Exploring the structural sensitivity in some spatially-explicit models of ecological dynamics

Mathematical models are frequently used to infer predictions about population dynamics in real ecosystems. However, parametrization of intra- and interspecific interactions is usually approximate, as the amount and quality of ecological information is never sufficient to make a ‘precise’ decision about the mathematical function(s) to use. The question therefore arises as to how sensitive the model properties can be with regard to the choice of the function - the problem known as “structural sensitivity”. In this article, we explore the structural sensitivity of a predator–prey model with additive Allee effect in prey growth and density-dependent death rate for predator. We test the sensitivity of both temporal (non-spatial) and spatiotemporal (spatially-explicit) models using three qualitatively similar but numerically different parametrizations of the predator functional response, such as Holling type II (fraction-linear), Ivlev (exponential) and hyperbolic (trigonometric) functions. Using an array of the analytical and numerical tools, we show that both the temporal and spatiotemporal dynamics can be qualitatively different for the three chosen parametrizations. Also, our study clearly reveals that any hierarchical ranking of these parametrizations according to their destabilizing potential is not possible.