Comparing maximum likelihood and Bayesian methods for fitting hidden Markov models to multi-state capture-recapture data of invasive carp in the Illinois River

Abstract

Background: Hidden Markov Models (HMMs) are often used to model multi-state capture-recapture data in ecology. However, a variety of HMM modeling approaches and software exist, including both maximum likelihood and Bayesian methods. The diversity of these methods obscures the underlying HMM and can exaggerate minor differences in parameterization. Methods: In this paper, we describe a general framework for modelling multi-state capture-recapture data via HMMs using both maximum likelihood and Bayesian methods. We then apply an HMM to invasive silver carp telemetry data from the Illinois River and compare the results estimated by both methods. Results: Our analysis demonstrates disadvantages of relying on a single approach and highlights insights obtained from implementing both methods together. While both methods often struggled to converge, our results show biologically informative priors for Bayesian methods and initial values for maximum likelihood methods can guide convergence toward realistic solutions. Incorporating prior knowledge of the system can successfully constrain estimation to biologically realistic movement and detection probabilities when dealing with sparse data. Conclusions: Biologically unrealistic estimates may be a sign of poor model convergence. In contrast, consistent convergence behavior across approaches can increase the credibility of a model. Estimates of movement probabilities can strongly influence the predicted population dynamics of a system. Therefore, thoroughly assessing results from HMMs is important when evaluating potential management strategies, particularly for invasive species.