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The Tangled Nature Model of biological and cultural evolution featuresinteracting agents which compete for limited resources and reproduce in anerror prone fashion and at a rate depending on the `tangle' of interactionsthey maintain with others.  The set of interactions linking a TNM individual to others is key to itsreproductive success and arguably constitutes its most important property. Yet,in many studies, the interactions of an individual and those of its mutatedoff-spring are unrelated, a rather unrealistic feature corresponding to a pointmutation turning a giraffe into an elephant. To bring out the structural anddynamical effects of trait inheritance , we introduce and numerically analyze afamily of TNM models where a positive integer $K$ parametrises correlationsbetween 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 traitinheritance. We show that the distribution of the interactions generated by ourrule is nearly independent of the value of $K$. Changing $K$ strengthens thecore structure of the ecology, leads to population abundance distributionswhich are better approximated by log-normal probability densities and increasesthe probability that a species extant at time $t_{\rm w}$ is also extant at alater time $t$. In particular, survival probabilities are shown to decay aspowers of the ratio $t/t_{\rm w}$, similarity to the pure aging behaviourapproximately describing glassy systems of physical origin. Increasing thevalue of $K$ decreases the numerical value of the decay exponent of the powerlaw, which is a clear quantitative dynamical effect of trait inheritance.

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