Abundance-based detectability in a spatially-explicit metapopulation: a case study on a vulnerable beetle species in hollow trees.

In many fragmented habitats, the detectability of a population in a habitat patch closely depends on the local abundance of individuals. However, metapopulation studies rarely connect abundance and detectability. We propose a framework for using abundance-based estimates of detectability in the analysis of a spatially-explicit stochastic patch occupancy model (SPOM). We illustrate our approach with the example of Tenebrio opacus, a beetle inhabiting hollows in old trees, and have based it on a 6-year monitoring programme of adult beetles in an area harbouring a high density of old oaks. We validated our abundance-based methodology by showing that the estimates of detectability were positively and significantly correlated with those obtained from presence/absence data (Pearson r = 0.54, p < 2E-16) in our study system. We further showed that the height of the hollow on the tree and the area of its entrance hole, the living status and girth of the host tree, and the time of survey significantly affected the detectability of beetle populations. Median detectability was 51% for one survey. The SPOM analysis revealed a high but heterogeneous extinction risk among trees, suggesting a metapopulation dynamics between the "classic" and "mainland-island" paradigms. However, it also indicated unexplained beetle colonization of trees in our study, despite the fact that we included limited detectability in our estimation procedure. This may have been due to the cryptic larval stage of T. opacus and may thus invalidate the use of a classic SPOM in our study system.