Estimating the density dependence of stage-specific survival and fecundity using Integrated Population Models

Christie Le Coeur , Marcel E. Visser , Frédéric Barraquand

The density dependence of survival and reproduction parameters can change with age or stage, which is key to understand population regulation mechanisms. However, the multiplication of parameters in structured demographic models makes their estimation challenging. Integrated population models (IPMs) provide an interesting solution to this issue by combining different data sources. IPM simulation studies have so far shown reliable estimates of density dependence in two-stage models, but little is known about estimation quality in more complex demographic models. Here, we used simulations to assess the bias and precision of density dependence estimates in three- and four-stage models, motivated by the life history of the great tit (Parus major) and a 52-year population survey. Specifically, we examined the effects of study duration (15, 30 or 50 years, on both simulated and real data), strength of density dependence, number of density-dependent parameters, temporal trend, and model structure (three versus four stages). Overall, IPMs estimated the strength of density dependence with no to little bias, but with low precision, especially when some stages were density-independent. Estimation performance improved naturally with increasing study duration, but reliable estimates were obtained starting at 30-year monitoring despite the multiplicity of data sources, suggesting simpler stage structures for shorter durations. We also show that density-dependence was easier to detect in stable and increasing populations than in declining populations. These findings highlight the value of IPMs for assessing density dependence in structured populations, while emphasizing the need for careful model choice and interpretation given available data.