Theoretical models are useful to investigate the drivers of community dynamics. In the simplest case of neutral models, the events of death, birth and immigration of individuals are assumed to only depend on their abundance-thus, all types share the same parameters. The community level expectations arising from these simple models and their agreement to empirical data have been discussed extensively, often suggesting that in nature, rates might indeed be neutral or their differences might not be important. However, how robust are these model predictions to type-specific rates? Also, what are the consequences at the level of types? Here, we address these questions moving from simple neutral communities to heterogeneous communities. For this, we build a model where types are differently adapted to the environment. We compute the equilibrium distribution of the abundances. Then, we look into the occurrence-abundance pattern often reported in microbial communities. We observe that large immigration and biodiversity-common in microbial systems-lead to such patterns, regardless of whether the rates are neutral or non-neutral. We conclude by discussing the implications to interpret and test empirical data.
Keywords: biodiversity; ecology; mathematical model; migration; neutral theory; niche theory.