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Estimation of population trajectories from fitting population models to individual identification data: some issues

Justin Cooke

A population model is always required for interpreting mark-recapture data, although for some standard methods it may be a minimal model, such as a closed population model. The requirements for the population model are partly dictated by the nature of the data. For example, if the data are collected on a calving ground, it is necessary to model how often the whales visit the calving ground, which in turn requires that calving intervals be modelled. Experience shows that there is usually considerably heterogeneity in sighting probability related to factors such as age, sex, and reproductive status, and that such heterogeneity can change over time, such that the best model for sampling probability may contain many interaction terms. The popular practice of treating capture probabilities in different years as equal, whenever this yields a lower AIC, is discouraged, because it amounts to treating sample size as an index of relative abundance, without regard to sampling effort. This is inconsistent with the way the Committee normally considers abundance data.

Population models can be bulk models or individual-based, or hybrids between these. Individual-based models are in practice fitted using Bayesian methods and the result expressed as a posterior sample of population trajectories from which all quantities of interest can be computed. Prior distributions need to be chosen carefully so that posteriors for quantities of interest are valid and normalizable, and not unduly influenced by the priors, especially for small datasets. A method is proposed for defining implicit priors for sampling model parameters that ensures that the posteriors for biological quantities of interest, including population size, are independent of these. While a scale-invariant prior can be used for population size, the question of the appropriate priors for other biological parameters has not yet been definitively answered.

Verification of methods can involve substantial work. Testing methods by applying them to a limited suite of small test data sets is proposed as a simpler and quicker way to detect major problems.