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Type:	Package
Title:	Open Population Capture-Recapture
Version:	2.2.7
Date:	2024-10-23
Description:	Non-spatial and spatial open-population capture-recapture analysis.
Depends:	R (≥ 3.5.0), secr (≥ 4.6.1)
Imports:	abind, MASS, methods, nlme, parallel, plyr, Rcpp (≥ 0.12.14),RcppParallel (≥ 5.1.1), stats, stringr, utils
Suggests:	knitr, RMark, rmarkdown, testthat, R2ucare, secrlinear
LinkingTo:	BH, Rcpp, RcppParallel
VignetteBuilder:	knitr
License:	GPL-2 |GPL-3 [expanded from: GPL (≥ 2)]
LazyData:	yes
LazyDataCompression:	xz
SystemRequirements:	GNU make
URL:	https://www.otago.ac.nz/density/,https://github.com/MurrayEfford/openCR/
BugReports:	https://github.com/MurrayEfford/openCR/issues/
NeedsCompilation:	yes
Packaged:	2024-10-23 09:14:52 UTC; murra
Author:	Murray Efford [aut, cre]
Maintainer:	Murray Efford <murray.efford@otago.ac.nz>
Repository:	CRAN
Date/Publication:	2024-10-23 12:10:03 UTC

Open Population Capture–Recapture Models

Description

Functions for non-spatial open population analysis byCormack-Jolly-Seber (CJS) and Jolly-Seber-Schwarz-Arnason (JSSA)methods, and by spatially explicit extensions of thesemethods. The methods build on Schwarz and Arnason (1996), Borchers and Efford (2008) and Pledger et al. (2010) (seevignette for more comprehensive references and likelihood). The parameterisation of JSSA recruitment is flexible (options include population growth rate\lambda, per capita recruitmentf and seniority\gamma). Spatially explicit analyses may assume home-range centres are fixed or allow dispersal betweenprimary sessions according to various probability kernels, including bivariate normal (BVN) and bivariatet (BVT) (Efford and Schofield 2022).

Details

Data are observations of marked individuals from a ‘robust’ samplingdesign (Pollock 1982). Primary sessions may include one or moresecondary sessions. Detection histories are assumed to be stored in an object of class‘capthist’ from the packagesecr. Grouping of occasions intoprimary and secondary sessions is coded by the ‘intervals’ attribute(zero for successive secondary sessions).

A few test datasets are provided (microtusCH,FebpossumCH,dipperCH,gonodontisCH,fieldvoleCH) and some fromsecr are also suitable e.g.ovenCH andOVpossumCH.

Models are defined using symbolic formula notation. Possible predictorsinclude both pre-defined variables (b, session etc.), corresponding to‘behaviour’ and other effects), and user-provided covariates.

Models are fitted by numerically maximizing the likelihood. The functionopenCR.fit creates an object of classopenCR. Generic methods (print, AIC, etc.) are providedfor each object class.

A link at the bottom of each help page takes you to the help index.

SeeopenCR-vignette.pdf for more.

Author(s)

Murray Effordmurray.efford@otago.ac.nz

References

Borchers, D. L. and Efford, M. G. (2008) Spatially explicit maximumlikelihood methods for capture–recapture studies.Biometrics64, 377–385.

Efford, M. G. and Schofield, M. R. (2020) A spatial open-population capture–recapture model.Biometrics76, 392–402.

Efford, M. G. and Schofield, M. R. (2022) A review of movement models in open population capture–recapture.Methods in Ecology and Evolution13, 2106–2118. https://doi.org/10.1111/2041-210X.13947

Glennie, R., Borchers, D. L., Murchie, M. Harmsen, B. J., and Foster, R. J. (2019) Open population maximum likelihood spatial capture–recapture.Biometrics75, 1345–1355

Pledger, S., Pollock, K. H. and Norris, J. L. (2010) Opencapture–recapture models with heterogeneity: II. Jolly-Sebermodel.Biometrics66, 883–890.

Pollock, K. H. (1982) A capture–recapture design robust to unequal probability of capture.Journal of Wildlife Management46, 752–757.

Schwarz, C. J. and Arnason, A. N. (1996) A general methodology for theanalysis of capture-recapture experiments in openpopulations.Biometrics52, 860–873.

See Also

openCR.fit,capthist,ovenCH

Examples

## Not run: ## a CJS model is fitted by defaultopenCR.fit(ovenCH)## End(Not run)

Compare openCR Models

Description

Terse report on the fit of one or more spatially explicitcapture–recapture models. Models with smaller values of AIC (Akaike'sInformation Criterion) are preferred.

Usage

## S3 method for class 'openCR'AIC(object, ..., sort = TRUE, k = 2, dmax = 10,  use.rank = FALSE,                        svtol = 1e-5, criterion = c('AIC','AICc'), n = NULL)## S3 method for class 'openCRlist'AIC(object, ..., sort = TRUE, k = 2, dmax = 10,  use.rank = FALSE,                        svtol = 1e-5, criterion = c('AIC','AICc'), n = NULL)## S3 method for class 'openCR'logLik(object, ...)

Arguments

Details

Models to be compared must have been fitted to the same data and use thesame likelihood method (full vs conditional).

AIC with small sample adjustment is given by

\mbox{AIC}_c = -2\log(L(\hat{\theta})) + 2K +\frac{2K(K+1)}{n-K-1}

whereK is the number of “beta" parameters estimated. By default, the effective sample sizen is the number of individuals observed at least once (i.e. thenumber of rows incapthist). This differs from the default in MARK which for CJS models is the sum of the sizes of release cohorts (seem.array).

Model weights are calculated as

w_i = \frac{\exp(-\Delta_i / 2)}{\sum{\exp(-\Delta_i / 2)}}

Models for which dAIC >dmax are given a weight of zero and areexcluded from the summation. Model weights may be used to formmodel-averaged estimates of real or beta parameters withmodelAverage (see also Buckland et al. 1997, Burnham andAnderson 2002).

The argumentk is included for consistency with the genericmethodAIC.

Value

A data frame with one row per model. By default, rows are sorted by ascending AIC.

logLik.openCR returns an object of class ‘logLik’ that hasattributedf (degrees of freedom = number of estimatedparameters).

Note

The default criterion is AIC, not AICc as insecr 3.1.

Computed values differ from MARK for various reasons. MARK uses thenumber of observations, not the number of capture histories whencomputing AICc. It is also likely that MARK will count parametersdifferently.

It is not be meaningful to compare models by AIC if they relate todifferent data.

The issue of goodness-of-fit and possible adjustment of AIC foroverdispersion has yet to be addressed (cf QAIC in MARK).

References

Buckland S. T., Burnham K. P. and Augustin, N. H. (1997) Model selection: an integral part of inference.Biometrics53, 603–618.

Burnham, K. P. and Anderson, D. R. (2002)Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Second edition. New York: Springer-Verlag.

Hurvich, C. M. and Tsai, C. L. (1989) Regression and time series model selection in small samples.Biometrika76, 297–307.

See Also

AIC,openCR.fit,print.openCR,LR.test

Examples

## Not run: m1 <- openCR.fit(ovenCH, type = 'JSSAf')m2 <- openCR.fit(ovenCH, type = 'JSSAf', model = list(p~session))AIC(m1, m2)## End(Not run)

Kielder Field Voles

Description

Captures ofMicrotus agrestis on a large grid in a clearcut within Kielder Forest, northern England, June–August 2000 (Ergon and Gardner 2014). Robust-design data from four primary sessions of 3–5 secondary sessions each.

Usage

fieldvoleCH

Format

The format is a multi-session secr capthist object. Attribute ‘ampm’ codes for type of secondary session (am, pm).

Details

Ergon and Lambin (2013) provided a robust design dataset from a trapping study on field volesMicrotus agrestis in a clearcut within Kielder Forest, northern England – see also Ergon et al. (2011), Ergon and Gardner (2014) and Reich and Gardner (2014). The study aimed to describe sex differences in space-use, survival and dispersal among adult voles. Data were from one trapping grid in summer 2000.

Trapping was on a rectangular grid of 192 multi-catch (Ugglan Special) traps at 7-metre spacing. Traps were baited with whole barley grains and carrots; voles were marked with individually numbered ear tags.

Four trapping sessions were conducted at intervals of 21 to 23 days between 10 June and 15 August. Traps were checked at about 12 hour intervals (6 am and 6 pm).

The attribute ‘ampm’ is a data.frame with a vector of codes, one per secondary session, to separate am and pm trap checks (1 = evening, 2 = morning). The four primary sessions had respectively 3, 5, 4 and 5 trap checks.

Ergon and Gardner (2014) restricted their analysis to adult voles (118 females and 40 males). Histories of five voles (ma193, ma239, ma371, ma143, ma348) were censored part way through the study because they died in traps (T. Ergon pers. comm.).

Source

Data were retrieved from DRYAD (Ergon and Lambin (2013) foropenCR. Code for translating the DRYAD ASCII file into a capthist object is given in Examples.

References

Efford, M. G. (2019) Multi-session models in secr 4.1.https://www.otago.ac.nz/density/pdfs/secr-multisession.pdf

Ergon, T., Ergon, R., Begon, M., Telfer, S. and Lambin, X. (2011) Delayed density-dependent onset of spring reproduction in a fluctuating population of fieldvoles.Oikos120, 934–940.

Ergon, T. and Gardner, B. (2014) Separating mortality and emigration: modelling spaceuse, dispersal and survival with robust-design spatial capture–recapture data.Methods in Ecology and Evolution5, 1327–1336.

Ergon, T. and Lambin, X. (2013) Data from: Separating mortality and emigration:Modelling space use, dispersal and survival with robust-design spatial capture–recapture data.Dryad Digital Repository.doi:10.5061/dryad.r17n5.

Reich, B. J. and Gardner, B. (2014) A spatial capture–recapture model forterritorial species.Environmetrics25, 630–637.

Examples

summary(fieldvoleCH, terse = TRUE)m.array(fieldvoleCH)JS.counts(fieldvoleCH)attr(fieldvoleCH, 'ampm')## Not run: maleCH <- subset(fieldvoleCH, function(x) covariates(x) == 'M')fit <- openCR.fit(maleCH)predict(fit)# Read data object from DRYAD ASCII filedatadir <- system.file('extdata', package = 'openCR')EG <- dget(paste0(datadir,'/ergonandgardner2013.rdat'))# construct capthist objectonesession <- function (sess) {    mat <- EG$H[,,sess]    id <- as.numeric(row(mat))    occ <- as.numeric(col(mat))    occ[mat<0] <- -occ[mat<0]    trap <- abs(as.numeric(mat))     matrow <- rownames(mat)    df <- data.frame(session = rep(sess, length(id)),                      ID = matrow[id],                      occ = occ,                      trapID = trap,                     sex = c('F','M')[EG$gr],                     row.names = 1:length(id))    # retain captures (trap>0)    df[df$trapID>0, , drop = FALSE]}tr <- read.traps(data = data.frame(EG$X), detector = "multi")# recode matrix as mixture of zeros and trap numbersEG$H <- EG$H-1# code censored animals with negative trap number# two ways to recognise censoringcensoredprimary <- which(EG$K < 4)censoredsecondary <- which(apply(EG$J,1,function(x) any(x-c(3,5,4,5) < 0)))censored <- unique(c(censoredprimary, censoredsecondary))rownames(EG$H)[censored]# [1] "ma193" "ma239" "ma371" "ma143" "ma348"censorocc <- apply(EG$H[censored,,], 1, function(x) which.max(cumsum(x)))censor3 <- ((censorocc-1) %/% 5)+1       # sessioncensor2 <- censorocc - (censor3-1) * 5   # occasion within sessioncensori <- cbind(censored, censor2, censor3)EG$H[censori] <- -EG$H[censori] lch <- lapply(1:4, onesession)ch <- make.capthist(do.call(rbind,lch), tr=tr, covnames='sex')# apply intervals in monthsintervals(ch) <-  EG$dtfieldvoleCH <- ch# extract time covariate - each secondary session was either am (2) or pm (1)# EG$tod# 1 2 3  4  5# 1 2 1 2 NA NA# 2 2 1 2  1  1# 3 2 1 2  1 NA# 4 2 1 2  1  2# Note consecutive pm trap checks in session 2ampm <- split(EG$tod, 1:4)ampm <- lapply(ampm, na.omit)attr(fieldvoleCH, 'ampm') <- data.frame(ampm = unlist(ampm))## End(Not run)

Internal Functions

Description

Functions called byopenCR.fit whendetails$R == TRUE, and some others

Usage

prwi (type, n, x, jj, cumss, nmix, w, fi, li, openval, PIA, PIAJ, intervals, CJSp1)prwisecr (type, n, x, nc, jj, kk, mm, nmix, cumss, w, fi, li, gk, openval,     PIA, PIAJ, binomN, Tsk, intervals, h, hindex, CJSp1, moveargsi,     movementcode, sparsekernel, edgecode, usermodel, kernel = NULL,     mqarray = NULL, cellsize = NULL, r0)PCH1 (type, x, nc, cumss, nmix, openval0, PIA0, PIAJ, intervals)PCH1secr (type, individual, x, nc, jj, cumss, kk, mm, openval0, PIA0, PIAJ, gk0,    binomN, Tsk, intervals,  moveargsi, movementcode, sparsekernel, edgecode,     usermodel, kernel, mqarray, cellsize, r0) pradelloglik (type, w, openval, PIAJ, intervals)cyclic.fit (..., maxcycle = 10, tol = 1e-5, trace = FALSE)

Arguments

Details

cyclic.fit implements cyclic fixing more or less as described bySchwarz and Arnason (1996) and used by Pledger et al. (2010). Theintention is to speed up maximization when there are many (beta)parameters. However, fitting is slower than with a single call toopenCR.fit, and the function is here only as a curiosity(it is not exported in 1.2.0).

