Species assembly in model ecosystems, II: Results of the assembly process

TL;DR

This paper provides a detailed numerical analysis of a species assembly model, revealing how communities evolve towards recurrent states, with insights into invasion dynamics, stability, and resource dependence.

Contribution

It offers an exhaustive numerical study of the assembly process, complementing previous analytical work, and characterizes the dynamics and stability of ecological communities.

Findings

Recurrent states are reached quickly relative to system size.

Most invasions are accepted, causing small avalanches.

Communities become less resilient but more resistant over time.

Abstract

In the companion paper of this set (Capitan and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitan et al. (2009). This model is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities by new species invasions. In the present paper we provide an exhaustive numerical analysis of the model, describing the average time to the recurrent state, the statistics of avalanches, and the dependence of the results on the amount of available resource. Our results are based on the fact that the Markov chain provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession, in an exact manner. Since the absorption times into the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time). Thus, the final ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns. The assembly graph is dominated by pathways in which most invasions are accepted, triggering small extinction avalanches. Through the assembly process, communities become less resilient (e.g., have a higher return time to equilibrium) but become more robust in terms of resistance against new invasions.