Bayesian inference and model choice for Holling’s disc equation: a case study on an insect predator-prey system

Abstract

The dynamics of predator-prey systems relate strongly to the density (in)dependent attributes of the predator’s feeding rate, i.e., its functional response. The outcome of functional response models is often used in theoretical or applied ecology in order to extract information about the mechanisms associated with the feeding behavior of predators. The focus of this study centres upon Holling’s type II functional response model, commonly known as the disc equation, which describes an inverse-density dependent mortality caused by a single predator to its prey. A common method to provide inference on functional response data involves nonlinear least squares optimization, assuming independent Gaussian errors, an assumption often violated in practice due to the heteroscedasticity which is typically present in the data. Moreover, as prey depletion is common in functional response experiments, the differential form of disc equation ought to be used in principle. We introduce a related statistical model and adopt a Bayesian approach for estimating parameters in ordinary differential equation models. In addition, we explore model uncertainty via Bayes factors. Our approach is illustrated via the analysis of several data sets concerning the functional response of a widespread ladybird beetle (Propylea quatuordecimpunctata) to its prey (Aphis fabae), predicting the efficiency of this predator on a common and important aphid species. The results showed that the approach developed in this study is towards a direction for accurate estimation of the parameters that determine the shape of the functional response of a predator without having to make unnecessary assumptions. The R (www.r-project.org) code for fitting the proposed model to experimental data is made freely available.