Value

cyclic.fit returns a fitted model object of class ‘openCR’.

Other functions return numeric components of the log likelihood.

References

Pledger, S., Pollock, K. H. and Norris, J. L. (2010) Opencapture–recapture models with heterogeneity: II. Jolly-Sebermodel.Biometrics66, 883–890.

Schwarz, C. J. and Arnason, A. N. (1996) A general methodology for theanalysis of capture-recapture experiments in openpopulations.Biometrics52, 860–873.

See Also

openCR.fit

Examples

## Not run: openCR:::cyclic.fit(capthist = dipperCH, model = list(p~t, phi~t), tol = 1e-5, trace = TRUE)## End(Not run)

Summarise Non-spatial Open-population Data

Description

Simple conventional summaries of data held in secr ‘capthist’ objects.

Usage

JS.counts(object, primary.only = TRUE, stratified = FALSE)m.array(object, primary.only = TRUE, never.recaptured = TRUE,     last.session = TRUE, stratified = FALSE)bd.array(beta, phi)

Arguments

Details

The input is a capthist object representing a multi-session capture–recapture study. This may be (i) a single-session capthist in which occasions are understood to represent primary sessions, or (ii) a multi-session capthist object that is automatically converted to a single session object withjoin (any secondary sessions (occasions) are first collapsed withreduce(object, by = 'all')*, or (iii) a multi-session capthist object in which sessions are interpreted as strata.

The argumentprimary.only applies for single-session input with a robust-design structure defined by theintervals.last.session results in a final row with no recaptures.

If the covariates attribute ofobject includes a column named ‘freq’ then this is used to expand the capture histories.

Conventional Jolly–Seber estimates may be computed withJS.direct.

bd.array computes the probability of each possible combination of birth and death times (strictly, the primary session at which an animal was first and last available for detection), given the parameter vectors beta and phi. These cell probabilities are integral to JSSA models.

* this may fail with nonspatial data.

Value

ForJS.counts, a data.frame where rows correspond to sessions and columns hold counts as follows –

Form.array, a table object with rows corresponding to release cohorts and columns corresponding to first–recapture sessions. The size of the release cohort is shown in the first column. Cells in the lower triangle have value NA and print as blank by default.

See Also

join,JS.direct

Examples

JS.counts(ovenCH)m.array(ovenCH)## Not run: ## probabilities of b,d pairsfit <- openCR.fit(ovenCH, type = 'JSSAbCL')beta <- predict(fit)$b$estimatephi <- predict(fit)$phi$estimatebd.array(beta, phi)## End(Not run)

Jolly–Seber Estimates

Description

Non-spatial open-population estimates using the conventional closed-form Jolly–Seber estimators (Pollock et al. 1990).

Usage

JS.direct(object)

Arguments

Details

Estimates are the session-specific Jolly-Seber estimates with no constraints.

The reported SE of births (B) differ slightly from those in Pollock et al. (1990), and may be in error.

Value

A dataframe in which the first 5 columns are summary statistics (counts fromJS.counts) and the remaining columns are estimates:

Standard errors are in fields prefixed ‘se’; for N and B these include only sampling variation and omit population stochasticity. The covariance of successive phi-hat is in the field ‘covphi’.

References

Pollock, K. H., Nichols, J. D., Brownie, C. and Hines, J. E. (1990) Statistical inference for capture–recapture experiments.Wildlife Monographs107. 97pp.

See Also

JS.counts

Examples

# cf Pollock et al. (1990) Table 4.8JS.direct(microtusCH)

Plot Likelihood Surface

Description

Calculate log likelihood over a grid of values of two beta parametersfrom a fitted openCR model and optionally make an approximate contour plot of the loglikelihood surface.

This is a method for the generic functionLLsurface defined insecr.

Usage

## S3 method for class 'openCR'LLsurface(object, betapar = c("phi", "sigma"), xval = NULL, yval = NULL,    centre = NULL, realscale = TRUE, plot = TRUE, plotfitted = TRUE, ncores = NULL, ...)

Arguments

Details

centre is set by default to the fitted values of the betaparameters inobject. This has the effect of holding parametersother than those inbetapar at their fitted values.

Ifxval oryval is not provided then 11 values are set atequal spacing between 0.8 and 1.2 times the values incentre (onthe ‘real’ scale ifrealscale = TRUE and on the ‘beta’ scaleotherwise).

Contour plots may be customized by passing graphical parameters throughthe ... argument.

The value ofncores is passed toopenCR.fit.

Value

Invisibly returns a matrix of the log likelihood evaluated at eachgrid point

Note

LLsurface.openCR works for named ‘beta’ parameters rather than‘real’ parameters. The defaultrealscale = TRUE only works forbeta parameters that share the name of the real parameter to whichthey relate i.e. the beta parameter for the base level of the realparameter. This is because link functions are defined for realparameters not beta parameters.

Handling of multiple threads was changed in version 1.5.0 to align withLLsurface.secr.

The contours are approximate because they rely on interpolation.

See Also

LLsurface.secr

Examples

# not yet

Patuxent Meadow Voles

Description

Captures ofMicrotus pennsylvanicus at Patuxent Wildlife Research Center, Laurel, Maryland, June–December 1981. Collapsed (primary session only) data for adult males and adult females, and full robust-design data for adult males. Nichols et al. (1984) described the field methods and analysed a superset of the present data.

Usage

microtusCHmicrotusFCHmicrotusMCHmicrotusFMCHmicrotusRDCH

Format

The format is a single-session secr capthist object. As these arenon-spatial data, the traps attribute is NULL.

Details

Voles were caught in live traps on a 10 x 10 grid with traps 7.6 m apart. Traps were baited with corn. Traps were set in the evening, checked the following morning, and locked open during the day. Voles were ear-tagged with individually numbered fingerling tags. The locations of captures were not included in the published data.

Data collection followed Pollock's robust design with five consecutive days of trapping each month for six months (27 June 1981–8 December 1981). The data are for "adult" animals only, defined as those weighing at least 22g. Low capture numbers on the last two days of the second primary session (occasions 9 and 10) are due to a raccoon interfering with traps (Nichols et al. 1984). Six adult female voles and ten adult male voles were not released; their final captures are coded as -1 in the respective capthist objects.

microtusRDCH is the full robust-design dataset for adult males ((Williams et al. 2002 Table 19.1).

microtusFCH andmicrotusMCH are the collapsed datasets (binary at the level of primary session) for adult females and adult males from Williams et al. (2002 Table 17.5);microtusFMCH combines them and includes the covariate ‘sex’.

microtusCH is a combined-sex version of the data with different lineage (see below).

The ‘intervals’ attribute was assigned formicrotusRDCH to distinguish primary sesssions (interval 1 between prmary sessions; interval 0 for consecutive secondary sessions within a primary session). True intervals (start of one primary session to start of next) were 35, 28, 35, 28 and 34 days. See Examples to add these manually.

Williams, Nichols and Conroy (2002) presented several analyses of these data.

Program JOLLY (Hines 1988, Pollock et al. 1990) included a combined-sex version of the primary-session data that was used by Pollock et al. (1985) and Pollock et al. (1990)*. The numbers of voles released each month in the JOLLY dataset JLYEXMPL differ by 0–3 from the sum of the male and female data from Williams et al. (2002) (see Examples). Some discrepancies may have been due to voles for which sex was not recorded. The JOLLY version matches Table 1 of Nichols et al. (1984). The JOLLY version is distributed here as the objectmicrotusCH.

Differing selections of data from the Patuxent study were analysed by Nichols et al. (1992) and Bonner and Schwarz (2006).

* There is a typographic error in Table 4.7 of Pollock et al. (1990):r_i for the first period should be 89.

Source

References

Bonner, S. J. and Schwarz, C. J. (2006) An extension of the Cormack–Jolly–Seber model for continuouscovariates with application toMicrotus pennsylvanicus.Biometrics62, 142–149.

Hines, J. E. (1988) Program "JOLLY". Patuxent Wildlife Research Center.https://eesc.usgs.gov/mbr/software/jolly.shtml

Nichols, J. D., Pollock, K. H., Hines, J. E. (1984) The use of a robust capture-recapture design in small mammal population studies: a field example withMicrotus pennsylvanicus.Acta Theriologica29, 357–365.

Nichols, J. D., Sauer, J. R., Pollock, K. H., and Hestbeck, J. B. (1992) Estimating transition probabilities for stage-based population projection matrices using capture–recapturedata.Ecology73, 306–312.

Pollock, K. H., Hines, J. E. and Nichols, J. D. (1985) Goodness-of-fit tests for open capture–recapture models.Biometrics41, 399–410.

Pollock, K. H., Nichols, J. D., Brownie, C. and Hines, J. E. (1990) Statistical inference for capture–recapture experiments.Wildlife Monographs107. 97pp.

Williams, B. K., Nichols, J. D. and Conroy, M. J. (2002)Analysis and management of animal populations. Academic Press.

Examples

# cf Williams, Nichols and Conroy Table 17.6m.array(microtusFCH)m.array(microtusMCH)## Not run: # cf Williams, Nichols and Conroy Fig. 17.2fitfm <- openCR.fit(microtusFMCH, model = list(p~1, phi ~ session + sex))maledat <- expand.grid(sex = factor('M', levels = c('F','M')), session = factor(1:6))plot(fitfm, ylim=c(0,1), type = 'o')plot(fitfm, newdata = maledat, add = TRUE, xoffset = 0.1, pch = 16, type = 'o')# adjusting for variable intervalintervals(microtusCH) <-  c(35,28,35,28,34) / 30 intervals(microtusRDCH)[intervals(microtusRDCH)>0] <- c(35,28,35,28,34) / 30# The text file JLYEXMPL distributed with JOLLY is in the extdata folder of the R package# The microtusCH object may be rebuilt as followsdatadir <- system.file('extdata', package = 'openCR')JLYdf <- read.table(paste0(datadir,'/JLYEXMPL'), skip = 3,                     colClasses = c('character','numeric'))names(JLYdf) <- c('ch', 'freq')JLYdf$freq[grepl('2', JLYdf$ch)] <- -JLYdf$freq[grepl('2', JLYdf$ch)]JLYdf$ch <- gsub ('2','1', JLYdf$ch)microtusCH <- unRMarkInput(JLYdf)# Compare to combined-sex data from Williams et al. Table 17.5JS.counts(microtusCH) - JS.counts(microtusFMCH)## End(Not run)

List of Movement Models

Description

Movement of activity centres between primary sessions is modelled inopenCR as a random walk with step length governed by a circular probability kernel. The argument ‘movementmodel’ defines the kernel in several functions. More detail is provided in the vignettesopenCR-vignette.pdf.

