Assessing the effect of density on population growth when modeling individual encounter data.

The relative role of density-dependent and density-independent variation in vital rates and population size remains largely unsolved. Despite its importance to the theory and application of population ecology, and to conservation biology, quantifying the role and strength of density dependence is particularly challenging. We present a hierarchical formulation of the temporal symmetry approach, also known as the Pradel model, that permits estimation of the strength of density dependence from capture-mark-reencounter data. A measure of relative population size is built in the model and serves to detect density dependence directly on population growth rate. The model is also extended to account for temporal random variability in demographic rates, allowing estimation of the temporal variance of population growth rate unexplained by density dependence. We thus present a model-based approach that enable to test and quantify the effect of density-dependent and density-independent factors affecting population fluctuations in a single modeling framework. More generally, we use this modeling framework along with simulated and empirical data to show the value of including density dependence when modeling individual encounter data without the need for auxiliary data.