A probabilistic perspective of the multi-species competition model

Background/Question/Methods

The understanding of large ecosystems represents an important challenge in theoretical ecology. The complexity of these systems makes it necessary to use mathematical modeling. Introduced and analyzed by Tilman, the multi-species competition model represents a system of species competing for a set of habitat patches. In this model, the competition is hierarchical: the dynamics of each species' occurrences within the metacommunity depends mainly on its colonization rate and its extinction rate. For a better understanding of the restrictions induced on the colonization rate in a large-dimension system, we propose a probabilistic interpretation of the model by looking at colonization parameters following a given probability distribution.Our aim is to determine the law maximising the coexistence between the species. Based on this information, we can identify the spatial distribution of species and the assembly process of the ecosystem. To answer this question, we first carried out analytical and simulation-based work to investigate the optimal distribution, persistence and stability. Second, we analyzed two different types of assembly processes: a "top-down approach" starting from a pool of species by letting the dynamics elapse, and a "bottom-up approach" developing an invasion sequence that involves a historical contingency effect.

Results/Conclusions

The multi-species competition model represents a first step in our understanding of species-rich metacommunities. From a mathematical point of view, we find information on the stability and persistence of the model allowing the whole or a sub-population of species to coexist. We continue this investigation by providing insights into the shape of the distribution of the colonization rate: the heavier the distribution tail, the higher the probability of coexistence. Subsequently, the comparison of the two assembly processes shows us that the bottom-up approach seems to be much more restrictive in terms of the number of surviving species due to historical contingencies and cascade extinctions.To conclude, this probabilistic perspective of the multi-species competition model allows to put forward and compare two different types of distinct assemblages which converge towards a similar final result: the colonization rate of the different species must follow a fat-tail distribution for many species to coexist under the competition-colonization trade-off.