The distribution of the species abundances (SAD) changes during ecological succession. While present theories have successfully predicted patterns in SADs of many static systems, it is less known how the shape of SAD evolves before it reaches equilibrium. Moreover, most theories of SADs are not based on mechanistic models of population dynamics. Our objective is to develop a fundamental theory that predicts dynamic SADs, by combining trait-based Lotka-Volterra (LV) competition with immigration from regional species pool. Intrinsic growth rate and immigration rate of each species are functions of a trait variable so that the shape of SAD is determined by those functional forms. Exact solutions of the model cannot be derived analytically, so we use both analytical approximations and numerical solution. We test our theory using a microcosm experiment with phytoplankton communities (24 species) across a range of temperatures.
Our results show that there are three distinct phases of community succession: 1) an early phase dominated by exponential growth, 2) a middle phase of species sorting, and 3) a long-term equilibrium phase. In the early phase, SADs are determined by the distribution of growth rates and maintain a fixed shape with increasing mean and variance. In the middle phase, the community is increasingly dominated by a single best-adapted species. In the absence of immigration, the long-term equilibrium phase is characterized by low diversity. With immigration, the abundances of many rare species are determined by the balance of exclusion and immigration. In our theory, SADs can be determined from trait-abundance distributions (TADs). Likelihood fitting of theoretical SADs shows that different conditions of the experiment can be consistent with the different model forms and their parameters.