Coexistence, crossover and extirpation in coalescent communities and ecotones

When two ecological communities come into contact, the strength of their mixing determines whether species coexist, extirpate, or extend their ranges. We present analytical formulas and simulations describing these transitions. Specifically, we derive abundance shifts upon community coalescence, identify the critical mixing strength leading to first extinctions, establish an inequality condition guaranteeing coexistence, quantify how species ranges and penetration depths change with mixing rate, predict the threshold for species to cross an ecotone boundary, describe the conditions for native species extirpation, and derive when ecotones exhibit higher or lower richness than adjacent habitats. Our analysis, validated by numerical simulations, shows that species richness decreases with increasing homogenization and that our coexistence condition accurately predicts persistence. These results connect metacommunity theory with spatial coexistence mechanisms and provide measurable predictions for microbial and landscape ecotones.