A Modified AIlalysis of the Jolly-Seber CapturRecapture Model

Population estimates derived from the Jolly-Seber model occasionally give estimated probabilities of survival that are greater than unity, and estimated negative influxes of new animals. This paper suggests an intuitive solution to the problem. It also extends the model slightly, so that known deaths in the marked population, e.g. from tag returns, can be incorporated in the analysis. This extension may be important in studies where a significant proportion of marks is discovered on corpses and returned, and where a number of recaptures also occurs. Variances and confidence intervals for the proposed estimates are found by simulation. The modified estimation process is illustrated in the analysis of yellow wagtail (otacilla fava flavissima) data. Results from simulations are also presented. Standard errol s of the modified estimates, calculated by simulation, compare well with analytic standard errors of Jolly-Seber estimates when modifications are slight. Where modifications are more extensive, standard errors of the modified estimates tend to be smaller and more stable than those of the Jolly-Seber estimates. 1. Inttoduction The Jolly-Seber model was derived to deal with the situation where capture-recapture data are available on a population which is subject to death, birth and migration. The model allows for deaths in the population that are caused by capture ('losses on capture?), which is an important consideration for some studies. It does not, however, allow for other known deaths. In some studies, tag returns from dead animals provide vital information, and a method of analysis is available for this case (Seber, 1962). However, if capture-recapture data are available in addition to tag returns, a simple extension of the Jolly-Seber model can handle both sets of data simultaneously. A shortcoming of the Jolly-Seber model is that estimated survival probabilities can be greater than unity and that estimated numbers of new animals entering the population (births or immigrants) can be negative. This paper offers a commonsense approach to these problems. Barndorff-Nielsen (1972) looked at the problem of occasional estimated survival probabilities being greater than unity in the simpler case of a population without birth or immigration. He stated that his solution might or might not be the maximum likelihood solution. The approach in this paper is a generalization of that method to the Jolly-Seber model. The problem of deriving analytic variances for the modified estimates is complex and seemingly intractable. An alternative is to use Monte Carlo methods. The same approach yields confidence limits, without assuming that the estimators are normally distributed.