Estimating the strength of density dependence in the presence of observation errors using integrated population models

Assessing the strength of density dependence is crucial for understanding population dynamics, but its estimation is difficult. Because estimates of population size and demographic parameters usually include errors due to imperfect detection, estimations of the strength of density dependence will be biased if obtained with conventional methods and lack statistical power to detect density dependence. We propose a Bayesian integrated population model to study density dependence. The model allows assessing the effect of density both on the population growth rate as well as the demographic parameters while accounting for imperfect detection. We studied the performance of this model using simulation and illustrate its use with data on red-backed shrikes Lanius collurio. Our simulation results showed that the strength of density dependence is identifiable and it was estimated with higher precision using the integrated population model than the conventional regression model. As expected, the conventional regression model tended to overestimate density dependence at the population level whereas underestimates at the demographic level, but the bias was small. The analysis of the red-backed shrike data revealed negative density dependence at the population level most likely mediated by a density-dependent decline in adult survival. This work highlights the potential of integrated population models in assessing density dependence and its practical application in population studies.