Incorporating sampling error in the estimation of autoregressive
coefficients of animal population dynamics using capture-recapture data
Abstract
Population dynamics models combine density-dependence and environmental
effects. Ignoring sampling uncertainty might lead to biased estimation
of the strength of density-dependence. This is typically addressed using
state-space model approaches, which integrate sampling error and
population process estimates. Such models seldom include an explicit
link between the sampling procedures and the true abundance, which is
common in capture-recapture settings. However, many of the models
proposed to estimate abundance in the presence of heterogeneity lead to
incomplete likelihood functions and cannot be straightforwardly included
in state-space models. We assessed the importance of estimating sampling
error explicitly by taking an intermediate approach between ignoring
uncertainty in abundance estimates and fully specified state-space
models for density-dependence estimation based on autoregressive
processes. First, we estimated individual capture probabilities based on
a heterogeneity model, using a conditional multinomial likelihood,
followed by a Horvitz-Thompson estimate for abundance. Second, we
estimated coefficients of autoregressive models for the log abundance.
Inference was performed using the methodology of integrated nested
Laplace approximation (INLA). We performed an extensive simulation study
to compare our approach with estimates disregarding capture history
information, and using R-package VGAM, for different parameter
specifications. The methods were then applied to a real dataset of
gray-sided voles Myodes rufocanus from Northern Norway. We found
that density-dependence estimation was improved when explicitly
modelling sampling error in scenarios with low innovation variances, in
which differences in coverage reached up to 8% in estimating the
coefficients of the autoregressive processes. In this case, the bias
also increased assuming a Poisson distribution in the observational
model. For high innovation variances, the differences between methods
were small and it appeared less important to model heterogeneity.