Spatio-temporal pattern formation under varying functional response parametrizations

The limited availability of detailed ecological data introduces uncertainty in model predictions and constrains efforts to enhance the predictive power and robustness of nonlinear population dynamics models. While carefully chosen parameter values may yield a good fit to available datasets, alternative mathematical formulations of key component functions can sometimes provide an even better fit. The study of uncertainty in model predictions arising from such alternative formulations of component functions, such as those describing predation, is referred to as the study of structural sensitivity. In this work, we extend the concept of structural sensitivity to spatio-temporal ecological systems. We analytically derive parametric conditions that capture all possible cases for the number of homogeneous steady states, provide criteria for local bifurcations, and establish conditions for the existence or non-existence of spatially heterogeneous steady states, as well as for Turing instability, all expressed in terms of a generalized functional response. Numerical simulations using two ecologically well-established functional responses validate our analytical results and emphasize the importance of carefully selecting the mathematical formulation when modeling predator-prey interactions.