  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.
