A General Methodology for the Analysis of Capture-Recapture Experiments in Open Populations

Abstract

We trace the development of a likelihood function representation for the open-population capture-recapture (Jolly-Seber) experiment. We find that the modelling of the birth process in the general model is not consistent with the reduced death-only model and that all formulations to date lead to difficulties in imposing constraints upon the parameters of the birth process. We propose a generalisation to the usual Jolly-Seber representation that models births using a multinomial distribution from a super-population. We show how this leads to simplifications in the numerical optimization of the likelihood and how constraints upon the parameters of the model can now be easily imposed. We show how covariate models using auxiliary variables such as sampling effort or weather conditions to explain capture or survival rates can also be easily added. We also show how this model can be generalised to more than one group of animals. Finally a numerical example is provided which fits a class of models where the capture probabilities, survival probabilities and birth probabilities can each vary over time or among groups or both. This permits sequential model fitting within a comprehensive model framework; an approach akin to that of Lebreton et al (Ecological Monographs, 62, 67-118).

Assessing the design and power of capture-recapture studies to estimate demographic parameters for the Endangered Oceania humpback whale population

“…The POPAN model (Schwarz & Arnason 1996, Arnason & Schwartz 1999, a derivative of the Jolly-Seber model (Jolly 1965, Seber 1965, estimates N S , defined as the total number of individuals that are ever exposed to capture between the first and last survey occasions, comprising individuals that join the population between the first and last surveys in addition to individuals present at the start of the first survey. A proportion of the N S enters the survey area during each survey occasion and is available for capture: this is estimated by a parameter termed the probability of entry for each survey occasion.…”

“…The primary assumptions of the POPAN model are general to most capture−recapture models and include: (1) the study area is constant, (2) marks are permanent and read correctly, (3) all individuals (within a demographic class) have equal capture probability and (4) all individuals have equal survival probability (Schwarz & Arnason 1996). These assumptions will be dealt with in turn in the following sections.…”

“…Over this 6 yr period, the SPWRC identified individual whales using a combination of photographs of natural markings (photo-ID, n = 660) and DNA profiles from skin biopsy samples (n = 840). The sighting histories of these individuals were used in a capture−recapture framework to estimate abundance with the POPAN formulation of the Jolly Seber model developed by Schwarz & Arnason (1996). The superpopulation (N S ) estimate for Oceania from 1999 to 2005 was 4329 (95% confidence limits, CL: 3345, 5315) whales and the estimated annual population growth rate for this period was λ = 1.03 (95% CL: 0.90−1.18) based on the DN A profile data (Constantine et al 2012).…”

First time series of estimated humpback whale (Megaptera novaeangliae) abundance in Prince William Sound

“…The mark-recapture program MARK was used to obtain maximum likelihood parameter estimates (MLE's) and to compare various models using the POPAN implementation of the Jolly-Seber model (Schwarz and Arnason 1996;White and Burnham 1999). Like most commonly-used mark-recapture models, the Jolly-Seber model generates estimates of parameters by modeling sighting histories as a multinomial distribution.…”

“…Sightings of all first year calves were removed from the mark-recapture analyses as their probability of capture is complicated by co-occurrence with their mothers. The POPAN procedure in program MARK runs a variety of the widely used and accepted models for open populations (Schwarz and Arnason 1996;Schwarz 2001) and was chosen because it generates annual estimates of abundance (N t ) to form a time series. This model is a modified version of the traditional open Jolly-Seber model and, based on the sighting histories, estimates survival, φ t , and probability of capture, p t , "births" or net number of new entrants into the population (pent) in year t, and N , the overall population size.…”