Introduction:

The Tangled Nature Model of evolution is an individual based, stochastic model, which describes, with good agreement with actual observations, the evolution of a simple ecology. Its most remarkable feature is that its dynamics alternates between periods of meta-stable configurations and periods of hectic transitions, where the model does not show clear occupancy patterns and the population is spread randomly across the type space.

Hypothesis and methods:

The aim of this project is to analyze the stability of the stable configurations (qESS states) shown in the model by using a dynamical system approach. Indeed, we can derive a deterministic system of equations which approximates the dynamics of the model. Clearly, we can analyze the local stability of its fixed points by linearizing the equations about the equilibrium configurations. The idea in this work is to run simulations of the stochastic model to obtain specific configurations of the qESS states and use their averaged occupancy of these configurations to calculate the linearized dynamical matrix. The eigenvalues of this matrix are expected to be able to give useful information about the stability of the meta-stable states. In this presentation we will describe in details the ideas introduced and describe the results obtained.