"Two Stories of Stability and Structure in Ecological Communities"Haas, PierreStable coexistence of species in complex ecological communities results from the conspiracy of different biological structures or structures of the network of species interactions. In this talk, I will give two examples of minimal models that elucidate fundamental constraints on stability of coexistence that arise from such structures. In the first part of the talk, I will consider phenotypic switching as an example of such a biological structure, and analyse a minimal model of the competition of two species in which one species switches, both stochastically and in response to the other species, to a phenotype resilient to competition [1]. Combining exact and numerical results, I will reveal the mechanism by which responsive switching can stabilise coexistence even when stochastic switching on its own has no effect on stability. In the second part of the talk, I will turn to the effect of the network of competitive, mutualistic, and predator-prey interactions on stability of coexistence [2]. I will show that the possibility of stable coexistence in ecologies with Lotka-Volterra interactions is determined completely by "irreducible ecologies", and I will reveal how exhaustive analysis of all such interaction networks of N<6 species suggests that, strikingly, these irreducible ecologies form an exponentially small subset of all ecologies, as do the mathematically curious "impossible ecologies" in which stable coexistence is non-trivially impossible. [1] Haas, Gutierrez, Oliveira, and Goldstein, Phys. Rev. Res. 4, 033224 (2022) [2] Meng, Horvát, Modes, Haas, arXiv:2309.16261 |
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