multimarkClosedSCR {multimark}

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,
  ...
)

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.

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

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.

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.

See Also

processdataSCR.

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)