The Tangled Nature Model of evolutionary dynamics reconsidered: structural and dynamical effects of trait inheritance

The Tangled Nature Model of biological and cultural evolution features interacting agents which compete for limited resources and reproduce in an error prone fashion and at a rate depending on the `tangle' of interactions they maintain with others. The set of interactions linking a TNM individual to others is key to its reproductive success and arguably constitutes its most important property. Yet, in many studies, the interactions of an individual and those of its mutated off-spring are unrelated, a rather unrealistic feature corresponding to a point mutation turning a giraffe into an elephant. To bring out the structural and dynamical effects of trait inheritance , we introduce and numerically analyze a family of TNM models where a positive integer $K$ parametrises correlations between the interactions of an agent and those of its mutated offspring. For $K=1$ a single point mutation randomizes all the interactions, while increasing $K$ up to the length of the genome ensures an increasing level of trait inheritance. We show that the distribution of the interactions generated by our rule is nearly independent of the value of $K$. Changing $K$ strengthens the core structure of the ecology, leads to population abundance distributions which are better approximated by log-normal probability densities and increases the probability that a species extant at time $t_{\rm w}$ is also extant at a later time $t$. In particular, survival probabilities are shown to decay as powers of the ratio $t/t_{\rm w}$, similarity to the pure aging behaviour approximately describing glassy systems of physical origin. Increasing the value of $K$ decreases the numerical value of the decay exponent of the power law, which is a clear quantitative dynamical effect of trait inheritance.