No effect of model distribution on long-term trends, even with underdispersion

Abstract

While many studies have illustrated the decline of animal populations—particularly of farmland birds—the statistical analyses, design, and protocols used have raised some concerns and criticism. Using a 27-year dataset (1996–2022) based on recording the number of skylarks (Alauda arvensis) at 160 longitudinal count points, our study confronts two approaches commonly used to model long-term trends. The first uses a single model (based on a priori ecological knowledge), while the second is an a posteriori approach that relies on a multi-model selection among candidate models that account for probability distributions to describe the error structure. Here we investigate whether the statistical distribution of modelled variables and the method of including covariates in the model affect trend estimates. With a large amount of data and in the case of underdispersion, we found that the model distribution used had no impact on the estimation of the long-term trend. Moreover, adding confounding covariates did not change or improve the trend estimation, at least when data were obtained from a well-designed protocol (our case). In contrast to other studies reporting an effect of the model's distribution on long-term trends, especially in the presence of overdispersion, our results offer a new perspective on the presence of underdispersion, where simple models perform equally well as complex ones. Further research is now needed on multiple species data or on smaller data sets to check the generality of our findings.