The last `noccas` columns indicate whether or not the trap was operating on each of the occasions, where ‘1’ indciates the trap was operating and ‘0’ indicates the trap was not operating. `studyArea` is a 3-column matrix defining the study area and available habitat. Each row corresponds to a grid cell. The first 2 columns (“x” and “y”) indicate the Cartesian x- and y-coordinate for the centroid of each grid cell, and the third column (“avail”) indicates whether the cell is available habitat (=1) or not (=0). All grid cells must have the same resolution. Note that rows should be ordered in raster cell order (raster cell numbers start at 1 in the upper left corner, and increase from left to right, and then from top to bottom). `centers` is a `N`-vector indicating the grid cell (i.e., the row of `studyArea`) that contains the true (latent) activity centers for each individual in the population. If `spatialInputs=NULL` (the default), then all traps are assumed to be operating on all occasions, the study area is assumed to be composed of `ncells` grid cells, grid cells within `buffer` of the trap array are assumed to be available habitat, and the activity centers are randomly assigned to grid cells of available habitat.
`buffer`	A scaler indicating the buffer around the bounding box of `trapCoords` for defining the study area and available habitat when `spatialInputs=NULL`. Default is `buffer=3*sqrt(sigma2_scr)`. Ignored unless `spatialInputs=NULL`.
`ncells`	The number of grid cells in the study area when `studyArea=NULL`. The square root of `ncells` must be a whole number. Default is `ncells=1024`. Ignored unless `spatialInputs=NULL`.
`scalemax`	Upper bound for grid cell centroid x- and y-coordinates. Default is `scalemax=10`, which scales the x- and y-coordinates to be between 0 and 10. Ignored unless `spatialInputs=NULL`.
`plot`	Logical indicating whether to plot the simulated trap coordinates, study area, and activity centers using `plotSpatialData`. Default is `plot=TRUE`

Details

Please be very careful when specifying your own spatialInputs; multimarkClosedSCR and markClosedSCR do little to verify that these make sense during model fitting.

Value

A list containing the following:

`Enc.Mat`	Matrix containing the observed encounter histories with rows corresponding to individuals and (`ntraps`*`noccas`) columns corresponding to traps and sampling occasions. The first `noccas` columns correspond to trap 1, the second `noccas` columns corresopond to trap 2, etc.
`trueEnc.Mat`	Matrix containing the true (latent) encounter histories with rows corresponding to individuals and (`ntraps`*`noccas`) columns corresponding to traps and sampling occasions. The first `noccas` columns correspond to trap 1, the second `noccas` columns corresopond to trap 2, etc.
`spatialInputs`	List of length 2 with objects named `trapCoords` and `studyArea`: `trapCoords` is a matrix of dimension `ntraps` x (2 + `noccas`) indicating the Cartesian coordinates and operating occasions for the traps, where rows correspond to trap, the first column the x-coordinate, and the second column the y-coordinate. The last `noccas` columns indicate whether or not the trap was operating on each of the occasions, where ‘1’ indciates the trap was operating and ‘0’ indicates the trap was not operating. `studyArea` is a 3-column matrix containing the coordinates for the centroids a contiguous grid of cells that define the study area and available habitat. Each row corresponds to a grid cell. The first 2 columns indicate the Cartesian x- and y-coordinate for the centroid of each grid cell, and the third column indicates whether the cell is available habitat (=1) or not (=0). All cells must have the same resolution.
`centers`	`N`-vector indicating the grid cell (i.e., the row of `spatialInputs$studyArea`) that contains the true (latent) activity centers for each individual in the population.

Author(s)

Brett T. McClintock

References

Bonner, S. J., and Holmberg J. 2013. Mark-recapture with multiple, non-invasive marks. Biometrics 69: 766-775.

McClintock, B. T., Conn, P. B., Alonso, R. S., and Crooks, K. R. 2013. Integrated modeling of bilateral photo-identification data in mark-recapture analyses. Ecology 94: 1464-1471.

Royle, J.A., Karanth, K.U., Gopalaswamy, A.M. and Kumar, N.S. 2009. Bayesian inference in camera trapping studies for a class of spatial capture-recapture models. Ecology 90: 3233-3244.

Examples

#simulate data for data.type="sometimes" using defaults
data<-simdataClosedSCR(data.type="sometimes")

#simulate data for data.type="sometimes" using defaults
data<-simdataClosedSCR(data.type="sometimes")

Tiger data

Description

Example tiger data for multimark package.

Format

These spatial capture-recapture data with a single mark type are summarized in a list of length 3 containing the following objects:

Enc.Mat is a 44 x (noccas*ntraps) matrix containing observed encounter histories for 44 tigers across noccas=48 sampling occasions and ntraps=120 traps.

studyArea is a 3-column matrix containing the coordinates for the centroids of the contiguous grid of cells that define the study area and available habitat. Each row corresponds to a grid cell. The first 2 columns indicate the Cartesian x- and y-coordinate for the centroid of each grid cell, and the third column indicates whether the cell is available habitat (=1) or not (=0). The grid cells are 0.336 km^2 resolution.

These data were obtained from the R package SPACECAP and modified by projecting onto a regular rectangular grid consisting of square grid cells (as is required by the spatial capture-recapture models in multimark).

Details

We thank Ullas Karanth, Wildlife Conservation Society, for providing the tiger data for use as an example with this package.

Source

Royle, J.A., Karanth, K.U., Gopalaswamy, A.M. and Kumar, N.S. 2009. Bayesian inference in camera trapping studies for a class of spatial capture-recapture models. Ecology 90: 3233-3244.

Examples

data(tiger)
#plot the traps and available habitat within the study area
plotSpatialData(trapCoords=tiger$trapCoords,studyArea=tiger$studyArea)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

# Fit spatial model to tiger data
Enc.Mat<-tiger$Enc.Mat
trapCoords<-tiger$trapCoords
studyArea<-tiger$studyArea
tiger.dot<-markClosedSCR(Enc.Mat,trapCoords,studyArea,iter=100,adapt=50,burnin=50)
summary(tiger.dot$mcmc)
data(tiger)
#plot the traps and available habitat within the study area
plotSpatialData(trapCoords=tiger$trapCoords,studyArea=tiger$studyArea)

# This example is excluded from testing to reduce package check time
# Example uses unrealistically low values for nchain, iter, and burnin

# Fit spatial model to tiger data
Enc.Mat<-tiger$Enc.Mat
trapCoords<-tiger$trapCoords
studyArea<-tiger$studyArea
tiger.dot<-markClosedSCR(Enc.Mat,trapCoords,studyArea,iter=100,adapt=50,burnin=50)
summary(tiger.dot$mcmc)

Package 'multimark'

Help Index

Bobcat data

Description

Format

Source

See Also

Examples

Bobcat spatial capture-recapture data

Description

Format

Details

Source

See Also

Examples

Calculate population density estimates

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Calculate posterior capture and survival probabilities

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Calculate posterior capture and recapture probabilities

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Calculate posterior capture and recapture probabilities

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Fit open population survival models for “traditional” capture-mark-recapture data consisting of a single mark type

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Fit closed population abundance models for “traditional” capture-mark-recapture data consisting of a single mark type

Description

Usage

Arguments

Details

Value

Author(s)

See Also

Examples

Fit spatial population abundance models for “traditional” capture-mark-recapture data consisting of a single mark type

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Fit open population survival models for capture-mark-recapture data consisting of multiple non-invasive marks

Description

Usage

Arguments

Details

Class `"multimarkSCRsetup"`

Class `"multimarksetup"`