How do simple evolutionary strategies and investment optimizations affect ecological patterns? The case of generalized Taylor's Law

Abstract

Taylor's Law (TL) relates the variance to the mean of a random variable via power law. In ecology it applies to populationsand it is a common empirical pattern shared among different ecosystems. Measurements give power law exponent to be between 1 and 2, and more often to cluster around 2, whereas theoretical models predict TL exponent can assume any real value. In this paper, adopting the framework of multiplicative growth models in a Markovian environment, we investigate the possibility of evolutionary strategies to be responsible for TL exponent to be in a finite range. We implement three different strategies the individuals can follow and for each strategy set two different optimization investment objectives. In all the studied cases we find TL exponent can assume any real value due to the existence of regions of the model parameters in which the exponent can diverge. Furthermore, under natural hypothesis on the dynamics of the environment, the shapes of these regions do not depend on different strategies adopted and nor on the optimization objective. Thus the introduction of strategies dose not affect the range of TL exponent in the model. In our theoretical framework rare events are shaping the value of the TL exponent, suggesting, as hinted by previous works, that empirical values may be a statistical artifact following from under sampling.