Movement models inopenCR 2.2

Kernel models:

* incomplete implementation

Kernel-free models (buffer dependent):

Relationships among models

Some models may be derived as special cases of others, for example

RDL and RDG are almost indistinguishable when move.b > 2.

Deprecated names of movement models

These old names appeared in earlier releases. They still work, but may be removed in future.

Additional movement models that may be removed without notice

“annularR” uses a variable radius (R = move.b x kernelradius x spacing) and weights each cell according to the length of arc it intersects; “annularR” is not currently allowed inopenCR.fit. For the ‘annular’ models 'move.a' is the proportion at the centre (probability of not moving).

References

Clark, J. S, Silman, M., Kern, R., Macklin, E. and HilleRisLambers, J. (1999) Seed dispersal near and far: patterns across temperate and tropical forests.Ecology80, 1475–1494.

Efford, M. G. and Schofield, M. R. (2022) A review of movement models in open population capture–recapture.Methods in Ecology and Evolution13, 2106–2118. https://doi.org/10.1111/2041-210X.13947

Ergon, T. and Gardner, B. (2014) Separating mortality and emigration: modelling space use, dispersal and survival with robust-design spatial capture–recapture data.Methods in Ecology and Evolution5, 1327–1336.

Gardner, B., Sollmann, R., Kumar, N. S., Jathanna, D. and Karanth, K. U. (2018) State space and movement specification in open population spatial capture–recapture models.Ecology and Evolution8, 10336–10344doi:10.1002/ece3.4509.

Nathan, R., Klein, E., Robledo-Arnuncio, J. J. and Revilla, E. (2012) Dispersal kernels: review. In: J. Clobert et al. (eds)Dispersal Ecology and Evolution. Oxford University Press. Pp. 187–210.

Van Houtan, K. S., Pimm, S. L., Halley, J. M., Bierregaard, R. O. Jr and Lovejoy, T. E. (2007) Dispersal of Amazonian birds in continuous and fragmented forest.Ecology Letters10, 219–229.

See Also

make.kernel,gkernel,dkernel,pkernel,qkernel,openCR.fit

Orongorongo Valley Brushtail Possums

Description

A subset of brushtail possum (Trichosurus vulpecula) data from the Orongorongo Valley live-trapping study of Efford (1998) and Efford and Cowan (2005) that was used by Pledger, Pollock and Norris (2003, 2010). TheOVpossumCH dataset insecr is a different selection of data from the same study. Consult ?OVpossumCH for more detail.

The data comprise captures in February of each year from 1980 to 1988.

Usage

FebpossumCH

Format

The format is a 9-sessionsecr capthist object. Capture locations are not included.

Details

The data are captures of 448 animals (175 females and 273 males) over 9 trapping sessions comprising 4–10 occasions each. All were independent of their mothers, but age was not otherwise distinguished. The individual covariatesex takes values ‘F’ or ‘M’.

Pledger, Pollock and Norris (2010) fitted 2-class finite mixture models for capture probability p and apparent survival phi, with or without allowance for temporal (between year) variation, using captures from only the first day of each trapping session. The first-day data relate to 270 individuals (115 females and 155 males).

Source

M. Efford unpubl. See Efford and Cowan (2004) for acknowledgements.

References

Efford, M. G. (1998) Demographic consequences of sex-biased dispersal ina population of brushtail possums.Journal of Animal Ecology67, 503–517.

Efford, M. G. and Cowan, P. E. (2004) Long-term population trend ofTrichosurus vulpecula in the Orongorongo Valley, NewZealand. In:The Biology of Australian Possums andGliders. Edited by R. L. Goldingay and S. M. Jackson. SurreyBeatty & Sons, Chipping Norton. Pp. 471–483.

Pledger, S., Pollock, K. H. and Norris, J. L. (2010) Opencapture–recapture models with heterogeneity: II. Jolly–Sebermodel.Biometrics66, 883–890.

Examples

summary(FebpossumCH) m.array(FebpossumCH)JS.counts(FebpossumCH)FebD1CH <- subset(FebpossumCH, occasion = 1)## Not run: # reading the text file 'poss8088.data'datadir <- system.file('extdata', package = 'openCR')poss8088df <- read.table (paste0(datadir,'/poss8088.data'), header = TRUE)capt <- poss8088df[,c('session','id','day','day','sex')]# duplication of day is a trick to get a dummy trapID column in the right place# this is needed because make.capthist does not have nonspatial optioncapt$day.1[] <- 1  # keep only February samplescapt <- capt[capt$session %% 3 == 1,]# build nonspatial secr capthist object using dummy trapping gridFebpossumCH <- make.capthist(capt, make.grid(1,2,ID='numx'))# discard dummy traps objectsfor (i in 1:9) attr(FebpossumCH[[i]], 'traps') <- NULLnames(FebpossumCH) <- 1980:1988 sessionlabels(FebpossumCH) <- 1980:1988## End(Not run)

Session-specific Ages

Description

A matrix showing the age of each animal at each secondary session (occasion).

Usage

age.matrix(capthist, initialage = 0, minimumage = 0, maximumage = 1,     collapse = FALSE, unborn = minimumage)

Arguments

Details

age.matrix is used byopenCR.design for the predictors ‘age’ and ‘Age’.

Computations use the intervals attribute ofcapthist, which may be non-integer.

Ages are inferred for occasions before first detection, back to the minimum age.

Value

Either a numeric matrix with dimensions (number of animals, number of secondary occasions)or ifcollapse = TRUE a character matrix with one column.

See Also

openCR.design

Examples

age.matrix(join(ovenCH), maximumage = 2, collapse = TRUE)

Class Membership Probability for Mixture Models

Description

Finite mixture models treat class membership as a latent random variable. The probability of an individual's membership in each class may be inferred retrospectively from the relative likelihoods.

Usage

## S3 method for class 'openCR'classMembership(object, fullCH = NULL, ...)

Arguments

Details

It is assumed that the input model includes finite mixture terms (h2 or h3).

As the detection histories are saved in compressed (“squeezed”) form in openCR objects the original animal identifiers are lost and the order of animals may change. These may be restored by providingfullCH.

No class can be assigned from a CJS model for animals detected only in the final session.

Value

Matrix with one row per individual and columns for each class and the class number of the most likely class.

Note

In earlier versionsopenCR.fit always computed class membership and saved it in component ‘posterior’ of the fitted model.classMembership replaces that functionality.

See Also

openCR.fit,squeeze

Examples

## Not run: jch <- join(ovenCH)   fit <- openCR.fit(ovenCH, model=p~h2)classMembership(fit, jch)## End(Not run)

Cloning to Evaluate Identifiability

Description

The identifiability of parameters may be examined by refitting a model with cloned data (each capture history replicatednclone times). For identifiable parameters the estimated variances are proportional to1/nclone.

Usage

cloned.fit(object, nclone = 100, newdata = NULL, linkscale = FALSE)

Arguments

Details

The key output is the ratio of SE for estimates from the uncloned and cloned datasets, adjusted for the level of cloning (nclone). For identifiable parameters the ratio is expected to be 1.0.

Cloning is not implemented for spatial models.

The comparison may be done either on the untransformed scale (using approximate SE) or on the link scale.

Value

Dataframe with columns* –

* ‘estimate’ becomes ‘beta’ whenlinkscale = TRUE.

References

Lele, S.R., Nadeem, K. and Schmuland, B. (2010) Estimability and likelihood inference for generalizedlinear mixed models using data cloning.Journal of the American Statistical Association105, 1617–1625.

See Also

openCR.fit

Examples

## Not run: fit <- openCR.fit(dipperCH)cloned.fit(fit)## End(Not run)

Array of Parameter Estimates

Description

Estimates from one or more openCR models are formed into an array.

Usage

## S3 method for class 'openCR'collate(object, ..., realnames = NULL, betanames = NULL,     newdata = NULL, alpha = 0.05, perm = 1:4, fields = 1:4)## S3 method for class 'openCRlist'collate(object, ..., realnames = NULL, betanames = NULL,     newdata = NULL, alpha = 0.05, perm = 1:4, fields = 1:4)

Arguments

Details

collate extracts parameter estimates from a set of fitted openCRmodel objects.fields may be used to select a subset of summaryfields ("estimate","SE.estimate","lcl","ucl") by name or number.

Value

A 4-dimensional array of model-specific parameter estimates. By default, the dimensions correspond respectively to

• rows innewdata (usually sessions),

• models,

• statistic fields (estimate, SE.estimate, lcl, ucl), and

• parameters ("phi", "sigma" etc.).

It often helps to reorder the dimensions with theperm argument.

See Also

modelAverage.openCR,make.table

Probability Distribution After Movement

Description

Compute the compounding effect of a random walk defined by a discrete kernel. The number of steps and the edge algorithm are specified by the user. The function was used to generate Fig. 3 of Efford (2022). The final distribution may be summed for points lying within an arbitrary polygon. This is a simple way to compute the expected proportion remaining within a particular region (i.e. not “emigrating").

Usage

cumMove(X, mask, kernel, edgemethod = c("truncate", "wrap", "none"), nstep = 1, mqarray = NULL, settlecov = NULL)proportionInPolygon(mask, poly, cov = "pm")

Arguments

Details

The inputX may be -

• a vector of length 2 for the coordinates of a single point

• a mask with covariate 'pm' representing the initial distribution

• a SpatialPolygons object fromsp. Animals are assumed initially to be distributed uniformly across mask points that lie within the polygon.

The default edgemethod truncates the kernel at the edge and re-normalizes the cell probabilities so that all destinations lie within the boundary of the mask.

settlecov may name a covariate ofmask that has settlement weights in range 0–1.

ForproportionInPolygon, the input mask may be the output fromcumMove. The polygonpoly may be specified as forpointsInPolygon (e.g., SpatialPolygons object or 2-column matrix of coordinates) or as a list with components x and y. A list of polygon specifications is also accepted.

mqarray is computed automatically if not provided. Precomputing the array can save time but is undocumented.

Value

For cumMove - a mask object with initial probability distribution in covariate 'pm0' and final distribution in covariate 'pm'.

For proportionInPolygon - vector of the summed weights (probabilities) for cells centred in the polygon(s) as a proportion of all non-missing weights.

References

Efford, M. G. (2022) . Efficient discretization of movement kernels for spatiotemporal capture–recapture.Journal of Agricultural, Biological and Environmental Statistics. In press. https://doi.org/10.1007/s13253-022-00503-4

See Also

make.kernel,pointsInPolygon

Examples

sp <- 10msk <- make.mask(nx = 51, ny = 51, type = 'rect', spacing = sp,     buffer = 0)k <- make.kernel('BVN', 20, spacing = sp, move.a = 50, clip = TRUE,     sparse = TRUE)# initial distribution a central pointX <- apply(msk, 2, mean)   par(mfrow = c(1,4), mar = c(1,1,2,1))for (step in 0:2) {    X <- cumMove(X, msk, k, nstep = min(step,1))    plot(X, cov = 'pm', dots = FALSE, legend = FALSE, breaks =         seq(0,0.006,0.0001))        mtext(side = 3, line = 0, paste('Step', step), cex = 0.9)    contour(        x = unique(X$x),         y = unique(X$y),         z = matrix(covariates(X)$pm, nrow = length(unique(X$x))),         levels = c(0.0002),         drawlabels = FALSE,        add = TRUE)}## Not run: # initial distribution across a polygonX0 <- matrix(c(200,200,300,300,200,200,300,300,200,200), ncol = 2)X <- X0par(mfrow = c(1,4), mar = c(1,1,2,1))for (step in 0:3) {    X <- cumMove(X, msk, k, nstep = min(step,1))    plot(X, cov = 'pm', dots = FALSE, legend = FALSE, breaks =         seq(0,0.006,0.0001))        mtext(side = 3, line = 0, paste('Step', step), cex = 0.9)    contour(        x = unique(X$x),         y = unique(X$y),         z = matrix(covariates(X)$pm, nrow = length(unique(X$x))),         levels = c(0.0002),         drawlabels = FALSE,        add = TRUE)}polygon(X0)proportionInPolygon(X, X0)## End(Not run)

Derived Parameters From openCR Models

Description

For ..CL openCR models, compute the superpopulation size or density. For all openCR models, compute thetime-specific population size or density from the estimatedsuperpopulation size and the turnover parameters.

