I will present simulations in which strategies in a two-player game
evolve by mutations applied directly to entries of the payoff matrix.
In these models, byproduct cooperation emerges, in which there is no
cost associated with cooperative behavior and no temptation to defect.
I will present a related set of ecological models in which the
interaction terms of a Lotka-Volterra matrix evolve in the same way,
to the same end: cost-free cooperation, also known as byproduct
mutualism. With these simulation results as a springboard, I will
present a mathematical treatment of the relationship between
interaction terms and phenotypes in evolution.
Results/Conclusions
In the above-mentioned simulations, diversification and byproduct
cooperation are observed. The mathematical analysis of the evolution of
interactions and phenotypes is very similar to the analysis of evolution
in the presence of phenotypic constraints or tradeoffs. In both cases
there is a tension between the direction of the fitness gradient and the
range of available variation. The case of interactions is further
complicated by each interaction term's dependence on two phenotypes rather
than one, so that its motion involves both a direct effect of selection
(via the population affected by the interaction) and an indirect effect
(via the other population). Within this structure, we find a hidden pull
toward mutualism: the fitness gradient depends only on the direct effect,
and always points in the direction of mutualism, even though mutualism may
not be the outcome because of indirect effects or lack of available
variation. Whether mutualism appears or not boils down to whether these
two considerations work against it strongly enough.
