Structural sensitivity and resilience in a predator–prey model with density-dependent mortality
C. Aldebert, D. Nerini, M. Gauduchon and J.C. Poggiale
Ecological Complexity 28, 163-173, 2016
Numerous formulations with the same mathematical properties can be relevant to model a biological process. Different formulations can predict different model dynamics like equilibrium vs. oscillations even if they are quantitatively close (structural sensitivity). The question we address in this paper is: does the choice of a formulation affect predictions on the number of stable states? We focus on a predator–prey model with predator competition that exhibits multiple stable states. A bifurcation analysis is realized with respect to prey carrying capacity and species body mass ratio within range of values found in food web models. Bifurcation diagrams built for two type-II functional responses are different in two ways. First, the kind of stable state (equilibrium vs. oscillations) is different for 26.0–49.4% of the parameter values, depending on the parameter space investigated. Using generalized modelling, we highlight the role of functional response slope in this difference. Secondly, the number of stable states is higher with Ivlev's functional response for 0.1–14.3% of the parameter values. These two changes interact to create different model predictions if a parameter value or a state variable is altered. In these two examples of disturbance, Holling's disc equation predicts a higher system resilience. Indeed, Ivlev's functional response predicts that disturbance may trap the system into an alternative stable state that can be escaped from only by a larger alteration (hysteresis phenomena). Two questions arise from this work: (i) how much complex ecological models can be affected by this sensitivity to model formulation? and (ii) how to deal with these uncertainties in model predictions?