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We develop a multi-state model to estimate the size of a closed population from capture-recapture studies. We consider the case where capture-recapture data are not of a simple binary form, but where the state of an individual is also recorded upon every capture as a discrete variable. The proposed multi-state model can be regarded as a generalisation of the commonly applied set of closed population models to a multi-state form. The model allows for heterogeneity within the capture probabilities associated with each state while also permitting individuals to move between the different discrete states. A closed-form expression for the likelihood is presented in terms of a set of sufficient statistics. The link between existing models for capture heterogeneity is established, and simulation is used to show that the estimate of population size can be biased when movement between states is not accounted for. The proposed unconditional approach is also compared to a conditional approach to assess estimation bias. The model derived in this paper is motivated by a real ecological data set on great crested newts, Triturus cristatus. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

The Cormack–Jolly–Seber (CJS) model assumes that all marked animals have equal recapture probabilities at each sampling occasion, but heterogeneity in capture often occurs and should be taken into account to avoid biases in parameter estimates. Although diagnostic tests are generally used to detect trap-dependence or transience and assess the overall fit of the model, heterogeneity in capture is not routinely tested for. In order to detect and identify this phenomenon in a CJS framework, we propose a test of positive association between previous and future encounters using Goodman–Kruskal’s gamma. This test is based solely on the raw capture histories and makes no assumption on model structure. The development of the test is motivated by a dataset of Sandwich terns (Thalasseus sandvicensis), and we use the test to formally show that they exhibit heterogeneity in capture. We use simulation to assess the performance of the test in the detection of heterogeneity in capture, compared to existing and corrected diagnostic goodness-of-fit tests, Leslie’s test of equal catchability and Carothers’ extension of the Leslie test. The test of positive association is easy to use and produces good results, demonstrating high power to detect heterogeneity in capture. We recommend using this new test prior to model fitting as the outcome will guide the model-building process and help draw more accurate biological conclusions. Supplementary materials accompanying this paper appear online. [ABSTRACT FROM AUTHOR]

. Data are often collected from wild animals that have been marked at unknown age. As a result, standard probability models, fitted by maximum likelihood, cannot incorporate age dependence in probabilities of annual survival. We propose and fit new mixture models to ring-recovery data on birds ringed of unknown age, in which it is possible to incorporate age dependence in survival. It is shown that it is important to analyse simultaneously data on animals marked as young, and of known age, as otherwise the mixture model is parameter redundant. The potential of the approach is illustrated by a new analysis of data on mallards, Anas platyrhynchos, and the wider performance of the approach is demonstrated through simulation. The models provide a way of analysing correctly large numbers of historical data sets. [ABSTRACT FROM AUTHOR]

1. Ring-recovery data can be used to obtain estimates of survival probability which is a key demographic parameter of interest for wild animal populations. Conditional modelling of ring-recovery data is needed when cohort numbers are unavailable or unreliable. It is often necessary to include in such analysis a recovery probability that is declining as a function of time, and failure to do this can result in biased estimates of annual survival. 2. Corresponding estimates of survival probability need to be reliable in order for correct conclusions to be drawn regarding the effects of climate change. 3. We show that standard logistic modelling of a decline in recovery probability is unsatisfactory, and propose and investigate a range of alternative procedures. 4. Methods are illustrated by application to a recovery data set on grey herons. The model selected is a scaled-logistic model, and it is shown to provide a unifying analysis of several data sets collected on different common bird species. The model makes specific predictions, providing potential new insights and avenues for ecological research. The wider performance of this model is evaluated through simulation. 5. In this study, we propose a new scaled-logistic model for the analysis of ring-recovery data without cohort numbers, which incorporates a reporting probability that declines over time. The model is shown to perform well in simulation studies and for both a single real data set and several real data sets in combination. Its use has the potential to reduce bias in estimates of wild animal survival that currently do not incorporate such reporting probabilities. Alternative models are shown to possess undesirable features. [ABSTRACT FROM AUTHOR]