Heterogeneity in song rates in the Collared Flycatcher (Ficedula albicollis) explained with the availability parameter in generalized N-mixture models: Its importance for abundance estimates in avian aural counts

Binomial N-mixture models are commonly applied to estimate abundance unaffected by imperfect detection, but are known to be sensitive to violations of assumptions. One of the model's assumptions, the independence of detections has rarely been tested. It requires that during a survey, detection of one individual does not affect detection of another individual. This assumption can be frequently violated in passerine birds, which exhibit territorial behaviour by singing, since neighbouring individuals are likely to motivate each other to vocalize, leading to non-independence in singing activity and in the following detection rate. Here, we explored this phenomenon with the generalized, binomial version of the N-mixture model, where detection probability is decomposed into availability probability φ – which can be interpreted as per capita song rate or the probability of vocalising – and actual detection probability p, given vocalisations take place. Using repeated counts of the Collared Flycatcher (Ficedula albicollis) as a case study, and treating the maximum observed counts C at a site i as an explanatory covariate for φ, we showed that per capita song rates increased with observed counts at a site. Hence, if song rates vary due to local abundance, including C as an explanatory variable for song rate addressed with φ, helps to explain this variation (which otherwise goes undetected) and improves inferences under the model. This had strong effects on the resulting abundance estimates: if this relationship was ignored in the models, total estimated population sizes were consequently lower by as much as 22–27%, compared to when this effect was included. Since it is likely that song rates may commonly be density-dependent in birds manifesting territorial behaviours by singing, further tests addressing violations of independence assumptions in these models are needed. As suggested by Kéry and Royle (2016), despite some form of circularity likely being involved, modelling heterogeneity in the detection process with the help of C in standard N-mixture models (which, given availability, conflate availability with detection in a single parameter) should be applicable as well.