The effect of fitness differences in death-birth models with immigration

Mathematical models have been instrumental in understanding the dynamics of ecological systems. Notable examples are models where the events of death, birth, and migration of individuals within a community only depend on their abundance. In other words, rates are equal regardless of the specific population.The proven utility of such models, used from gut microbiomes to forests, lies in their capacity to contrast experimental data to a 'neutral' prediction. Surprisingly, such predictions often agree with experimental data, indicating that population-specific rates might be absent or at most irrelevant.But what if, instead, rates are assumed to be population-specific in these models? What patterns emerge? How resilient are the neutral community patterns? Our work addresses these questions incrementally, going from simple to many-populations communities. We focus on changes in various community composition indicators, specifically, on the occurrence-abundance pattern and how to identify 'non-neutrality' in data.