Usage

## S3 method for class 'openCR'derived(object, newdata = NULL, all.levels = FALSE, Dscale = 1,     HTbysession = FALSE, ...)## S3 method for class 'openCRlist'derived(object, newdata = NULL, all.levels = FALSE, Dscale = 1,     HTbysession = FALSE, ...)openCR.esa(object, bysession = FALSE, stratum = 1)openCR.pdot(object, bysession = FALSE, stratum = 1)

Arguments

Details

Derived estimates of density and superD are multiplied byDscale. UseDscale = 1e4 for animals per 100 sq. km.openCR.esa andopenCR.pdot are used internally byderived.openCR.

IfHTbysession then a separate H-T estimate is derived for each primary session; otherwise a H-T estimate of the superpopulation is used in combination with turnover parameters (phi, beta) to obtain session-specific estimates. Results are often identical.

The output is an object with its own print method (seeprint.derivedopenCR).

The code does not yet allow user-specified newdata.

Value

derived returns an object of class c(“derivedopenCR",“list"), list with these components:

Ifnewdata has multiple levels then the value is a list of such objects, one for each level.

openCR.pdot returns a vector of experiment-wide detectionprobabilities under the fitted model (one for each detected animal).

openCR.esa returns a vector of effective sampling areas underthe fitted model (one for each detected animal). If 'bysession = TRUE' the result is a list with one component per session.

Note

Prior to 1.4.5, openCR.esa did not expand the result for squeezed capture histories (freq>1) and did not return a list when bysession = TRUE.

See Also

openCR.fit,print.derivedopenCR

Examples

## Not run: # override default method to get true ML for L1L1CL <- openCR.fit(ovenCH, type = 'JSSAlCL', method = 'Nelder-Mead')predict(L1CL)derived(L1CL)## compare to aboveL1 <- openCR.fit(ovenCH, type = 'JSSAl', method = 'Nelder-Mead')predict(L1)derived(L1)## End(Not run)

Dippers

Description

Lebreton et al. (1992) demonstrated Cormack-Jolly-Seber methods with a dataset on European Dipper (*Cinclus cinclus*) collected by Marzolin (1988) and the data have been much used since then. Dippers were captured annually over 1981–1987. We use the version included in the RMark package (Laake 2013).

Usage

dipperCH

Format

The format is a single-session secr capthist object. As these arenon-spatial data, the traps attribute is NULL.

Details

Dippers were sampled in 1981–1987.

Source

MARK example dataset ‘ed.inp’. Also RMark (Laake 2013). See Examples.

References

Laake, J. L. (2013).RMark: An R Interface for Analysis of Capture–Recapture Data with MARK.AFSC Processed Report 2013-01, 25p. Alaska Fisheries Science Center, NOAA, National Marine Fisheries Service, 7600 Sand Point Way NE, Seattle WA 98115.

Lebreton, J.-D., Burnham, K. P., Clobert, J., and Anderson,D. R. (1992) Modeling survival and testing biological hypotheses usingmarked animals: a unified approach with case studies.EcologicalMonographs62, 67–118.

Marzolin, G. (1988) Polygynie du Cincle plongeur (*Cinclus cinclus*) dans les c?tes de Lorraine.L'Oiseau et la Revue Francaised'Ornithologie58, 277–286.

See Also

read.inp

Examples

m.array(dipperCH)## Not run: # From file 'ed.inp' in MARK input formatdatadir <- system.file('extdata', package = 'openCR')dipperCH <- read.inp(paste0(datadir, '/ed.inp'), grouplabel='sex',    grouplevels = c('Male','Female'))intervals(dipperCH) <- rep(1,6)    sessionlabels(dipperCH) <- 1981:1987   # labels only# or extracted from the RMark package with this codeif (require(RMark)) {    if (all (nchar(Sys.which(c('mark.exe','mark64.exe', 'mark32.exe'))) < 2))        stop ("MARK executable not found; set e.g. MarkPath <- 'c:/Mark/'")    data(dipper)                       # retrieve dataframe of dipper capture histories    dipperCH2 <- unRMarkInput(dipper)  # convert to secr capthist object    intervals(dipperCH2) <- rep(1,6)        sessionlabels(dipperCH2) <- 1981:1987   # labels only} else message ("RMark not found")# The objects dipperCH and dipperCH2 differ in the order of factor levels for 'sex'## End(Not run)

Expected Distance Moved

Description

Movement models inopenCR differ in their parameterisation so direct comparison can be difficult. The expected distance moved is a convenient statistic common to all models. This function computes the expected distance from various inputs, including fitted models.

Usage

expected.d(movementmodel, move.a, move.b, truncate = Inf, mask = NULL,     min.d = 1e-4, ...)

Arguments

Details

The inputmovementmodel may be

• fitted openCR model

• user kernel function g(r)

• kernel object

• character name of kernel model seeMovement models

Iftruncate (R) is finite ormovementmodel is a function then the expected value is computed by numerical integrationE(d) = \int_0^R r.f(r) dr. In the event that f(0) is not finite,min.d is used as the lower bound.

mask is used only for ‘uncorrelated’ and ‘uncorrelatedzi’ movement. For these models the expected movement is merely the average distance between points on the mask, weighted by (1-zi) if zero-inflated (uncorrelatedzi).

The ... argument is useful for (i) selecting a session from a fitted model, or(ii) specifying the upper or lower confidence limits from a single-parameter fitted model via the ‘stat’ argument ofmake.kernel.

Value

A numeric value (zero for 'static' model, NA if model unrecognised).

References

Efford, M. G. and Schofield, M. R. (2022) A review of movement models in open population capture–recapture.Methods in Ecology and Evolution13, 2106–2118. https://doi.org/10.1111/2041-210X.13947

See Also

Movement models,make.kernel,pkernel,qkernel

Examples

expected.d('BVT', move.a = 20, move.b = 1)expected.d('BVT', move.a = 20, move.b = 1, truncate = 300)k <- make.kernel(movementmodel = 'BVT', spacing = 10, move.a = 20, move.b = 1)expected.d(k)

Gonodontis Moths

Description

Non-spatial open-population capture–recapture data of Bishop et al. (1978) for nonmelanic maleGonodontis bidentata at Cressington Park, northwest England.

Usage

gonodontisCH

Format

The format is a single-session secr capthist object. As these arenon-spatial data, the traps attribute is NULL.

Details

The data are from a study of the relative fitness of melanic andnonmelanic morphs of the mothGonodontis bidentata at severalsites in England (Bishop et al. 1978). Crosbie (1979; see also Crosbieand Manly 1985) selected a subset of the Bishop et al. data (nonmelanicmales from Cressington Park) to demonstrate innovations in Jolly-Sebermodelling, and the same data were used by Link and Barker (2005) andSchofield and Barker (2008). The present data are those used by Crosbie(1979) and Link and Barker (2005).

Male moths were attracted to traps which consisted of a cage containing phermone-producing females surrounded by an enclosure which the males could enter but not leave. New virgin females were usually added every 1 to 4 days. Moths were marked at each capture with a date-specific mark in enamel paint or felt-tip pen on the undersurface of the wing. Thus, although moths at Cressington Park were not marked individually, each moth was a flying bearer of its own capture history.

The data comprise 689 individual capture histories for moths captured at 8 traps operated over 17 days (24 May–10 June 1970). The traps were in a square that appears have been about 40 m on a side. The location of captures is not included in the published data. All captured moths appear to have been marked and released (i.e. there were no removals recorded). All captures on Day 17 were recaptures; it is possible that unmarked moths were not recorded on that day.

Both Table 1 and Appendix 1 (microfiche) of Bishop et al. (1978) refer to 690 capture histories of nonmelanics at Cressington Park. In the present data there are only 689, and there are other minor discrepancies. Also, Crosbie and Manly (1985: Table 1) refer to 82 unique capture histories (“distinct cmr patterns”) when there are only 81 in the present dataset (note that two moths share 00000000000000011).

Source

Richard Barker provided an electronic copy of the data used by Link and Barker (2005), copied from Crosbie (1979).

References

Bishop, J. A., Cook, L. M., and Muggleton, J. (1978). The response of two species of moth toindustrialization in northwest England. II. Relative fitness of morphsand population size.Philosophical Transactions of the Royal Society of LondonB281, 517–540.

Crosbie, S. F. (1979)The mathematical modelling of capture–mark–recapture experiments on animal populations. Ph.D. Thesis, University of Otago, Dunedin, New Zealand.

Crosbie, S. F. and Manly, B. F. J. (1985) Parsimonious modelling of capture–mark–recapture studies.Biometrics41, 385–398.

Link, W. A. and Barker, R. J. (2005) Modeling association among demographic parametersin analysis of open-population capture–recapture data.Biometrics61, 46–54.

Schofield, M. R. and Barker, R. J. (2008) A unified capture–recapture framework.Journal of AgriculturalBiological and Environmental Statistics13, 458–477.

Examples

summary(gonodontisCH)m.array(gonodontisCH)## Not run: # compare default (CJS) estimates from openCR, MARKfit <- openCR.fit(gonodontisCH)predict(fit)if (require(RMark)) {    MarkPath <- 'c:/Mark/'   # customize as needed    if (!all (nchar(Sys.which(c('mark.exe','mark64.exe', 'mark32.exe'))) < 2)) {       mothdf <- RMarkInput(gonodontisCH)       mark(mothdf)       cleanup(ask = FALSE)    } else message ("mark.exe not found")} else message ("RMark not found")## End(Not run)

Discrete Movement Kernel

Description

Functions to create, plot and summarise a discrete representation of a movement kernel.

Usage

make.kernel(movementmodel = c("BVN", "BVE", "BVC", "BVT","RDE", "RDG", "RDL", "UNI"),     kernelradius = 10, spacing, move.a, move.b,     sparsekernel = FALSE, clip = FALSE, normalize = TRUE,         stat = c('estimate','lcl', 'ucl'), session = 1, r0 = 1/sqrt(pi), ...)## S3 method for class 'kernel'plot(x, type = "kernel", contour = FALSE, levels = NULL, text = FALSE,    title = NULL, add = FALSE, xscale = 1, ...)## S3 method for class 'kernel'summary(object, ...)

Arguments

Details

A kernel object is a type of mask with cell probabilities stored in the covariate ‘kernelp’. All kernels are truncated at kernelradius x spacing.

Themovementmodel may also be a function or a previously fitted openCR model that includes movement. If a fitted openCR object, parameter values and kernel attributes are derived from that object and other arguments are ignored.

The parameter ‘move.a’ is a scale parameter in metres, except for the UNIzi and INDzi models for which it is the zero-inflation parameter (‘move.b’ is the zero-inflation parameter for BVNzi, BVEzi and RDEzi).

'Sparse' kernels include only those grid cells that lie on 4 axes (N-S, E-W, NW-SE, NE-SW); cell probabilities are adjusted to maintain nearly the same distance distribution as the non-sparse equivalents.

Movement models are listed inMovement models and further described in the vignettesopenCR-vignette.pdf.

Plot type may be one or more of –

Type “kernel" by default includes an informative title with font size from the graphical parameter ‘cex.main’. Settitle = "" to suppress the title.

Useful properties of theoretical (not discretized) kernels may be recovered withmatchscale,pkernel,dkernel andqkernel.

The obscure argumentr0 controls the value assigned to the central cell of a discretized kernel. For positiver0 the value is F(r0*cellsize), where F is the cumulative probability distribution of distance moved. Otherwise the cell is assigned the value g(0)*cellarea, where g() is the 2-D kernel probability density (this fails where g(0) is undefined or infinite).

Value

make.kernel returns an object of class c('kernel','mask','data.frame').

The kernel object has attributes:

The empirical cumulative distribution is a dataframe with columns for the sorted cell radii ‘r’ and the associated cumulative probability ‘cumprob’ (one row per cell).

summary.kernel returns an object with these components, displayed with the corresponding print method.

The empirical mean inexpectedmoveemp is usually the most pertinent property of a fitted kernel.

Note

The plot method for kernels supercedes the functionplotKernel that has been removed.

References

Clark, J. S, Silman, M., Kern, R., Macklin, E. and HilleRisLambers, J. (1999) Seed dispersal near and far: patterns across temperate and tropical forests.Ecology80, 1475–1494.

