Hierarchical modelling and estimation of abundance and population trends in metapopulation designs


*Correspondence author. E-mail:,


1. Population assessment in changing environments is challenging because factors governing abundance may also affect detectability and thus bias observed counts. We describe a hierarchical modelling framework for estimating abundance corrected for detectability in metapopulation designs, where observations of ’individuals’ (e.g. territories) are replicated in space and time. We consider two classes of models; first, we regard the data as independent binomial counts and model abundance and detectability based on a product-binomial likelihood. Secondly, we use the more complex detection–non-detection data for each territory to form encounter history frequencies, and analyse the resulting multinomial/Poisson hierarchical model. Importantly, we extend both models to directly estimate population trends over multiple years. Our models correct for any time trends in detectability when assessing population trends in abundance.

2. We illustrate both models for a farmland and a woodland bird species, skylark Alauda arvensis and willow tit Parus montanus, by applying them to Swiss BBS data, where 268 1 km2 quadrats were surveyed two to three times during 1999–2003. We fit binomial and multinomial mixture models where log(abundance) depended on year, elevation, forest cover and transect route length, and logit(detection) on year, season and search effort.

3. Parameter estimates were very similar between models with confidence intervals overlapping for most parameters. Trend estimates were similar for skylark (−0.074 ± 0.041 vs. −0.047 ± 0.019) and willow tit (0.044 ± 0.046 vs. 0.047 ± 0.018). As expected, the multinomial model gave more precise estimates, but also yielded lower abundance estimates for the skylark. This may be due to effects of territory misclassification (lumping error), which do not affect the binomial model.

4. Both models appear useful for estimating abundance and population trends free from distortions by detectability in metapopulation designs with temporally replicated observations. The ability to obtain estimates of abundance and population trends that are unbiased with respect to any time trends in detectability ought to be a strong motivation for the collection of replicate observation data.