Game theory in inter-species mutualism and parasitism
https://www.sciencedirect.com/science/article/pii/S0003347201919372
In the natural world there are many cases where two organisms from different species cooperate in order to produce a net gain; however, sometimes this behavior seems paradoxical and the observer is left wondering how it developed. One well-characterized example of this is between reef fish and their cleaner fish, who eat the ectoparasites from the host fish. The host fish is cleaned of parasites, and the cleaner fish earn themselves a meal. In this game, the players are the species themselves and the payoff is fitness, defined as an increase in the organism’s ability to survive and reproduce successfully. We assume that the individual organisms themselves are acting in terms of their instincts, and are not able to cognitively “choose” which strategy to adopt. The choosing of strategies occurs through natural selection: if behavior A leads to an increase in fitness compared to a mutually exclusive behavior B, organisms that exhibit behavior A will survive and have more offspring which will also exhibit behavior A and will eventually outcompete individuals expressing behavior B, and eventually over many generations there will only be individuals expressing behavior A in the populations, provided a new behavior that is even better than A does not enter the population. This model of behavioral evolution fits our definition of game theory because each player species seeks to maximize its gain and also through the passage of time evolves to adopt the best strategy for a given situation: in other words, natural selection over time is rational.
Returning to our cleaner fish and host fish, there are two behaviors that the cleaner fish can engage in: one is to eat the parasites from the host fish, which confers a benefit to both species. The other strategy is to cheat and eat the mucus lining of the host fish, which gives a bigger benefit to the cleaner fish but in turn hurts the host. Barring any other factors, cheating seems to be the dominant strategy for the cleaner fish, since it brings the bigger fitness gain for the cleaner-turned-parasite fish. So why does this cleaner/host relationship still exist? Over time, the host has evolved a behavior that punishes parasite fish- upon having its mucus eaten, the host will prohibit the cleaner from approaching it, leading to a net loss for the cleaner fish and the host. This results in another behavior change for the two species, in which they now have a mixed equilibrium between cleaning and parasitism, and allowing the cleaner fish to approach or chasing them away. Over time, more intricate behaviors have emerged such as a signal from the cleaner fish to the host fish and the emergence of a only parasitic species, and the frequency of these behaviors and the population size of the parasite-only species are also governed by the same rules of game theory.