MathDBPersistence threshold conjecture for species and environments
Persistence threshold conjecture for species and environments
Consider the Moran model with a finite set of species and a finite set of environments. Persistence means that the system persists rather than becoming extinct.
Persistence threshold conjecture. Persistence of the system is possible if and only if the number of environments is at least the number of species.
The paper states that this assertion has been proved for systems with two or three species, while configurations with three species and three environments can exhibit persistence. Explicit conditions for persistence in general remain unknown.
Sources & referencesView supporting material
Primary source
Arnaud Guillin, Arnaud Personne and Edouard Strickler, “Persistence in the Moran model with random switching”, arXiv:1911.01108 (2019).
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