Efford, M. G. and Schofield, M. R. (2022) A review of movement models in open population capture–recapture.Methods in Ecology and Evolution13, 2106–2118. https://doi.org/10.1111/2041-210X.13947

Ergon, T. and Gardner, B. (2014) Separating mortality and emigration: modelling space use, dispersal and survival with robust-design spatial capture–recapture data.Methods in Ecology and Evolution5, 1327–1336.

Nathan, R., Klein, E., Robledo-Arnuncio, J. J. and Revilla, E. (2012) Dispersal kernels: review. In: J. Clobert et al. (eds)Dispersal Ecology and Evolution. Oxford University Press. Pp. 187–210.

See Also

Movement models,mask,matchscale,dkernel,pkernel,qkernel

Examples

k <- make.kernel(movementmodel = 'BVT', spacing = 10, move.a = 20, move.b = 1)summary(k)# read a previously fitted movement model packaged with 'openCR'fit <- readRDS(system.file("exampledata", "spmOV.RDS", package = "openCR"))k <- make.kernel(fit)plot(k)if (interactive()) {   spotHeight(k, dec = 3)  # click on points; Esc to exit}

Tabulate Estimates From Multiple Models

Description

Session-specific estimates of real parameters (p, phi, etc.) are arranged in a rectangular table.

Usage

make.table(fits, parm = "phi", fields = "estimate", strata = 1,     collapse = FALSE, ...)

Arguments

Details

The input will usually be frompar.openCR.fit.

collate.openCR is a flexible alternative.

Value

A table object.

See Also

collate.openCR,par.openCR.fit,openCRlist

Examples

## Not run: arglist <- list(    constant = list(capthist = ovenCHp, model = phi~1),     session.specific = list(capthist = ovenCHp, model = phi~session))fits <- par.openCR.fit(arglist, trace = FALSE)print(make.table(fits), na = ".")## End(Not run)

Create Default Design Data

Description

Internal function used to generate a dataframe containing design datafor the base levels of all predictors in an openCR object.

Usage

## S3 method for class 'openCR'makeNewData(object, all.levels = FALSE, ...)

Arguments

Details

makeNewData is used bypredict in lieu ofuser-specified ‘newdata’. There is seldom any need to callmakeNewData directly.

makeNewData uses saved agelevels for grouping ages (openCR >= 2.2.6).

Value

A dataframe with one row for each session, and columns for thepredictors used byobject$model.

See Also

openCR.fit

Examples

## Not run: ## null example (no covariates)ovenCJS <- openCR.fit(ovenCH)makeNewData(ovenCJS)## End(Not run)

Match Kernel

Description

Finds scale parameter (move.a) of a movement model that corresponds to desired quantile, or expected distance moved.

Usage

matchscale(movementmodel, q = 40, expected = NULL, p = 0.5, lower = 1e-05, upper = 1e+05,    move.b = 1, truncate = Inf)

Arguments

Details

The default behaviour is to find the movement parameter for the given combination of q and p.

The alternative, when a value is provided for ‘expected’, is to find the movement parameter corresponding to the given expected distance.

Thetruncate argument must be specified for movementmodel ‘UNIzi'. For movementmodel 'UNI’ there is no parameter and the radius of truncation is varied to achieve the requested quantile q corresponding to cumulative probability p, or the desired expected distance.

Value

Numeric value for move.a (scale parameter or zero-inflation in the case of ‘UNIzi’) or truncation radius (‘UNI’).

See Also

Movement models,pkernel,make.kernel,expected.d

Examples

matchscale('BVN', 40, 0.5)matchscale('BVT', 40, 0.5, move.b = 1)matchscale('BVT', 40, 0.5, move.b = 5)matchscale('BVT', move.b = 5, expected = 10)

Data Manipulation

Description

Miscellaneous functions

Usage

primarysessions(intervals)secondarysessions(intervals)

Arguments

Details

These functions are used internally.

Value

primarysessions –

Integer vector with the number of the primary session to which each secondary session belongs.

secondarysessions –

Integer vector with secondary sessions numbered sequentially within primary sessions.

Examples

int <- intervals(join(ovenCH))primary <- primarysessions(int)primary# number of secondary sessions per primarytable(primary) # secondary session numberssecondarysessions(int)

Averaging of OpenCR Models Using Akaike's Information Criterion

Description

AIC- or AICc-weighted average of estimated ‘real’ or ‘beta’ parametersfrom multiple fitted openCR models.

The modelAverage generic is imported from secr (>= 4.5.0).

Usage

## S3 method for class 'openCR'modelAverage(object, ..., realnames = NULL, betanames = NULL,     newdata = NULL, alpha = 0.05, dmax = 10, covar = FALSE, average = c("link",     "real"), criterion = c("AIC","AICc"), CImethod = c("Wald", "MATA"))    ## S3 method for class 'openCRlist'modelAverage(object, ..., realnames = NULL, betanames = NULL,     newdata = NULL, alpha = 0.05, dmax = 10, covar = FALSE, average = c("link",     "real"), criterion = c("AIC","AICc"), CImethod = c("Wald", "MATA"))

Arguments

Details

Models to be compared must have been fitted to the same data and use thesame likelihood method (full vs conditional). Ifrealnames =NULL andbetanames = NULL then all real parameters will beaveraged; in this case all models must use the same real parameters. Toaverage beta parameters, specifybetanames (this is ignored if avalue is provided forrealnames). Seepredict.openCRfor an explanation of the optional argumentnewdata;newdata is ignored when averaging beta parameters.

Model-averaged estimates for parameter\theta are given by

\hat{\theta} = \sum\limits _k w_k \hat{\theta}_k

where the subscriptk refers to a specificmodel and thew_k are AIC or AICc weights (seeAIC.openCR for details). Averaging of real parameters may bedone on the link scale before back-transformation(average="link") or after back-transformation(average="real").

Models for which dAIC >dmax (or dAICc >dmax) are given aweight of zero and effectively are excluded from averaging.

Also,

\mbox{var} (\hat{\theta}) = \sum\limits _{k} { w_{k}( \mbox{var}(\hat{\theta}_{k} | \beta _k) + \beta _k ^2)}

where\hat{\beta} _k = \hat{\theta}_k - \hat{\theta} and the variances are asymptotic estimatesfrom fitting each modelk. This follows Burnham and Anderson(2004) rather than Buckland et al. (1997).

Two methods are offered for confidence intervals. The default ‘Wald’uses the above estimate of variance. The alternative ‘MATA’(model-averaged tail area) avoids estimating a weighted variance andis thought to provide better coverage at little cost in increasedinterval length (Turek and Fletcher 2012). Turek and Fletcher (2012)also found averaging with AIC weights (herecriterion = 'AIC')preferable to using AICc weights, even for smallsamples.CImethod does not affect the reported standard errors.

Value

A list (one component per parameter) of model-averaged estimates, theirstandard errors, and a100(1-\alpha)% confidenceinterval. The interval for real parameters is backtransformed from thelink scale. If there is only one row innewdata or betaparameters are averaged or averaging is requested for only one parameterthen the array is collapsed to a matrix. Ifcovar = TRUE then alist is returned with separate components for the estimates and thevariance-covariance matrices.

References

Buckland S. T., Burnham K. P. and Augustin, N. H. (1997) Modelselection: an integral part of inference.Biometrics53,603–618.

Burnham, K. P. and Anderson, D. R. (2002)Model Selection andMultimodel Inference: A Practical Information-Theoretic Approach.Second edition. New York: Springer-Verlag.

Burnham, K. P. and Anderson, D. R. (2004) Multimodel inference -understanding AIC and BIC in model selection.Sociological Methods& Research33, 261–304.

Turek, D. and Fletcher, D. (2012) Model-averaged Wald confidenceintervals.Computational statistics and data analysis56,2809–2815.

See Also

AIC.openCR,make.table,openCR.fit,openCRlist

Examples

## Compare two models fitted previouslycjs1 <- openCR.fit(dipperCH, model=p~1)cjs2 <- openCR.fit(dipperCH, model=p~session)AIC(cjs1, cjs2)modelAverage(cjs1, cjs2)## orcjs12 <- openCRlist(cjs1, cjs2)modelAverage(cjs12)

Moving Window Functions

Description

Apply a function to successive multi-session windows from a capthist object. The default function isopenCR.fit, but any function may be used whose first argument accepts a capthist object.

Usage

moving.fit (..., width = 3, centres = NULL, filestem = NULL,     trace = FALSE, FUN = openCR.fit)extractFocal (ocrlist, ...)

Arguments

Details

moving.fit appliesFUN to successive multi-session subsetsof the data in thecapthist argument.width should be an odd integer.centres may be used to restrict the range of windows considered; the default is to use all complete windows (width%/%2 + 1)...).

If afilestemis specified then each result is output to a file that may be loaded withload. This is useful if fitting takes a long time and analysesmay be terminated before completion.

extractFocal returns the focal-session (central) estimates from amoving.fit withFUN = openCR.fit. The ... argument is passed topredict.openCR; it may be used, for example, to choose a different alpha level for confidence intervals.

extractFocal is untested for complex models (e.g. finite mixtures).

Value

A list in which each component is the output from FUN applied to one subset. The window width is saved as attribute ‘width’.

See Also

openCR.fit

Examples

## number of individuals detectedmoving.fit(capthist = OVpossumCH, FUN = nrow)## Not run: ## if package R2ucare installedif (requireNamespace("R2ucare"))    moving.fit(capthist = OVpossumCH, FUN = ucare.cjs, width = 5, tests = "overall_CJS")## using default FUN = openCR.fitmf1 <- moving.fit(capthist = OVpossumCH, type = 'JSSAfCL',      model = list(p~t, phi~t))lapply(mf1, predict)extractFocal(mf1)     msk <- make.mask(traps(OVpossumCH[[1]]), nx = 32)mf2 <- moving.fit(capthist = OVpossumCH, mask = msk, type = 'JSSAsecrfCL')extractFocal(mf2)## End(Not run)

Defunct Functions in PackageopenCR

Description

These functions are no longer available inopenCR.

Usage

# Defunct in 2.1.0openCR.make.newdata()# Defunct in 2.0.0plotKernel()

Details

Internal functionopenCR.make.newdata was replaced with a method for the openCR class of the genericmakeNewData.

plotKernel was replaced with a plot method for the kernel class.

See Also

openCR-deprecated

Deprecated Functions in PackageopenCR

Description

These functions will be removed from future versions ofopenCR.

Usage

# Deprecated in 2.2.6# None

See Also

openCR-defunct

Design Data for Open population Models

Description

Internal function used byopenCR.fit.

Usage

openCR.design(capthist, models, type, naive = FALSE, stratumcov = NULL,     sessioncov = NULL, timecov = NULL, agecov = NULL,     dframe = NULL, contrasts = NULL, initialage = 0,     minimumage = 0, maximumage = 1, agebreaks = NULL, CJSp1 = FALSE, ...)

Arguments

Details

This is an internalopenCR function that you are unlikely everto use. ... may be used to passcontrasts.arg tomodel.matrix.

Each real parameter is notionally different for each unique combinationof individual, secondary session, detector and latent class, i.e., forn individuals,S secondary sessions,K detectors andm latent classes there arepotentiallyn \times S \times K \times m differentvalues. Actual models always predict a much reduced set of distinctvalues, and the number of rows in the design matrix is reducedcorrespondingly; a parameter index array allows these to retrieved forany combination of individual, session and detector.

openCR.design is less tolerant thanopenCR.fit regardingthe inputs ‘capthist’ and ‘models’. Model formulae are processed byopenCR.fitto a standard form (a named list of formulae) before they are passed toopenCR.design, and multi-session capthist objects areautomatically ‘reduced’ and ‘joined’ for open-population analysis.

Iftimecov is a single vector of values (one for each secondary session) then it is treated as a covariate named ‘tcov’.Ifsessioncov is a single vector of values (one for each primary session) then it is treated as a covariate named ‘scov’.

Theinitialage andmaximumage arguments are usually passed via theopenCR.fit ‘details’ argument.

agecov may be used to group ages. It should have length (or number of rows) equal tomaximumage + 1. Alternatively, age classes may be defined with the argumentagebreaks; this is preferred from openCR 2.2.6.

