Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others. In neutral models of biodiversity all populations are assumed to change incrementally due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by abrupt and severe reduction in size of the population of a single species freeing up resources for the remaining ones. This mechanism may be relevant e.g. for communities of bacteria, with strain-specific collapses caused e.g. by invading bacteriophages, or for other ecosystems where infectious diseases play an important role. The emergent dynamics of our system is characterized by cyclic ''diversity waves'' triggered by collapses of globally dominating populations. The population diversity peaks at the beginning of each wave and exponentially decreases afterwards. Species abundances have bimodal time-aggregated distribution with the lower peak formed by populations of recently collapsed or newly introduced species while the upper peak -species that has not yet collapsed in the current wave. In most waves both upper and lower peaks are composed of several smaller peaks. This self-organized hierarchical peak structure has a long-term memory transmitted across several waves. It gives rise to a scale-free tail of the time-aggregated population distribution with a universal exponent of 1.7. We show that diversity wave dynamics is robust with respect to variations in the rules of our model such as diffusion between multiple environments, species-specific growth and extinction rates, and bet-hedging strategies.
Author SummaryThe rate of unlimited exponential growth is traditionally used to quantify fitness of species or success of organizations in biological and economic context respectively. However, even modest population growth quickly saturates any environment. Subsequent resource redistribution between the surviving populations is assumed to be driven by incremental Data Availability Statement: All relevant data are within the paper and its Supporting Information files.Funding: Work at Brookhaven was supported by grants PM-031 from the Office of Biological Research of the U.S. Department of Energy. Work at Copenhagen was supported by Danish National Research Foundation. The funders played no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.Competing Interests: The authors have declared that no competing interests exist.changes due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by sudden and severe collapses of entire populations freeing up resources for the growth of others. The emergent property of this type of dynamics are cyclic "diversity waves" each triggered by a collapse of the globally dominating population. Gradual extinctions of species...