Abstract
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility, reproduction and predation, with predation following the cyclic rules of the popular rock, paper and scissors game. The study uncovers the possibility to distinguish between time evolutions that start from slightly different initial states, guided by the Hamming distance which heuristically unveils the chaotic behavior. The finding opens up a quantitative approach that relates the correlation length to the average density of maxima of a typical species, and an ensemble of stochastic simulations is implemented to support the procedure. The main result of the work shows how a single and simple experimental realization that counts the density of maxima associated with the chaotic evolution of the species serves to infer its correlation length. We use the result to investigate others distinct complex systems, one dealing with a set of differential equations that can be used to model a diversity of natural and artificial chaotic systems, and another one, focusing on the ocean water level.
Highlights
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature
In this work we studied the presence of chaos in a system with three distinct species, that evolve under the standard rules of mobility, predation and reproduction
We first used the Hamming distance density to heuristically characterize the chaotic behavior embedded in the stochastic evolution of the system
Summary
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. In this work we consider stochastic network simulations of the May and Leonard type[5,7], following two recent investigations, one describing how local dispersal may promote biodiversity in a real-life game[8] and the other suggesting that population mobility may be central feature to describe real ecosystems[10]. These studies develop simulations that engender cyclic competition, which is modeled as in the rock-paper-scissors game, controlled by the simple rules: paper wraps rock, rock crushes scissors and scissors cut paper[6]. We recall the works[13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31] that are www.nature.com/scientificreports/
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