Synchronization in Ecological Networks: A Byproduct of Darwinian Evolution?

The paper considers the evolution of a particular class of networks of identical chaotic oscillators, namely that of ecological networks. In these networks, nodes represent patches where a certain number of plant and animal populations interact on ecological timescale, arcs represent migration flows due to dispersal, and Darwinian evolution is responsible for variations, on a longer evolutionary timescale, of the demographic parameters characterizing the populations. Up to now, this problem has been mainly studied with reference to single-population patches described by one-dimensional discrete-time models and by considering only the dispersal rates of migrating populations as an evolving trait. Here, we propose a method of investigation which allows to study multipopulation patches described by continuous-time models with evolving traits influencing various demographic parameters (including or not dispersal). The method is casted within the frame of the so-called master stability function approach for the analysis of synchronization of coupled systems, and the results obtained in a first and very simple application support the conjecture that evolution drives ecological networks toward weak forms of synchronization.