Neutral-like abundance distributions in the presence of selection in a continuous fitness landscape

- Neutral theories yield realistic species abundance curves, but are incompatible with the known role of fitness differences in structuring communities.
- A “fitness gap” between the fittest species and all others leads to a single dominant species, inconsistent with the Fisher log-series.
- Models with a continuous fitness landscape yield neutral-like distributions, despite the presence of selection.
- This finding is robust to details of the landscape, and even applies to evolutionary games (e.g., the Hamilton-May model).
- Environmental noise transforms the decay of the species abundance curve at high abundances from exponential to power-law.

The neutral theory of biodiversity has successfully explained the observed composition of many ecological communities but it relies on strict demographic equivalence among species and provides no room for evolutionary processes such as selection and adaptation. Here we show how to embed the neutral theory within the Darwinian framework. In a continuous fitness landscape with a quadratic maximum, typical for quantitative traits, selection does restrict the extant species to have trait values close to optimal, but due to the continuous nature of the landscape, there are always many such species available, and so competition among them is effectively neutral. For sufficiently small mutational steps, the community structure fits perfectly to the Fisher log-series species abundance distribution. In general, the selection-mutation process, when superimposed on demographic and environmental noise, yields a small set of characteristic patterns for species abundance curves. A survey of these patterns is given.