Extinction and Extirpation Conditions in Coalescent and Ecotonal Metacommunities

Abstract: Here we present extinction, extirpation and coexistence conditions where / when two communities combine. We consider one specific model where two communities coalesce, and another model where the communities coexist side by side, blending in a transitionary zone called the ecotone. Specifically, (1) we analytically calculate the shifts in abundances as a function of mixing strength. (2) Obtain a critical value for the mixing strength leading to extinction. (3) Derive an inequality condition for full coexistent mixing. (4) find how the individual communities penetrate into one other as a function of mixing strength. (5) derive the conditions for one species to cross the ecotone and invade an neighboring community and (6) conditions for a native species to get extirpated. Lastly, (7) we spatially investigate the species richness within the ecotone and derive a condition that determines whether the ecotone will have higher or lower richness compared to its surrounding habitats.