Speciation in a MacArthur model predicts growth, stability and adaptation in ecosystems dynamics.

Ecosystems dynamics is often considered as a coupling of resource consumption by species that evolve in size. Such resource-population dynamics is captured by MacArthur-type models. One biologically relevant feature that needs to be captured by such models is the introduction of new and different species. Such speciation introduces a stochastic component in the otherwise deterministic MacArthur theory. We describe here how speciation can be implemented to yield a model that displays many of the salient dynamic features of ecosystem evolution, including readily observable rank diversity metrics. Speciation adds two different noise components that nevertheless produce stable equilibria and limit cycle behavior. Importantly, our Speciating MacArthur model (SMA) produces other natural dynamical features. We find that the ecosystem size is bounded even without implementing species-level carrying capacity. Furthermore, we observe resource shock resilience and drift in species composition. The model reproduces priority effects. The Speciating MacArthur model so provides an attractively simple foundation to explore the rich dynamics in evolving ecosystems.