Value

A list with the components

Note

The component validlevels is TRUE in many cases for which aparameter is redundant or confounded (e.g. validlevels["phi",J-1]);these are sorted out ‘post hoc’ by examining the fitted values,their asymptotic variances and the eigenvalues of the Hessianmatrix.

See Also

openCR.fit

Examples

## this happens automatically in openCR.fitovenCH1 <- join(reduce(ovenCH, by = "all", newtraps=list(1:44)))openCR.design (ovenCH1, models = list(p = ~1, phi = ~session),    interval = c(1,1,1,1), type = "CJS")

Fit Open Population Capture–Recapture Model

Description

Nonspatial or spatial open-population analyses are performed on dataformatted for ‘secr’. Several parameterisations are provided for thenonspatial Jolly-Seber Schwarz-Arnason model (‘JSSA’, also known as‘POPAN’). Corresponding spatial models are designated‘JSSAsecr’. The prefix ‘PLB’ (Pradel-Link-Barker) is used for versions of the JSSA models that are conditional on the number observed. Cormack-Jolly-Seber (CJS) models are also fitted.

Usage

openCR.fit (capthist, type = "CJS", model = list(p~1, phi~1, sigma~1),     distribution = c("poisson", "binomial"), mask = NULL,     detectfn = c("HHN", "HHR", "HEX", "HAN", "HCG", "HVP", "HPX"), binomN = 0,     movementmodel = c('static', 'BVN', 'BVE', 'BVT', 'RDE', 'RDG','RDL','IND', 'UNI',      'BVNzi', 'BVEzi', 'RDEzi', 'INDzi', 'UNIzi'), edgemethod =     c("truncate", "wrap", "none"), kernelradius = 30, sparsekernel = TRUE,     start = NULL, link = list(), fixed = list(), stratumcov = NULL,     sessioncov = NULL, timecov = NULL, agecov = NULL, dframe = NULL,     dframe0 = NULL, details = list(), method = "Newton-Raphson", trace = NULL,     ncores = NULL, stratified = FALSE, ...)

Arguments

Details

The permitted nonspatial models are CJS, Pradel, Pradelg, JSSAbCL = PLBb, JSSAfCL = PLBf, JSSAgCL = PLBg, JSSAlCL = PLBl, JSSAb, JSSAf, JSSAg, JSSAl, JSSAB and JSSAN.

The permitted spatial models are CJSsecr, JSSAsecrbCL = PLBsecrb, JSSAsecrfCL = PLBsecrf, JSSAsecrgCL = PLBsecrg, JSSAsecrlCL = PLBsecrl, JSSAsecrb, JSSAsecrf, JSSAsecrg, JSSAsecrl, JSSAsecrB, JSSAsecrN, secrCL, and secrD.

SeeopenCR-vignette.pdf for a table of the ‘real’ parameters associated with each model type.

Parameterisations of the JSSA models differ in how they includerecruitment: the core parameterisations express recruitment either as aper capita rate (‘f’), as a finite rate of increase for the population(‘l’ for lambda) or as per-occasion entry probability (‘b’ for theclassic JSSA beta parameter, aka PENT in MARK). Each of these models maybe fitted by maximising either the full likelihood, or the likelihoodconditional on capture in the Huggins (1989) sense, distinguished by thesuffix ‘CL’. Full-likelihood JSSA models may also be parameterized interms of the time-specific absolute recruitment (BN, BD) or thetime-specific population size(N) or density (D).

‘secrCL’ and ‘secrD’ are closed-population spatial models.

Data are provided assecr ‘capthist’ objects, with somerestrictions. For nonspatial analyses, ‘capthist’ may besingle-session or multi-session, with any of the main detector types. Forspatial analyses ‘capthist’ should be a single-session dataset of a pointdetector type (‘multi’, ‘proximity’ or ‘count’) (see alsodetails$distribution below). In openCR the occasions of a single-sessiondataset are treated as open-population temporal samples except that occasions separated by an interval of zero (0) are from the same primary session (multi-sessioninput is collapsed to single-session if necessary).

model formulae may include the pre-defined terms‘session’,‘Session’, ‘h2’, and ‘h3’ as insecr. ‘session’is the name given to primary sampling times in ‘secr’, so a fullytime-specific CJS model islist(p ~ session, phi~ session). ‘t’ is a synonym of ‘session’. ‘Session’ is for atrend over sessions. ‘h2’ and ‘h3’ allow finite mixture models.

Learned (behavioural) responses (‘b’, ‘B’, etc.) were redefined and extended in version 1.3.0. Thevignette should be consulted for current definitions.

Formulae may also include named occasion-specific and session-specific covariates in the dataframe arguments ‘timecov’ and ‘sessioncov’ (occasion = secondary session of robust design). Named age-specific covariates in 'agecov' are treated similarly. Individual covariates present as an attribute ofthe ‘capthist’ input may be used in CJS and ..CL models. Groups are notsupported in this version, but may be implemented via a factor-levelcovariate in ..CL models.

distribution specifies the distribution of the number ofindividuals detected; this may be conditional on the population size (or number in themasked area) ("binomial") or unconditional ("poisson").distribution affects the sampling variance of the estimateddensity. The default is "poisson" as insecr.

Movement models are list atMovement models. Their use is described in thevignette.

edgemethod controls movement probabilities at the mask edge in spatial models that include movement. "none" typically causes bias in estimates; "wrap" wraps kernel probabilities to the opposing edge of a rectangular mask; "truncate" scales the values of an edge-truncated kernel so that they always sum to 1.0 (safer and more general than "wrap").

The mlogit link function is used for the JSSA (POPAN) entry parameter ‘b’ (PENT in MARK) and for mixture proportions, regardless oflink.

Spatial models use one of the hazard-based detection functions (seedetectfn) and require datafrom independent point detectors (secr detector types ‘multi’, ‘proximity’ or ‘count’).

Code is executed in multiple threads unless the user specifiesncores = 1 or there is only one core available ordetails$R == TRUE. Settingncores = NULL uses the existing value from the environment variable RCPP_PARALLEL_NUM_THREADS (seesetNumThreads) or 2 if that has not been set.

Optional stratification was introduced inopenCR 2.0.0. SeeopenCR-vignette.pdf for details.

The ... argument may be used to pass a vector of unequal intervals to join (interval), or to vary the tolerance for merging detector sites (tol).

Thestart argument may be

- a vector of beta parameter values, one for each of the NP beta parameters in the model

- a named vector of beta parameter values in any order

- a named list of one or more real parameter values

- a single fitted secr or openCR model whose real parameters overlap with the current model

- a list of two fitted models

In the case of two fitted models, the values are melded. This is handy for initialising an open spatial model from a closed spatial model and an open non-spatial model. If a beta parameter appears in both models then the first is used.

details is a list used for various specialized settings –

Ifmethod = "Newton-Raphson" thennlm isused to maximize the log likelihood (minimize the negative loglikelihood); otherwiseoptim is used with thechosen method ("BFGS", "Nelder-Mead", etc.). If maximization fails awarning is given appropriate to the method.method = "none" may be used to compute or re-compute the variance-covariance matrix at given starting values (i.e. providing a previously fitted model as the value ofstart).

Parameter redundancies are common in open-population models. The outputfromopenCR.fit includes the singular values (eigenvalues) of theHessian - a useful post-hoc indicator of redundancy (e.g., Gimenez etal. 2004). Eigenvalues are scaled so the largest is 1.0. Very smallscaled values represent redundant parameters - in my experience withsimple JSSA models a threshold of 0.00001 seems effective.

[There is an undocumented option to fix specific ‘beta’ parameters.]

Numeric ages may be grouped into age classes by providing ‘agebreaks’. In models, ~age then refers to the age-class factor. See thevignette for more detail.

Value

Ifdetails$LLonly == TRUE then a numeric vector is returned with logLik in position 1, followed by the named coefficients.

Otherwise, an object of class ‘openCR’ with components

The environment variable RCPP_PARALLEL_NUM_THREADS is updated with the value ofncores if provided.

Note

Different parameterisations lead to different model fits when used withthe default ‘model’ argument in which each real parameter is constrainedto be constant over time.

The JSSA implementation uses summation over feasible 'birth' and 'death'times for each capture history, following Pledger et al. (2010). Thisenables finite mixture models for individual capture probability (notfully tested), flexible handling of additions and losses on capture (akaremovals) (not yet programmed), and ultimately the extension to 'unknownage' as in Pledger et al. (2009).

openCR uses the generalized matrix inverse ‘ginv’ from the MASSpackage rather than ‘solve’ from base R, as this seems more robust tosingularities in the Hessian. Also, the default maximization method is ‘BFGS’rather than ‘Newton-Raphson’ as BFGS appears more robust in the presenceof redundant parameters.

Earlier versions ofopenCR.fit computed latent class membership probabilities for each individual in finite mixture models and saved them in component ‘posterior’. Now seeclassMembership for that functionality.

From 1.5.0 onwards the number of threads uses the environment variable RCPP_PARALLEL_NUM_THREADS, as insecr.fit. This may be set oncein a session withsecr::setNumThreads.

The default movement arguments changed inopenCR 2.1.1. Nowkernelradius = 30, sparsekernel = TRUE.

References

Gimenez, O., Viallefont, A., Catchpole, E. A., Choquet, R. and Morgan,B. J. T. (2004) Methods for investigating parameter redundancy.Animal Biodiversity and Conservation27, 561–572.

Huggins, R. M. (1989) On the statistical analysis of captureexperiments.Biometrika76, 133–140.

Pledger, S., Efford, M., Pollock. K., Collazo, J. and Lyons, J. (2009)Stopover duration analysis with departure probability dependent onunknown time since arrival. In: D. L. Thompson, E. G. Cooch andM. J. Conroy (eds)Modeling Demographic Processes in MarkedPopulations. Springer. Pp. 349–363.

Pledger, S., Pollock, K. H. and Norris, J. L. (2010) Opencapture–recapture models with heterogeneity: II. Jolly-Sebermodel.Biometrics66, 883–890.

Pradel, R. (1996) Utilization of capture-mark-recapture for the studyof recruitment and population growth rate.Biometrics52, 703–709.

Schwarz, C. J. and Arnason, A. N. (1996) A general methodology for theanalysis of capture-recapture experiments in openpopulations.Biometrics52, 860–873.

See Also

classMembership.openCR,derived.openCR,openCR.design,par.openCR.fit,predict.openCR,summary.openCR

Examples

## Not run: ## CJS defaultopenCR.fit(ovenCH)## POPAN Jolly-Seber Schwarz-Arnason, lambda parameterisationL1 <- openCR.fit(ovenCH, type = 'JSSAl')predict(L1)JSSA1 <- openCR.fit(ovenCH, type = 'JSSAf')JSSA2 <- openCR.fit(ovenCH, type = 'JSSAf', model = list(phi~t))JSSA3 <- openCR.fit(ovenCH, type = 'JSSAf', model = list(p~t,phi~t))AIC (JSSA1, JSSA2, JSSA3)predict(JSSA1)RMdata <- RMarkInput (join(reduce(ovenCH, by = "all")))if (require(RMark)) {    MarkPath <- 'c:/Mark/'    if (!all (nchar(Sys.which(c('mark.exe', 'mark64.exe', 'mark32.exe'))) < 2)) {        openCHtest <- process.data(RMdata, model = 'POPAN')        openCHPOPAN <- mark(data = openCHtest, model = 'POPAN',            model.parameters = list(p = list(formula = ~1),            pent = list(formula = ~1),            Phi = list(formula = ~1)))        popan.derived(openCHtest, openCHPOPAN)        cleanup(ask = FALSE)    } else message ("mark.exe not found")} else message ("RMark not found")## End(Not run)

Bundle openCR Models

Description

Fitted models are bundled together for convenience.

Usage

openCRlist (...)## S3 method for class 'openCRlist'x[i]

Arguments

Details

openCRlist forms a special list (class ‘openCRlist’) of fitted model (openCR) objects.This may be used as an argument ofAIC,predict,make.table etc.

Methods are provided for the generic functionc and list extraction ‘[’.

