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
collapses of the entire 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 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 are characterized by a 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.Comment: 15 pages (including SI), 6 figures + 7 supplementary figure