Evolutionary Game Theory - Co-Evolution

Co-Evolution

Two types of dynamics have been discussed so far in this article:

• Evolutionary games which lead to a stable situation or point of stasis for contending strategies which result in an Evolutionary Stable Strategy
• Evolutionary games which exhibit a cyclic behaviour (as with RPS game) where the proportions of contending strategies continuously cycle over time within the overall population

- Darwins orchid(Angraecum sesquipedale)and the moth Morgan's Sphinx (Xanthopan morgani) like many insect and flower "partners" have a mutual relationship where the moth gains pollen and the flower pollination. To insure efficiency in this particular exchange the pair have evolved a mechanism which excludes the waste of pollen transfer to/from another flower species and assures feeding pollin only to the "proper" pollinator. The mechanism is an extraordinarily long proboscis on the moth and a equally long neckery on the orchid

A third dynamic can exist in certain more complex systems, where combinations of effects are in play, which contain not only intra-species competition but also inter-species competition as well. This is the realm of co-evolution. Examples include predator-prey competition and host-parasite competition. There are also co-evolutionary situations possible where two species interact where mutual interests are at play in the dynamic. Evolutionary game models have been created to encompass both these co-evolutionary situations for pairwise and multi-species coevolutionary systems. The general dynamic differs between competitive systems and mutualistic systems.

In competitive (non-mutualistic) inter-species coevolutionary system the species are involved in an “arms race” - where adaptions that are better at competing against the other species are less likely to be culled. Both game payoffs and replicator dynamics are thereby affected to reflect this. The “counterstrategy” of the other competitor species is similarly affected, exposing them to a positive selection pressure for any effective counter-strategy – in effect creating an overall competitive arms race. Underlying this total situation is an ecological effect in which the population dynamic of the competing species itself influences outcomes- e.g. a mutant strategy in a prey population which enables that species to drive its sole prey species to extinction is itself doomed. This all leads in effect to a “Red Queen” dynamic where, as in Alice in Wonderland, the protagonists must “run as fast as they can to just stay in one place”.

A number of EGT models have been produced to encompass coevolutionary situations. Modelling these multi-component coevolutionary systems mathematically is necessarily complex. This is particularly true, as a key factor applicable in these coevolutionary systems is the continuous adaption of strategy taking place in the dynamics of such arms races. Most other evolutionary games, e.g. resource conflicts, do not need to include this process of dynamic mutation in the analysis of game dynamics itself. Therefore coevolutionary modelling often involves a cross-over area, where both EGT and Genetic Algorithms reflecting mutational effects are used in the models, often having computers simulate the dynamics of the overall coevolutionary game. The resulting dynamics are studied as various parameters are modified. Because a multitude of variables are simultaneously at play in these complex dynamics, solutions become the province of muli-variable optimality, rather than simply a single ESS. The mathematical criteria of determining stable points are Pareto efficiency and Pareto dominance, which is a measure of solution optimality peaks in these interdependent multivariable systems.

In a paper by Carl Bergstrom and Michael Lachmann, the authors successfully apply evolutionary game theory models to understand the division of benefits in mutualistic interactions between organisms. Darwinian assumptions about fitness are modeled using replicator dynamics to show that the organism evolving at a slower rate in a mutualistic relationship will gain a disproportionately high share of the benefits or payoffs. This application of EGT provided an interesting and perhaps unexpected twist on the Red Queen Hypothesis which concludes evolution favored faster rates of evolution.