Survival (CJS) {wiqid}

Survival from recapture data with Cormack-Jolly-Seber (CJS) model

Description

Calculation of apparent survival (accounting for recapture probability) from mark-recapture data, with time-dependent phi or p, possibly with covariates. Function survCHSaj allows for different survival parameters for juveniles and adults; juveniles are assumed to become adults after the first interval. BsurvCJS is a Bayesian version.

Usage

survCJS(DH, model=list(phi~1, p~1), data=NULL, freq=1, group, interval=1,
    ci = 0.95, link=c("logit", "probit"), ...)

survCJSaj(DHj, DHa=NULL, model=list(phiJ~1, phiA~1, p~1), data=NULL,
    freqj=1, freqa=1, ci = 0.95, link=c("logit", "probit"), ...)

BsurvCJS(DH, model=list(phi~1, p~1), data = NULL, freq=1, priors=NULL,
    chains=3, draws=1e4, burnin=1000, thin=1, adapt=1000,
    parallel = NULL, seed=NULL, priorOnly=FALSE, ...)

Arguments

DH

a 1/0 matrix with detection histories with a row for each animal captured and a column for each capture occasion.

model

a list of formulae symbolically defining a linear predictor for each parameter in terms of covariates.

data

a data frame with a row for each survival interval / recapture occasion and columns for each of the covariates used to estimate phi or p.

freq

a scalar or a vector of length nrows(DH) with the frequency of each detection history. Negative values indicate trap losses.

group

an optional factor of length nrows(DH); if provided, group can be included in the model definition, see Examples.

interval

the time interval between capture occasions; scalar if all intervals are equal or a vector of length ncols(DH) - 1; the units used must be the same as those for the apparent survival estimate, eg, for annual survival use years.

DHj, DHa

detection history matrices for animals marked as juveniles and adults respectively; DHa should be NULL if no animals were marked as adults.

freqj, freqa

frequencies of each detection history in DHj and DHa; freqa is ignored if DHa = NULL.

ci

the required confidence interval.

link

the link function to use, either logit or probit; see Links.

...

other arguments passed to nlm.

priors

a list with elements for prior mean and variance for coefficients; see Details.

chains

the number of Markov chains to run.

draws

the minimum number of values to return; the actual number returned may be slightly higher, as it will be a multiple of chains.

burnin

the number of values to discard at the beginning of each chain.

thin

the thinning rate. If set to n > 1, n values are calculated for each value returned.

adapt

the number of iterations to run in the JAGS adaptive phase.

priorOnly

if TRUE, the function produces random draws from the appropriate prior distributions, with a warning.

parallel

if TRUE or NULL and sufficient cores are available, the MCMC chains are run in parallel; if TRUE and insufficient cores are available, a warning is given.

seed

a positive integer, the seed for the random number generators.

Details

BsurvCJS uses a probit link to model apparent survival and detection as a function of covariates; most software uses a logistic (logit) link. See Links. Coefficients on the probit scale are about half the size of the equivalent on the logit scale.

Priors for BsurvCJS are listed in the priors argument, which may contain elements:

muPhi and muP : the means for apparent survival and detection coefficients respectively. This may be a vector with one value for each coefficient, including the intercept, or a scalar, which will be used for all. The default is 0.

sigmaPhi and sigmaP : the variance for apparent survival and detection coefficients respectively. This may be (1) a vector with one value for each coefficient, including the intercept, which represents the variance, assuming independence, or (2) a scalar, which will be used for all. The function does not currently allow a variance-covariance matrix. The default is 1, which is somewhat informative.

When specifying priors, note that numerical covariates are standardized internally before fitting the model. For an intercept-only model, a prior of Normal(0, 1) on the probit scale implies a Uniform(0, 1) or Beta(1, 1) prior on the probability scale.

Value

survCJS and survCJSaj return an object of class wiqid, a list with elements:

call

The call used to produce the results

beta

Estimates of the coefficients in the linear predictors for phi and p.

beta.vcv

The variance-covariance matrix for the beta estimates.

real

Back-transformed estimates of phi and p for each interval / occasion.

logLik

a vector with elements for log(likelihood), number of parameters, and effective sample size. If the variance-covariance matrix cannot be calculated, the second element should be NA.

There are print, logLik, and nobs methods for class wiqid.

BsurvCJS returns an object of class Bwiqid, a data frame with columns for each p and psi value containing the series of MCMC draws, and attributes for details of the MCMC run.

Benchmarks

Output of survCJS has been checked against program MARK with the dipper data set: coefficients are not the same as MARK uses models without an intercept, but the real values agree to 3 decimal places.

Author(s)

Mike Meredith

References

Lebreton, J-D; K P Burnham; J Clobert; D R Anderson. 1992. Modeling survival and testing biological hypotheses using marked animals: a unified approach with case studies. Ecological Monographs 62:67-118.

Examples

data(dippers)

DH <- dippers[1:7]  # Extract the detection histories
survCJS(DH)  # the phi(.) p(.) model
survCJS(DH, phi ~ .time)  # the phi(t) p(.) model
df <- data.frame(flood = c(FALSE, TRUE, TRUE, FALSE, FALSE, FALSE))
survCJS(DH, phi ~ flood, data=df)  # the phi(flood) p(.) model
# Including a grouping factor:
survCJS(DH, phi ~ flood*group, data=df, group=dippers$sex)

# With unequal intervals - suppose no data were collected in year 5:
DH1 <- DH[, -5]
survCJS(DH1, phi ~ .time, interval = c(1, 1, 1, 2, 1))

# See also the examples in the dippers help file.