Value

openCRlist object

See Also

AIC.openCRpredict.openCRmake.table

Examples

## Not run: fit0 <- openCR.fit (dipperCH)fitt <- openCR.fit (dipperCH, model=phi~t)fits <- openCRlist(fit0,fitt)AIC(fits)make.table(fits, 'phi')## End(Not run)

Fit Multiple openCR Models

Description

This function is a wrapper foropenCR.fit.

Usage

par.openCR.fit (arglist, ncores = 1, seed = 123, trace = FALSE, logfile = NULL,     prefix = "")

Arguments

Details

In openCR >= 1.5.0, setting ncores > 1 is deprecated and triggers a warning: multithreading makes it faster to set ncores = 1 in par.openCR.fit.

trace overrides any settings inarglist.

It is convenient to provide the names of the capthist and mask argumentsin each component of arglist as character values (i.e. in quotes); objects thusnamed are exported from the workspace to each worker process (see Examples).

Usingncores>1 is obsolete under the multithreading regime inopenCR >= 1.5.0. It is usually slower thanncores = 1. If used it has these effects:

– worker processes are generated using theparallel package,

– one model is fitted on each worker, and

– if no logfile name is provided then a temporary file name will be generated in tempdir().

Value

Forpar.openCR.fit - openCRlist of model fits (seeopenCR.fit andopenCRlist). Names are created by prefixingprefix to thenames ofargslist. Iftrace is TRUE then the totalexecution time and finish time are displayed.

Note

Any attempt inarglist to setncores > 1 for a particular openCR fit was ignored inopenCR < 1.5.0. Now it is allowed.

See Also

openCR.fit,Parallel,make.table,openCRlist

Examples

## Not run: m1 <- list(capthist = ovenCH, model = list(p~1, phi~1)) m2 <- list(capthist = ovenCH, model = list(p~session, phi~1))m3 <- list(capthist = ovenCH, model = list(p~session, phi~session) )setNumThreads(7)  # on quadcore Windows PCfits <- par.openCR.fit (c('m1','m2','m3'), ncores = 1)AIC(fits)## End(Not run)

Kernel Distribution Functions

Description

Distribution of distance moved for each of the main movement kernels. Theoretical probability density, cumulative distribution function, and quantile function (inverse of the cumulative distribution function).

Usage

pkernel(q, movementmodel = c("BVN", "BVE", "BVC", "BVT", "RDE", "RDG", "RDL"),     move.a, move.b, truncate = Inf, lower.tail = TRUE)dkernel(r, movementmodel = c("BVN", "BVE", "BVC", "BVT", "RDE", "RDG", "RDL"),     move.a, move.b, truncate = Inf)qkernel(p, movementmodel = c("BVN", "BVE", "BVC", "BVT", "RDE", "RDG", "RDL"),     move.a, move.b, truncate = Inf, lower.tail = TRUE)gkernel(r, movementmodel = c("BVN", "BVE", "BVC", "BVT", "RDE", "RDG", "RDL"),    move.a, move.b, truncate = Inf)

Arguments

Details

Some formulae are given in openCR-vignette.pdf.gkernel gives the 2-D probability density of the bivariate kernelg(r) = f(r) / (2\pi r); the remaining functions describe the distribution of distance movedf(r).

Computation ofqkernel formovementmodel = 'BVE' uses numerical root finding (functionuniroot).

Truncation (truncate = limit for finitelimit) adjusts probabilities upwards by 1/pkernel(limit,..., truncate = Inf) so that pkernel(limit, ..., truncate = limit) equals 1.0.By default the distribution is not truncated.

Value

Forpkernel –

Vector of cumulative probabilities corresponding to q. The cumulative probability is 1.0 for q > truncate.

Fordkernel –

Vector of probability density at radial distance r (zero for r > truncate).

Forqkernel –

Vector of quantiles (distances moved) corresponding to cumulative probabilities p.

Forgkernel –

Vector of 2-D probability density at radial distance r (zero for r > truncate).

References

Efford, M. G. and Schofield, M. R. (2022) A review of movement models in open population capture–recapture.Methods in Ecology and Evolution13, 2106–2118. https://doi.org/10.1111/2041-210X.13947

See Also

Movement models,make.kernel,matchscale

Examples

# plot 3 distributions chosen with matchscale to intersect at p = 0.5q <- 0:100plot(q, pkernel(q, 'BVN', 34), type = 'l', ylab = 'Cumulative probability')lines(q, pkernel(q, 'BVT', move.a = 104, move.b = 5), col = 'darkgreen', lwd = 2)lines(q, pkernel(q, 'BVT', move.a = 40, move.b = 1), col = 'orange', lwd = 2)points(40, 0.5, pch = 16)legend(62, 0.36, lty=1, lwd = 2, col = c('black','darkgreen','orange'),    legend = c('BVN sigma=34', 'BVT a=104, b=5', 'BVT a=40, b=1'))# medianabline(v = qkernel(0.5, 'BVN', 34))

Plot Derived Estimates

Description

Session-specific estimates of the chosen parameter are plotted.

Usage

## S3 method for class 'derivedopenCR' plot(x, par = "phi", add = FALSE, xoffset = 0, ylim = NULL,     useintervals = TRUE, intermediate.x = TRUE, ...)

Arguments

Details

If ylim is not provided it is set automatically.

Confidence intervals are not available in this version.

Value

The x coordinates (including xoffset) are returned invisibly.

See Also

plot.openCR

Examples

## Not run: fit <- openCR.fit(dipperCH, type='JSSAfCL', model = phi~session)der <- derived(fit)plot(der,'N', pch = 16, cex = 1.3)## End(Not run)

Plot Estimates

Description

Session-specific estimates of the chosen parameter are plotted.

Usage

## S3 method for class 'openCR' plot(x, par = "phi", newdata = NULL, add = FALSE, xoffset = 0, ylim = NULL,     useintervals = TRUE, CI = TRUE, intermediate.x = TRUE, alpha = 0.05, stratum = 1, ...)

Arguments

Details

If ylim is not provided it is set automatically.

For customization you may wish to prepare a base plot withplot(... , type = 'n') and useadd = TRUE.

Value

The x coordinates (including xoffset) are returned invisibly.

See Also

predict,plot.derivedopenCR)

Examples

## Not run: fit <- openCR.fit(join(ovenCH), type='CJS', model = phi~session)plot(fit,'phi', pch = 16, cex=1.3, yl=c(0,1))## End(Not run)

openCR Model Predictions

Description

Evaluate an openCR capture–recapture model. That is, compute the ‘real’ parameters corresponding to the ‘beta’ parameters of a fitted model for arbitrary levels of any variables in the linear predictor.

Usage

## S3 method for class 'openCR' predict(object, newdata = NULL, se.fit = TRUE, alpha = 0.05, savenew = FALSE, ...) ## S3 method for class 'openCRlist' predict(object, newdata = NULL, se.fit = TRUE, alpha = 0.05, savenew = FALSE, ...)

Arguments

Details

Predictions are provided for each row in ‘newdata’. The default (constructed bymakeNewData) is to limit those rows to the first-used level of factor predictors; to include all levels passall.levels = TRUE tomakeNewData in the ... argument.

See Also

AIC.openCR,openCR.fit

Examples

## Not run: c1 <- openCR.fit(ovenCH, type='CJS', model=phi~session)predict(c1)## End(Not run)

Print Method for Derived Estimates

Description

Formats output fromderived.openCR.

Usage

## S3 method for class 'derivedopenCR'print(x, Dscale = NULL, legend = FALSE, ...)

Arguments

Details

By default (i.e. when not not specified in the in the ... argument),row.names = FALSE anddigits = 4.

See Also

derived.openCR

Print or Summarise openCR Object

Description

Print results from fitting a spatially explicit capture–recapture model, or generate a list of summary data.

Usage

## S3 method for class 'openCR' print(x, newdata = NULL, alpha = 0.05, svtol = 1e-5,...)## S3 method for class 'openCR' summary(object, newdata = NULL, alpha = 0.05, svtol = 1e-5, deriv = FALSE, ...)

Arguments

Details

Results are potentially complex and depend upon the analysis (see below). Optionalnewdata should be a dataframe with a column for each of the variables in the model. Ifnewdata is missing then a dataframe is constructed automatically. Defaultnewdata are for a naive animal on the first occasion; numeric covariates are set to zero and factor covariates to their base (first) level. Confidence intervals are 100 (1 – alpha) % intervals.

AICc is computed with the default sample size (number of individuals) and parameter count (use.rank = FALSE).

Value

Thesummary method constructs a list of outputs similar to those printed by theprint method, but somewhat more concise and re-usable:

* spatial models only

References

Burnham, K. P. and Anderson, D. R. (2002)Model selection and multimodel inference: a practical information-theoretic approach. Second edition. New York: Springer-Verlag.

See Also

AIC.openCR,openCR.fit

Examples

## Not run: c1 <- openCR.fit(ovenCH, type='CJS', model=phi~session)c1## End(Not run)

Import Data from RMark Input Format

Description

read.inp forms a capthist object from a MARK input (.inp) file.

Usage

read.inp(filename, ngroups = 1, grouplabel = 'group', grouplevels = NULL,     covnames = NULL, skip = 0)

Arguments

Details

Comments bracketed with ‘/*' and '*/’ will be removed automatically.

Ifgrouplevels is specified thenngroups is taken from the number of levels (ngroups is overridden). An individual covariate is output, named according togrouplabel. The order of levels ingrouplevels should match the order of the group frequency columns in the input. This also determines the ordering of levels in the resulting covariate.

Value

A single-session capthist object with no traps attribute.

See Also

RMarkInput,unRMarkInput

Examples

datadir <- system.file('extdata', package = 'openCR')dipperCH <- read.inp(paste0(datadir, '/ed.inp'), ngroups = 2)summary(dipperCH)

Reverse Primary Sessions

Description

Therev method for capthist objects reverses the order of the primary sessions while retaining the order of secondary sessions within each primary session.

Usage

## S3 method for class 'capthist'rev(x)

Arguments

Details

rev() is used to demonstrate 'reversed time' analyses (Nichols 2016)in which seniority (gamma) is estimated as reversed-time survival (phi)The approach is numerically equivalent to direct modelling of seniority (see Examples). Direct modelling allows more control and is more intuitive.

Ifx is not overtly multi-session and has no intervals attribute then each occasion is treated as a primary session.

Value

Capthist object with same observations as input, but re-ordered. The order of attributessessionlabels andintervals is also reversed.A default intervals attribute is added if the input lacks one.

References

Nichols, J. D. (2016) And the first one now will later be last:time-reversal in Cormack–Jolly–Seber Models.Statistical Science31, 175–190.

Examples

summary(rev(ovenCH), terse = TRUE)# These three models give the same result for gamma except for# gamma(1982) which is confounded with p and not separately estimable:## Not run: dipperPradel <- openCR.fit(dipperCH, type = "Pradelg", model = list(p~t, phi~t, gamma~t))revdipper <- openCR.fit(rev(dipperCH), model=list(p~t, phi~t))dipperJSSA <- openCR.fit(dipperCH, type='JSSAgCL', model=list(p~t, phi~t, gamma~t))predict(dipperPradel)$gammapredict(revdipper)$phipredict(dipperJSSA)$gamma## End(Not run)

Simulate Capture Histories

Description

Generate non-spatial or spatial open-population data and fit models.

Usage

sim.nonspatial (N, turnover = list(), p, nsessions, noccasions = 1, intervals = NULL,     recapfactor = 1, seed = NULL, savepopn = FALSE, ...)    runsim.nonspatial (nrepl = 100, seed = NULL, ncores = NULL, fitargs = list(),     extractfn = predict, ...)runsim.spatial (nrepl = 100, seed = NULL, ncores = NULL, popargs = list(),     detargs = list(), fitargs = list(), extractfn = predict, intervals = NULL)sumsims (sims, parm = 'phi', session = 1, dropifnoSE = TRUE, svtol = NULL,     maxcode = 3, true = NULL)runsim.RMark (nrepl = 100, model = "CJS", model.parameters = NULL, extractfn,    seed = NULL, ...)

