Evolutionary Games and Ecosystems (7)

Caesar or Pompeius

Evolution of Aggression in Competitive Species

Alert readers of previous chapter must have noticed the qualification "except in the exceptional case of aggressions of both players being very week." which has been placed for the condition for extinction of one of two species. In fact, for Lotka-Volterra equation, in case of very small numbers for aggression constant, there is a stable fixed point. But what is the proper value of the agression constant? Is it a given fixed number for a given situation? Take an example of two boxers, you and your archrival. It is up to you to make the decision to go atacking with your killer punch. Going full force too early, you run the risk of counteratack later. so you typically start by jabbing. It is natural to assume in this case, as well as in the case of two species of animals, that both parties tweak the degree of aggression in search of their own advantage. So both prties have choice to make and the result depends on the decisions of both - nothing but an exact game theoretical situation!

Instability in Competitive System and Dilemma Situation

In the following table, we have written the payoff table, calculated from Lotka-Volterra dynamics, for two competing species with strong and week aggression intensity. Since the model is not fully specified to the numbers, we only have qualitative table, which is quite enough for our current discussion.

When both parties refrain from atacking the other so much, they both survive in their own way, which we represent as (0). If both parties attack each other, both get hurt (-). If you refrain from atacking while the other party attacks, you get hurt in a great deal (--). The other party scores gain because your atacking capability is reduced (+). So you would be better of attacking irrespective to your opponents attitude, and this should be the same for the other party. So both atacks and the results is that both are worse off compared to stay peaceful. This is nothing but the prisoner's dilemma! Namely, in competitive system, two parties evolve to increase their mutal aggression in response to the other's aggression, and even initially stable "week aggression case" would be eventually changed into unstable "strong aggression" case by the evolution of aggression. Caltage must be destroyed.