Importance sampling and Bayesian model comparison in ecology and evolution

Bayesian approaches to the modelling of ecological systems are increasingly popular, but there are competing methods for formal model comparisons. Here, we focus on the task of performing multimodel inference through estimating posterior model weights, which encompasses uncertainties in the choice of competing model structure into the inference outputs.Model-based approaches such as reversible-jump Markov chain Monte Carlo (RJ-MCMC) are flexible and allow multimodel inference, but can be complex to implement and optimise, and so we translate a model-based approach for ecological applications using Importance Sampling to estimate the marginal likelihood of the data given a particular model. This approach allows for model comparison through the estimation of Bayes' Factors or interpretable posterior model probabilities, yielding model weights that facilitate multimodel inference through Bayesian model averaging.We demonstrate Importance Sampling with two case study investigations in animal demography: censused analysis of banded mongoose (Mungos mungo) survival where missing data are uncommon, and capture-mark-recapture analysis of European badger (Meles meles) survival where data are commonly missing.We compare outcomes of the model comparison using the Importance Sampling approach to those obtained through single-model inference approaches using Deviance information criteria and the Watanabe-Akaike information criteria. The results of the Importance Sampling method aligns with RJ-MCMC model comparisons while often being more straightforward to fit and optimise, particularly if the competing models are non-nested.