Modeling Survival and Testing Biological Hypotheses Using Marked Animals: A Unified Approach with Case Studies

Abstract

The understanding of the dynamics of animal populations and of related ecological and evolutionary issues frequently depends on a direct analysis of life history parameters. For instance, examination of trade—offs between reproduction and survival usually rely on individually marked animals, for which the exact time of death is most often unknown, because marked individuals cannot be followed closely through time. Thus, the quantitative analysis of survival studies and experiments must be based on capture—recapture (or resighting) models which consider, besides the parameters of primary interest, recapture or resighting rates that are nuisance parameters. Capture—recapture models oriented to estimation of survival rates are the result of a recent change in emphasis from earlier approaches in which population size was the most important parameter, survival rates having been first introduced as nuisance parameters. This emphasis on survival rates in capture—recapture models developed rapidly in the 1980s and used as a basic structure the Cormack—Jolly—Seber survival model applied to an homogeneous group of animals, with various kinds of constraints on the model parameters. These approaches are conditional on first captures; hence they do not attempt to model the initial capture of unmarked animals as functions of population abundance in addition to survival and capture probabilities. This paper synthesizes, using a common framework, these recent developments together with new ones, with an emphasis on flexibility in modeling, model selection, and the analysis of multiple data sets. The effects on survival and capture rates of time, age, and categorical variables characterizing the individuals (e.g., sex) can be considered, as well as interactions between such effects. This "analysis of variance" philosophy emphasizes the structure of the survival and capture process rather than the technical characteristics of any particular model. The flexible array of models encompassed in this synthesis uses a common notation. As a result of the great level of flexibility and relevance achieved, the focus is changed from fitting a particular model to model building and model selection. The following procedure is recommended: (1) start from a global model compatible with the biology of the species studied and with the design of the study, and assess its fit; (2) select a more parsimonious model using Akaike's Information Criterion to limit the number of formal tests; (3) test for the most important biological questions by comparing this model with neighboring ones using likelihood ratio tests; and (4) obtain maximum likelihood estimates of model parameters with estimates of precision. Computer software is critical, as few of the models now available have parameter estimators that are in closed form. A comprehensive table of existing computer software is provided. We used RELEASE for data summary and goodness—of—fit tests and SURGE for iterative model fitting and the computation of likelihood ratio tests. Five increasingly complex examples are given to illustrate the theory. The first, using two data sets on the European Dipper (Cinclus cinclus), tests for sex—specific parameters, explores a model with time—dependent survival rates, and finally uses a priori information to model survival allowing for an environmental variable. The second uses data on two colonies of the Swift (Apus apus), and shows how interaction terms can be modeled and assessed and how survival and recapture rates sometimes partly counterbalance each other. The third shows complex variation in survival rates across sexes and age classes in the roe deer (Capreolus capreolus), with a test of density dependence in annual survival rates. The fourth is an example of experimental density manipulation using the common lizard (Lacerta vivipara). The last example attempts to examine a large and complex data set on the Greater Flamingo (Phoenicopterus ruber), where parameters are age specific, survival is a function of an environmental variable, and an age × year interaction term is important. Heterogeneity seems present in this example and cannot be adequately modeled with existing theory. The discussion presents a summary of the paradigm we recommend and details issues in model selection and design, and foreseeable future developments.