Species assembly in model ecosystems. II: Results of the assembly process. (English) Zbl 1307.92319
Summary: In the companion paper of this set [the authors, ibid. 269, No. 1, 330–343 (2010; Zbl 1307.92318)] we have developed a full analytical treatment of the model of species assembly introduced in [the authors, “Statistical mechanics of ecosystem assembly”, Phys. Rev. Lett. 103, No. 16, Article ID 168101, 4 p. (2009; doi:10.1103/PhysRevLett.103.168101)]. 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.
MSC:
| 92D25 | Population dynamics (general) |
| 92D40 | Ecology |
| 60J20 | Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.) |
Citations:
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