"Chaotic turnover in a model of strongly interacting species"De Monte, SilviaMicrobial communities harbour hundreds or thousands of species, whose ecological dynamics is classically modelled by generalized Lotka-Volterra equations. In the absence of information about the structure of the community, interactions are typically chosen randomly and resumed in their statistics: the mean and the variance. The dynamical phases of such equations when 'weak' interactions scale with the number of species revealed the existence of a phase where species coexistence occurs out of equilibrium. In this work, we have addressed the 'strong' interactions regime - where competition makes only a handful of species dominate the community - and with immigration - that prevents extinctions. We show that, at any time, the low-dimensional dominant community coexists with a majority of 'rare' species, whose abundance decreases as a power law of exponent larger than 1 - as observed in plankton communities. Over time, the dominant community is regularly superseded by a subset of rare species, in a continuous chaotic turnover of species akin to observed fluctuations of plankton strains. Every species undergoes a boom-bust, intermittent dynamics that brings it - with variable frequency - to partake of the dominant sub-community. We propose an approximate 'focal species' model with multiplicative, correlated noise that captures the common features of every species' dynamic. We show that this model, parametrized on the time series of one species, predicts the dependence of the power-law decay exponent on the interaction statistics, and connects the microscopic and macroscopic description of the population. Moreover, we discuss how, in any community with a large but finite richness, species differ from one another in their dynamics. |
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