Complexity and demographic stability in population models

We present a result, which relates the stability of a population, as defined by the rate of decay of fluctuations induced by demographic stochasticity, with evolutionary entropy.

This entropy is a measure of the variability in the age of reproducing individuals in the population. Its definition is based on concepts originally developed in statistical mechanics and the proof of our result uses the theory of large deviations in dynamical systems.

In this talk we will mainly focus on the biological interpretation of our mathematical result. In addition we discuss a possible generalization of our ideas to metabolic networks, which can be mathematically described by graphs.