Qualitative and quantitative responses to press perturbations in ecological networks

Predicting the sign of press perturbation responses in ecological networks is challenging, due to the poor knowledge of the strength of the direct interactions among the species, and to the entangled coexistence of direct and indirect effects. We show in this paper that, for a class of networks that includes mutualistic and monotone networks, the sign of press perturbation responses can be qualitatively determined based only on the sign pattern of the community matrix, without any knowledge of parameter values. For other classes of networks, we show that a semi-qualitative approach yields sufficient conditions for community matrices with a given sign pattern to exhibit mutualistic responses to press perturbations; quantitative conditions can be provided as well for community matrices that are eventually nonnegative. We also present a computational test that can be applied to any class of networks so as to check whether the sign of the responses to press perturbations is constant in spite of parameter variations.