"Chaos and noise: disorder in population dynamics"Ramirez, Maria AlejandraEvolutionary game dynamics is a framework used to model the dynamics of strategy abundances in a population. For finite populations, dynamics that appear to lack a pattern or principle of organisation can arise from sources like demographic noise and chaos. The former refers to the stochasticity caused by the probabilistic nature of birth and death events, while the latter is related to deterministic dynamical complexity. Currently, the effect of noise on dynamics displaying complex behaviour is not yet understood. Therefore, we analyse the interplay between complex dynamics of a chaotic system, and stochasticity, arising from demographic noise. For this, we compare the dynamics that arises in a chaotic deterministic system with the dynamics of the equivalent stochastic system subject to with demographic noise. In particular, our analysis focuses on quantifying the relevant characteristics of the dynamics with numerical measures. For example, we use tools from time series analysis and chaos theory to quantify the permutation entropy and the fractal dimension of the system. Our results confirm the intuitive idea that, for small population sizes, the system's stochasticity dominates the dynamics. On the other hand, for large enough population sizes, the population dynamics is strongly influenced by the so-called underlying deterministic skeleton, which can exhibit chaotic behaviour. Overall, our results can help to understand dynamically complex systems affected by demographic noise. Precisely, we found that focusing on the deterministic skeleton can be beneficial to describe and predict complex dynamics of a large but finite population. |
« back