Selecting age structure in integrated population models

Integrated population modelling is widely used in ecology when data at the individual level are combined with independent time series measuring population abundance. However there is no formal assessment of how to select the best integrated model. Here we focus on the important case of determining the age-structure for annual survival probabilities of wild animals, involving comparing state-space models with different numbers of states. The work is motivated by real data sets, and evaluated by simulation. We reject the naive use of AIC, and advocate the use of likelihood-ratio tests, based on combined data. We demonstrate using simulation that typical asymptotic chi-square distributions of likelihood-ratio test statistics to compare integrated models apply when the corresponding state-space models have the same state variables. In addition, for linear state- space models with matching initial conditions the correct chi-square distributions may also hold when models apparently have different state-spaces. The results for comparing integrated models also have relevance for state-space modelling alone. A senescence case study is provided which incorporates a step-up approach and illustrates the use of the recommendations of the paper in practice.

Automated summary

Integrated population modelling is a widely used method in ecology, but there is a lack of formal assessment on selecting the best model. This study focuses on determining the age-structure for annual survival probabilities of wild animals using state-space models with different numbers of states. The authors reject the naive use of AIC and suggest using likelihood-ratio tests based on combined data. Simulation results show that the asymptotic chi-square distribution can be applied to compare integrated models when they have the same state variables.