Consequences of violating assumptions of integrated population models on parameter estimates

Abstract

While ecologists know that models require assumptions, the consequences of their violation become vague as model complexity increases. Integrated population models (IPMs) combine several datasets to inform a population model and to estimate survival and reproduction parameters jointly with higher precision than is possible using independent models. However, accuracy actually depends on an adequate fit of the model to datasets. We first investigated bias of parameters obtained from integrated population models when specific assumptions are violated. For instance, a model may assume that all females reproduce although there are non-breeding females in the population. Our second goal was to identify which diagnostic tests are sensitive to detect violations of the assumptions of IPMs. We simulated data mimicking a short- and a long-lived species under five scenarios in which a specific assumption is violated. For each simulated scenario, we fitted an IPM that violates the assumption (simple IPM) and an IPM that does not violate each specific assumption. We estimated bias and uncertainty of parameters and performed seven diagnostic tests to assess the fit of the models to the data. Our results show that the simple IPM was quite robust to violation of many assumptions and only resulted in small bias of the parameter estimates. Yet, the applied diagnostic tests were not sensitive to detect such small bias. The violation of some assumptions such as the absence of immigrants resulted in larger bias to which diagnostic tests were more sensitive. The parameters informed by the least amount of data were the most biased in all scenarios. We provide guidelines to identify misspecified models and to diagnose the assumption being violated. Simple models should often be sufficient to describe simple population dynamics, and when data are abundant, complex models accounting for specific processes will be able to shed light on specific biological questions.