Evolution 101: Adaptive Dynamics Models and Game Theory

This week’s Evolution 101 blog post is by MSU undergrad Faisal Tameesh and MSU grad student Emily Weigel. 

Mathematics developed from game theory has been used to study phenotypic evolution, or evolution in the way something “appears” or “behaves.” Particular models, known as adaptive dynamics models, use game-theoretic concepts of frequency-dependence — that the success, or fitness,  of an individual depends on the fitness and abundance of other phenotypes in the population —  to give more ecologically-realistic description for traits that continuously vary. These models link population and evolutionary dynamics to describe the spread (“invasion”) of very small mutations through a population.

To understand how adaptive dynamics models work, imagine a population in which all members share the same phenotypic trait. Let’s call this our “resident” population.  What we will then try to do is to describe mathematically how mutants (“invaders”), whose phenotype is just slightly different from the residents, could invade and spread within the population. What is the outcome of competition, then, between the residents and the invaders? Can they coexist, or will one population exclude the other? From here, scientists try to understand when a population is vulnerable to an invasion, or when an unbeatable strategy is reached — a so-called Evolutionarily Stable Strategy (ESS). These strategies are simply traits which, when the vast majority of individuals express them, no rare mutant with a different trait can invade and increase in numbers. If a successful invasion occurs, the invading population becomes the new resident population, and because evolutionary timescales are much longer compared to the ecological timescales under which the two phenotypes compete, this change is more or less instantaneous. The graphical tool called a Pairwise-Invasibility Plot (PIP) helps us visualize under what conditions a resident wins, an invader wins, or coexistence occurs. The following is an example of what this can look like.

Example Pairwise Invasibility Plot

These dynamics models are also related to the concept of game theory, which is the study of the interaction of intelligent, rational entities, such as humans or intricate computer programs, in an environment that is either natural or designed. The organisms must have some form of memory and a way to make their actions visible to their opponents. The memory is required to keep a log of the opponent’s actions to possibly detect patterns in behavior that can be responded to. Actions must be visible to one another, because, by default, an organism must be able to observe its opponent’s activities in order to come up with actions that will ultimately benefit it.

There are two main aspects of game theory: cooperation and defection. Evolutionary simulations have demonstrated that organisms may evolve to cooperate, so that both organisms benefit; however, these simulations have also shown that, under certain conditions, defection becomes a more feasible approach for an individual to survive in an environment. Whether an organism uses cooperation, defection, or both strategies depends on the environment and the task to accomplish.

Mathematical models can be created, depending on the behaviors of these organisms in terms of cooperation and defection; the organisms’ behaviors can be represented and possible predicted. These models consequently enable humans to gain a better understanding of processes in fields like psychology, economics, and biology. Computer scientists are also able to apply the models to create more challenging opponents in video games in the form of artificial intelligence. Findings like these can also pave the way of enhancing the interactions between intelligent machines and humans in the future. 

About Danielle Whittaker

Danielle J. Whittaker, Ph.D. Managing Director of BEACON
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