Statistical mechanics of ecosystem assembly

TL;DR

This paper presents a comprehensive, exactly solvable model of ecosystem assembly that maps all invasion pathways, characterizes the process as a Markov chain, and identifies unique stable endstates resistant to invasions.

Contribution

It introduces a toy model that allows exact computation of all assembly pathways and endstates, providing a clear framework for understanding ecosystem assembly dynamics.

Findings

The assembly process has a unique recurrent endstate.

The endstate is independent of assembly history.

All observables can be computed exactly in the model.

Abstract

We introduce a toy model of ecosystem assembly for which we are able to map out all assembly pathways generated by external invasions. The model allows to display the whole phase space in the form of an assembly graph whose nodes are communities of species and whose directed links are transitions between them induced by invasions. We characterize the process as a finite Markov chain and prove that it exhibits a unique set of recurrent states (the endstate of the process), which is therefore resistant to invasions. This also shows that the endstate is independent on the assembly history. The model shares all features with standard assembly models reported in the literature, with the advantage that all observables can be computed in an exact manner.