Ecological resilience in a circular world: Mutation and extinction in five-species ecosystems

In an ecosystem comprising coexisting species, mutations frequently occur. These mutations can be induced by various factors such as errors in DNA replication and exposure to chemicals. They constitute an intrinsic element of species evolution. This study investigates the impact of mutations on ecosystems, employing Gillespie simulations and the formulation of the First-passage extinction problem to assess their effects and examine extinction events. Our findings suggest first-extinction time and state distribution in a system with mutation follows intriguing behavior which promotes co-existence. There also exists a depression in the state space post which mutation extends the first-extinction time. Moreover, a system devoid of mutation exhibits a discernible inclination towards probabilities that lean in the direction of an endangered state space.