Feasibility and stability of large ecosystems
The stability of large ecosystems has been a longstanding problem in ecology. Since the seminal work by May we have tools and methods to study local asymptotic stability in terms of random matrices. In particular we know how stability scales with diversity and complexity and that they are in a inverse relation. This approach has been generalized to study the effect of different interaction types, making possible to identify which properties of interaction strengths are responsible for stability. Recent results
have also been able to include relevant aspects of the structure of empirical interaction networks.
Stability is related to perturbation of population abundances, while feasibility (and structural stability) is related to perturbations of growth rates and to the volume of the domain of growth rates leading to positive population.
Feasibility and stability, are different but not independent properties. Using new computational methods, we are able possible to determine feasibility for large ecosystems. In this talk I will show how feasibility scales with diversity and complexity for different interaction types. Moreover we address the connection between feasibility and stability, showing that simple relations hold. For instance the two quantities turns out to be equivalent for large mutualistic systems.
We introduce a new measure able to incorporate the probability of extinction given a perturbation of the growth rates. This quantity turns out to be in a very simple relation with local asymptotic stability, showing a beautiful and unexpected connection with the classical result of May.