Methods for comparing theoretical models parameterized with field data using biological criteria and Sobol analysis

Abstract

Prey–predator models are frequently developed to investigate trophic webs and to predict the population dynamics of prey and predators. However, the parameters of these models are often implemented without empirical data and may even be chosen arbitrarily. Commonly, only a few parameters are tested regarding their sensitivity and it is rare to read about the comparison between different prey–predator models (i.e. predation function structure). Here, we propose a method to compare four prey–predator models designed for two populations. We then apply this method to select the more biologically plausible one to model a simplified agricultural trophic system, including one predator compartment (the red fox Vulpes vulpes) and one prey group compartment (small mammals). These models are based on four Holling functional responses for the predation interaction and take the prey intrinsic growth rate into account through a Verhulst logistic function. Most parameters’ values (like attack rates or growth rates) were calculated from field data or based on literature review. We then used Sobol indices to conduct parameter exploration around mean parameter values to investigate and compare the model dynamics responses. Our first results showed that under our assumptions, the two most relevant models for our case study are the saturated Holling I and II models. We were also able to discriminate that among the 6 scaled parameters that vary, the model outputs are particularly sensitive to four of them (κ: saturation rate of the environment, Tr1: characteristic intrinsic decay time of the predators, Tc: characteristic growth time of the predator via the predation on the prey and λ: saturation rate of a predator’s stomach per time unit) and much less sensitive to two others (Tr2: characteristic intrinsic growth time of the prey and Ta: characteristic decay time of the prey due to the predation). These first encouraging results open the way for the next step, which will be to adapt this model construction to more complex prey–predator systems, with several predator and/or several prey compartments.