Nonlinear Crowding Effects in Cyclically Competing Ecological Communities

We consider cyclical ecological communities consisting of N species, where N = 1, 2 or 3. In classical models, intra-species competition, also known as the crowding effect, typically exhibits linear growth with population density. However, in more realistic ecological communities, crowding can deviate from this linear relationship, either growing faster than linear (F-community) or slower than linear (S-community). We develop a model that accounts for nonlinear crowding effects, which is applicable to both F and S communities. We demonstrate that faster crowding tends to promote coexistence, leading to increased biodiversity within the community. Conversely, slower crowding promotes single-species dominance, potentially leading to species exclusion. These distinctive outcomes arise across communities with N = 1, 2, 3 species.