A Bayesian approach to identifying and compensating for model misspecification in population models

State-space estimation methods are increasingly used in ecology to estimate productivity and abundance of natural populations while accounting for variability in both population dynamics and measurement processes. However, functional forms for population dynamics and density dependence often will not match the true biological process, and this may degrade the performance of state-space methods. We therefore developed a Bayesian semiparametric state-space model, which uses a Gaussian process (GP) to approximate the population growth function. This offers two benefits for population modeling. First, it allows data to update a specified "prior" on the population growth function, while reverting to this prior when data are uninformative. Second, it allows variability in population dynamics to be decomposed into random errors around the population growth function ("process error") and errors due to the mismatch between the specified prior and estimated growth function ("model error"). We used simulation modeling to illustrate the utility of GP methods in state-space population dynamics models. Results confirmed that the GP model performs similarly to a conventional state-space model when either (1) the prior matches the true process or (2) data are relatively uninformative. However, GP methods improve estimates of the population growth function when the function is misspecified. Results also demonstrated that the estimated magnitude of "model error" can be used to distinguish cases of model misspecification. We conclude with a discussion of the prospects for GP methods in other state-space models, including age and length-structured, meta-analytic, and individual-movement models.