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

Abstract

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.

Improving estimates of population status and trend with superensemble models

“…Although there are options to account for potential model misspecification in determination of species risk (e.g. coefficient averaging, Burnham & Anderson, 2002; generalized modelling, Yeakel, Stiefs, Novak, & Gross, 2011; or semiparametric methods, Thorson, Ono, & Munch, 2014), ensemble methods are a relatively simple way to combine predictions in a transparent manner. Beyond estimates of status and trend, ensemble methods could be used, for example, to increase the robustness of spatial predictions when designing networks of protected areas (Rassweiler, Costello, Hilborn, & Siegel, 2014) or to forecast potential spatial shifts in species distribution given climate impacts (Harsch, Zhou, HilleRisLambers, & Kot, 2014).…”

Forecast skill for predicting distribution shifts: A retrospective experiment for marine fishes in the Eastern Bering Sea

“…The latter includes both non‐parametric components and a parametric effect of temperature. I therefore follow previous studies in calling it a “semiparametric” forecast model (Shelton, Thorson, Ward, & Feist, ; Sugeno & Munch, ; Thorson, Ono, & Munch, ). I fit this model using package VAST (https://github.com/James-Thorson/VAST) in the R statistical environment (R Core Team ).…”

Estimating fisheries reference points from catch and resilience

“…The BSM was implemented as a Bayesian statespace estimation model Millar and Meyer 1999), which allowed accounting for variability in both population dynamics (process error) and measurement and sampling (observation error) (Thorson et al 2014).…”

“…Secondly, key parameters such as the natural mortality or the steepness of the assumed spawner-recruitment relationship are often fixed or heavily constrained, due to limited information in the available data (Lee et al 2011(Lee et al , 2012. By comparison, CMSY admits broad uncertainty in resilience and productivity and may therefore be more robust to model misspecifications (Thorson et al 2014). By comparison, CMSY admits broad uncertainty in resilience and productivity and may therefore be more robust to model misspecifications (Thorson et al 2014).…”