Abstract
Ecosystem stability is a central question both in theoretical and applied biology. Dynamical systems theory can be used to analyze how growth rates, carrying capacities, and patterns of species interactions affect the stability of an ecosystem. The response to increasing complexity has been extensively studied and the general conclusion is that there is a limit. While there is a complexity limit to stability at which global destabilisation occurs, the collapse rarely happens suddenly if a system is fully viable (no species is extinct). In fact, when complexity is successively increased, we find that the generic response is to go through multiple single-species extinctions before a global collapse. In this paper we demonstrate this finding via both numerical simulations and elaborations of theoretical predictions. We explore more biological interaction patterns, and, perhaps most importantly, we show that constrained interaction structures-a constant row sum in the interaction matrix-prevent extinctions from occurring. This makes an ecosystem more robust in terms of allowed complexity, but it also means singles-species extinctions do not precede or signal collapse-a drastically different behavior compared to the generic and commonly assumed case. We further argue that this constrained interaction structure-limiting the total interactions for each species-is biologically plausible.
Highlights
In theoretical studies of ecosystem stability, dynamical systems are often used
In our previously published work, we showed that this is the generic behavior of systems with random interaction structures, we updated the complexity limit for destabilization/collapse, and we introduced a limit beyond which systems can no longer be feasible [25]
Some previous studies have found that more symmetric interaction matrices can be stabilizing, we find that symmetry acts to destabilize generalized Lotka-Volterra (GLV)-type models [26]
Summary
In theoretical studies of ecosystem stability, dynamical systems are often used. These models were initially extended from a few species [1,2] to whole ecosystems by using random matrices to represent the interaction network among species. In our previously published work, we showed that this is the generic behavior of systems with random interaction structures, we updated the complexity limit for destabilization/collapse, and we introduced a limit beyond which systems can no longer be feasible [25]. This picture substantially changes both the prediction of a system’s response to perturbations as well as approach to collapse. Collapse? To answer this, we begin with an elaboration of our previous derivation of the extinction boundary
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