Arguments

Details

Forsim.nonspatial – Ifintervals is specified then the number of primary and secondary sessions is inferred fromintervals andnsessions andnoccasions are ignored. IfN andp are vectors of length 2 then subpopulations of the given initial size are sampled with the differing capture probabilities and the resulting capture histories are combined.

runsim.spatial is a relatively simple wrapper forsim.popn,sim.capthist, andopenCR.fit. Some arguments are set automatically: thesim.capthist argument 'renumber' is always FALSE; argument 'seed' is ignored within 'popargs' and 'detargs'; if no 'traps' argument is provided in 'detargs' then 'core' from 'popargs' will be used; detargs$popn and fitargs$capthist are derived from the preceding step. The 'type' specified in fitargs may refer to a non-spatial or spatial open-population model ('CJS', 'JSSAsecrfCL' etc.). If theintervals argument is specified it is used to set the intervals attribute of the simulated capthist object; turnover parameters insim.popn are not scaled byintervals.

Control of parallel processing changed inopenCR 1.5.0 to conform tosecr. Inrunsim.nonspatial andrunsim.spatial, ifncores is NULL (the default) then the number of cores used for multithreading byopenCR.fit is controlled by the environment variable RCPP_PARALLEL_NUM_THREADS. Use the secr functionsetNumThreads to set RCPP_PARALLEL_NUM_THREADS to a value greater than the default (2, fromopenCR 1.5 onwards).

Otherwise, (ncores specified in runsim.nonspatial or runsim.spatial) 'ncores' is set to 1 for each replicate and the replicates are split across the specified number of cores.

sumsims assumes output fromrunsim.nonspatial andrunsim.spatial with ‘extractfn = predict’ or ‘extractfn = summary’. Missing SE usually reflects non-identifiability of a parameter or failure of maximisation, so these replicates are dropped by default. Ifsvtol is specified then the rank of the Hessian is determined by counting eigenvalues that exceed svtol, and replicates are dropped if the rank is less than the number of beta parameters. A value of 1e-5 is suggested for svtol inAIC.openCR, but smaller values may be appropriate for larger models (MARK has its own algorithm for this threshold).

Replicates are also dropped bysumsims if the convergence code exceeds 'maxcode'. The maximisation functionsnlm (used for method = 'Newton-Raphson', the default), andoptim (all other methods) return different convergence codes; their help pages should be consulted. The default is to accept code = 3 fromnlm, although the status of such maximisations is ambiguous.

Value

sim.nonspatial –

A capthist object representing an open-population sample

runsim.nonspatial andrunsim.spatial –

List with one component (output from extractfn) for each replicate. Each component also has attributes 'eigH' and 'fit' taken from the output ofopenCR.fit. See Examples to extract convergence codes from 'fit' attribute.

sumsims –

Data.frame with rows ‘estimate’, ‘SE.estimate’, ‘lcl’, ‘ucl’, ‘RSE’, ‘CI.length’ and columns for median, mean, SD and n. If ‘true’ is specified there are additional rows are ‘Bias’ and ‘RB’, and columns for ‘rRMSE’ and ‘COV’.

See Also

sim.popn,sim.capthist

Examples

## Not run: cores <- 2   # for CRAN check; increase as availablech <- sim.nonspatial(100, list(phi = 0.7, lambda = 1.1), p = 0.3, nsessions = 8, noccasions=2)openCR.fit(ch, type = 'CJS')turnover <- list(phi = 0.85, lambda = 1.0, recrmodel = 'constantN')set.seed(123)## using type = 'JSSAlCL' and extractfn = predictfitarg <- list(type = 'JSSAlCL', model = list(p~t, phi~t, lambda~t))out <- runsim.nonspatial(nrepl = 100, N = 100, ncores = cores, turnover = turnover,    p = 0.2, recapfactor = 4, nsessions = 10, noccasions = 1, fitargs = fitarg)sumsims(out, 'lambda', 1:10)## using type = 'Pradelg' and extractfn = derived## homogeneous pfitarg <- list(type = 'Pradelg', model = list(p~t, phi~t, gamma~t))outg <- runsim.nonspatial(nrepl = 100, N = 100, ncores = cores, turnover = turnover,     p = 0.2, recapfactor = 4, nsessions = 10, noccasions = 1,     fitargs = fitarg, extractfn = derived)apply(sapply(outg, function(x) x$estimates$lambda),1,mean)turnover <- list(phi = 0.85, lambda = 1.0, recrmodel = 'discrete')## 2-class mixture for poutg2 <- runsim.nonspatial(nrepl = 100, N = c(50,50), ncores = cores, turnover = turnover,     p = c(0.3,0.9), recapfactor = 1, nsessions = 10, noccasions = 1,     fitargs = fitarg, extractfn = derived)outg3 <- runsim.nonspatial(nrepl = 100, N = c(50,50), ncores = cores, turnover = turnover,     p = c(0.3,0.3), recapfactor = 1, nsessions = 10, noccasions = 1,     fitargs = fitarg, extractfn = derived)apply(sapply(outg2, function(x) x$estimates$lambda),1,mean)plot(2:10, apply(sapply(outg2, function(x) x$estimates$lambda),1,mean)[-1],    type='o', xlim = c(1,10), ylim = c(0.9,1.1))## RMarkextfn <- function(x) x$results$real$estimate[3:11]MarkPath <- 'c:/mark'  # customise as neededturnover <- list(phi = 0.85, lambda = 1.0, recrmodel = 'discrete')outrm <- runsim.RMark (nrepl = 100, model = 'Pradlambda', extractfn = extfn,                        model.parameters = list(Lambda=list(formula=~time)),                       N = c(200,200), turnover = turnover, p = c(0.3,0.9),                       recapfactor = 1, nsessions = 10, noccasions = 1)extout <- apply(do.call(rbind, outrm),1,mean)## Spatialgrid <- make.grid()msk <- make.mask(grid, type = 'trapbuffer', nx = 32)turnover <- list(phi = 0.8, lambda = 1)poparg <- list(D = 10, core = grid, buffer = 100, Ndist = 'fixed', nsessions = 6,     details = turnover)detarg <- list(noccasions = 5, detectfn = 'HHN', detectpar = list(lambda0 = 0.5, sigma = 20))fitarg <- list(type = 'JSSAsecrfCL', mask = msk, model = list(phi~1, f~1))sims <- runsim.spatial (nrepl = 7, ncores = cores, pop = poparg, det = detarg, fit = fitarg)sumsims(sims)## extract the convergence code from nlm for each replicate in preceding simulationsapply(lapply(sims, attr, 'fit'), '[[', 'code')## if method != 'Newton-Raphson then optim is used and the code is named 'convergence'# sapply(lapply(sims, attr, 'fit'), '[[', 'convergence')## End(Not run)

Unique Capture Histories

Description

Compresses or expands capthist objects.

Usage

squeeze(x)unsqueeze(x)

Arguments

Details

Althoughsqueeze may be applied to spatial capthist objects, theeffect is often minimal as most spatial histories are unique.

The ‘freq’ covariate is used byopenCR.fit to weight summaries and likelihoods. It is currently ignored bysecr.fit.

Value

Both functions return a capthist object with one row for each unique capture history (including covariates). The individual covariate ‘freq’ records the number of instances of each unique history in the input.

See Also

openCR.fit

Examples

squeeze(captdata)

Stratum names

Description

Extract or replace the stratum names of acapthist object.

Usage

strata(object, ...)strata(object) <- value

Arguments

Details

Replacement values will be coerced to character.

Value

a character vector with one value for each session incapthist.

Note

openCR uses the term ‘stratum’ for an independent set of samples, rather like a ‘session’ insecr. Strata offer flexibility in defining and evaluating between-stratum models. The log likelihood for a stratifiedmodel is the sum of the separate stratum log likelihoods. Although this assumes independence of sampling, parameters may be shared across strata, or stratum-specific parameter values may be functions of stratum-level covariates. The detector array and mask can be specified separately for each stratum.

For open population analyses, each stratum comprises both primary and secondary sessions of Pollock's robust design ‘joined’ in a single-session capthist object.

The functionstratify can be useful for manipulating data into multi-stratum form.

Models are stratified only if the argumentstratified ofopenCR.fit() is set to TRUE. Strata will otherwise be treated as primary sessions and concatenated as usual withjoin().

See Also

openCR.fit,session,stratify

Examples

  # artificial example, treating years as strata  strata(ovenCH)

Stratify Capture-Recapture Data

Description

Arrange existing capthist data in stratified form.

Usage

stratify(..., intervals = NULL, MoreArgs = list(), covariate = NULL, bytraps = FALSE)

Arguments

Details

The argument ... may be

1. a list of single-session capthist, one for each stratum (sessions already joined)

2. a list of multi-session capthist, one for each stratum (sessions will be joined)

3. one single-session capthist, to split bycovariate (sessions already joined)

4. one multi-session capthist, to be joined as one then split bycovariate

Cases 1 and 2 result in one stratum for each component of the input list. Cases 3 and 4 result in one stratum for each level ofcovariate.

The result in Case 1 is identical toMS.capthist(...).

The argumentintervals refers to the intervals between primary sessions before joining (Cases 2,4 only) (see Examples).

MoreArgs may include the arguments remove.dupl.sites, tol, sites.by.name or drop.sites ofjoin; these otherwise take their default values.

Value

Multi-stratum (multi-session) capthist object for which each component has been ‘join’ed.

See Also

join,MS.capthist,openCR.fit,strata

Examples

# FebpossumCH comprises 9 annual February sessions.# The individual covariate 'sex' takes values 'F' and 'M', resulting in two strata.# 'intervals' can be omitted as the default does the same job.ch <- stratify(FebpossumCH, covariate = 'sex', intervals = rep(list(rep(1,8)),2))summary(ch, terse = TRUE)

Goodness-of-fit tests for the Cormack-Jolly-Seber model

Description

The packageR2ucare (Gimenez et al. 2018, 2022) provides the standard tests for CJS models from Burnham et al. (1987) along with tests for multi-state models as described by Pradel et al. (2005). This function is a wrapper for the tests relevant toopenCR (see Details). Original papers and the vignette forR2ucare should be consulted for interpretation.

Usage

ucare.cjs(CH, tests = "all", by = NULL, verbose = TRUE, rounding = 3, ...)

Arguments

Details

The possible tests are “test3sr", “test3sm", “test2ct", “test2cl", and “overall_CJS".

IfCH is a multi-session object then it will first be collapsed to a single-session object withjoin as usual inopenCR. IfCH has an intervals attribute indicating that the data are from a robust design (some intervals zero) then it will first be collapsed to one secondary session per primary session, with a warning.

Ifby is specified it should point to a categorical variable (factor or character) in the covariates attribute ofCH. Separate tests will be conducted for each group.

R2ucare was removed from CRAN in May 2022, but will return at some point. In the meantime, it may be necessary to install from GitHub with

if(!require(devtools)) install.packages("devtools")devtools::install_github("oliviergimenez/R2ucare")

Value

A list of results, possibly nested by the grouping variableby. The verbose form includes both the overall result of each test and its breakdown into components (‘details’).

References

Burnham, K. P., Anderson, D. R., White, G. C., Brownie, C. and Pollock, K. H. (1987)Design and Analysis Methods for Fish Survival Experiments Based on Release-Recapture. American Fisheries Society Monograph 5. Bethesda, Maryland, USA.

Choquet, R., Lebreton, J.-D., Gimenez, O., Reboulet, A.-M. and Pradel, R. (2009) U-CARE: Utilities for performing goodness of fit tests and manipulating CApture-REcapture data.Ecography32, 1071–1074.

Gimenez, O., Lebreton, J.-D., Choquet, R. and Pradel, R. (2018) R2ucare: An R package to perform goodness-of-fit tests for capture–recapture models.Methods in Ecology and Evolution9, 1749–1754.

Gimenez, O., Lebreton, J.-D., Choquet, R. and Pradel, R. (2022) R2ucare: Goodness-of-Fit Testsfor Capture-Recapture Models. R package version 1.0.2.https://github.com/oliviergimenez/R2ucare/

Lebreton, J.-D., Burnham, K. P., Clobert, J., and Anderson, D. R. (1992) Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies.Ecological Monographs62, 67–118.

Pradel, R., Gimenez O. and Lebreton, J.-D. (2005) Principles and interest of GOF tests for multistate capture–recapture models.Animal Biodiversity and Conservation28, 189–204.

See Also

m.array

Examples

if (requireNamespace("R2ucare"))    ucare.cjs(dipperCH, verbose = FALSE, by = 'sex')