Population Size and Stopover Duration Estimation Using Mark–Resight Data and Bayesian Analysis of a Superpopulation Model

Abstract

We present a novel formulation of a mark-recapture-resight model that allows estimation of population size, stopover duration, and arrival and departure schedules at migration areas. Estimation is based on encounter histories of uniquely marked individuals and relative counts of marked and unmarked animals. We use a Bayesian analysis of a state-space formulation of the Jolly-Seber mark-recapture model, integrated with a binomial model for counts of unmarked animals, to derive estimates of population size and arrival and departure probabilities. We also provide a novel estimator for stopover duration that is derived from the latent state variable representing the interim between arrival and departure in the state-space model. We conduct a simulation study of field sampling protocols to understand the impact of superpopulation size, proportion marked, and number of animals sampled on bias and precision of estimates. Simulation results indicate that relative bias of estimates of the proportion of the population with marks was low for all sampling scenarios and never exceeded 2%. Our approach does not require enumeration of all unmarked animals detected or direct knowledge of the number of marked animals in the population at the time of the study. This provides flexibility and potential application in a variety of sampling situations (e.g., migratory birds, breeding seabirds, sea turtles, fish, pinnipeds, etc.). Application of the methods is demonstrated with data from a study of migratory sandpipers.

Accounting for heterogeneity when estimating stopover duration, timing and population size of red knots along the Luannan Coast of Bohai Bay, China

“…In this study, we extended the Bayesian superpopulation model developed by Lyons et al (2016) by accounting for heterogeneity in encounter and staying probabilities through finite mixtures in order to provide unbiased estimates of stopover timing, duration, and population size of migratory birds. Using a combination of analyses of simulated and real data, we showed that heterogeneity in encounter and staying probabilities is present in real datasets and can cause severely biased parameter estimates, especially of stopover duration and population size.…”

Modelling individual migration patterns using a Bayesian nonparametric approach for capture–recapture data

“…As our results in the Supplementary Material [Matechou and Caron (2017a)] demonstrate, these two values can be considerably different if the intervals between sampling occasions are long compared to the average stopover duration of individuals in the population. In addition, individuals that arrived but departed before the start of the study are also accounted for, which is not the case in, for example, Lyons et al (2016), who mention that, typically, studies at stopover sites are planned so that they start before most individuals have arrived. However, since phenology is changing in recent years, satisfying this criterion can become increasingly more difficult.…”

“…Estimation of individual arrival/departure times. Since we are estimating individual arrival and departure times, similar to Lyons et al (2016), we are able to estimate individual stopover durations as well as other statistics that are potentially of interest, such as number of individuals present at any time point. However, in contrast to Lyons et al (2016), we do not assign an arrival time of one to all individuals that were already present at the start of the study, as our mixture model allows us to extend arrival to times prior to the start of the study while accounting for the probability of remaining at the site until the start of the study.…”

“…Since we are estimating individual arrival and departure times, similar to Lyons et al (2016), we are able to estimate individual stopover durations as well as other statistics that are potentially of interest, such as number of individuals present at any time point. However, in contrast to Lyons et al (2016), we do not assign an arrival time of one to all individuals that were already present at the start of the study, as our mixture model allows us to extend arrival to times prior to the start of the study while accounting for the probability of remaining at the site until the start of the study. For the applications considered in this paper, estimated individual arrival and departure times allowed us to compare the arrival pattern of individuals of different sex as well as the estimated stopover duration of individuals that were caught at least once with that of individuals that were never caught.…”

“…For example, although the data sets we considered were obtained using only one type of sampling, namely capture, the model can be readily extended for cases when multiple types of sampling are employed, such as capture-resight data. Additionally, the model can be extended for the case of integrated analysis of different (independent) data sets [Besbeas et al (2002), McCrea et al (2010), Matechou et al (2013a), Lyons et al (2016)], to allow for heterogeneity in capture probabilities between individuals [Basu and Ebrahimi (2001), Rocchetti, Bunge and Böhning (2011)] and, potentially, to account for misidentification of individuals [McClintock et al (2014)] which is a feature of some noninvasive sampling techniques, such as DNA sampling.…”