Field evaluation of abundance estimates under binomial and multinomial N-mixture models

Assessing and modelling abundance from animal count data is a very common task in ecology and management. Detection is arguably never perfect, but modern hierarchical models can incorporate detection probability and yield abundance estimates that are corrected for imperfect detection. Two variants of these models rely on counts of unmarked individuals, or territories (binomial N-mixture models, or binmix), and on detection histories based on territory-mapping data (multinomial N-mixture models or multimix). However, calibration studies which evaluate these two N-mixture model approaches are needed. We analysed conventional territory-mapping data (three surveys in 2014 and four in 2015) using both binmix and multimix models to estimate abundance for two common avian cavity-nesting forest species (Great Tit Parus major and Eurasian Blue Tit Cyanistes caeruleus). In the same study area, we used two benchmarks: occupancy data from a dense nestbox scheme and total number of detected territories. To investigate variance in estimates due to the territory assignment, three independent ornithologists conducted territory assignments. Nestbox occupancy yields a minimum number of territories, as some natural cavities may have been used, and binmix model estimates were generally higher than this benchmark. Estimates using the multimix model were slightly more precise than binmix model estimates. Depending on the person assigning the territories, the multimix model estimates became quite different, either overestimating or underestimating the 'truth'. We conclude that N-mixture models estimated abundance reliably, even for our very small sample sizes. Territory-mapping counts depended on territory assignment and this carried over to estimates under the multimix model. This limitation has to be taken into account when abundance estimates are compared between sites or years. Whenever possible, accounting for such hidden heterogeneity in the raw data of bird surveys, via including a 'territory editor' factor, is recommended. Distributing the surveys randomly (in time and space) to editors may also alleviate this problem.