Testing biological hypotheses in site occupancy models: a Bayesian approach

Jérôme Dupuis (1) , Jean Joachim (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 CEFS - Unité de recherche Comportement et Ecologie de la Faune Sauvage

The occupancy rate of a target species in a region divided in quadrats (or sites) is defined as the proportion of quadrats occupied by this species. This is a key quantity in site occupancy models which typically remains unknown after the data are collected, because the probability of detecting a target species in a given quadrat is < 1. Implementing tests on occupancy rates leads to a quite unusual situation, because an occupancy rate is not a statistical parameter, but a function of a discrete process partially observed. To deal with that difficulty, we adopt a Bayesian view within which the treatment of such tests turns out to be natural. We develop our approach for discrete-time site occupancy data, and we illustrate it by testing if the occupancy rate of a bird species increases over time (colonization test). A Bayesian model averaging is implemented to deal with the fact that several plausible models are viewed for the data at hand. We state a closed-form expression for the posterior probability of each model. The posterior probability of the null hypothesis (under a given model) is obtained by implementing a data augmentation algorithm. Finally, from a variety of examples, we show that the Bayesian methodology allows us to address a wide range of questions about occupancy.

Mots clés: Bayesian test; Colonization test; Data aumentation algorithm; Missing data model; Model averaging; Occupancy rates; Stability test

Domaines: Applications [stat.AP]

Jérôme Dupuis, Jean Joachim. Testing biological hypotheses in site occupancy models: a Bayesian approach. 2015. ⟨hal-01241022⟩