Using Game Theory to Understand Ecological Interactions

Written By Vaishnavi Kolluru

SHOUTOUT CHESSFUN FOR ARTICLE TOPIC IDEA; IF IT WASN'T FOR YOUR INPUT, I WOULD'VE AVOIDED ECOLOGY BUT THIS WAS FUN TO EXPLORE SO TY <3

(also everyone lmk if you have article ideas & you can get a shoutout too if you want! lol)

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In a biological sense, every action that an organism takes should contribute to increasing their reproductive fitness. For example, it's evolutionarily favorable to want to have sex and act on this desire, as sex (in theory) makes babies and thus passes on genes. It's pretty obvious that this action will directly increase fitness. However, there are times when the result is not as clear. When others' choices also dictate the outcome of your actions, decision-making gets complicated. To understand the mechanics of these situations, let's step back from biology for a second, and talk about game theory.

The Prisoner's Dilemma is the classic problem used to illustrate game theory for noobs. In this scenario, two prisoners who collaborated in committing a crime are questioned separately. If one confesses and the other doesn't, the confessor is set free while the other is given a 5 year sentence. If neither confesses, the sentence for both is reduced to one year. Finally, if both confess, both are given a 3 year sentence. This can be visualized as follows:

Uh so I copied this example from a website bc I forgot the exact numbers and this was the chart given but I feel like the 5 and 0 should be switched?? But maybe I’m tripping. Or maybe there’s no set standard for how to label the coordinates? Idk different sources have said different things. Lmk if you know tho and I’ll fix it.

The dilemma here is that, although both remaining silent creates the lowest total sentence for both prisoners, each prisoner has their own incentive to betray the other and confess, so that they don't have any jail time. If you think about it, there are many reasons and nuances to this situation for each prisoner to act the way they will. Ultimately, decisions will come down to personal philosophies, so there's no definitive answer to what an individual's best decision should be. That's why it's a dilemma.

This dilemma also exists for ecological species interactions; however, instead of jail time, the losers are presented with lowered evolutionary fitness. Given that evolutionary fitness is basically the purpose of life (in a biological sense, at least), the stakes are really high for these interactions; thus, it's important to be able to model them to predict behavior.

Here's a hypothetical situation (source: 2020 semis, q93):

As you can see, there's no clear answer as to what would be the best decision for either individual. (It’s actually the same numbers as the prisoner example!) That's why game theory is applicable.

Let's now look at a few factors involved in understanding these models.

In the context of evolutionary decision-making, the best decision for an individual is called an evolutionary stable strategy (ESS), which is a behavior that, when every member of the population has it, would outcompete any introduced variation. This isn't really compatible with most practical situations, so ESSs are often stable population-wide ratios of behavioral choices, rather than individualized behaviors that every member of the population practices.

A similar concept called Nash equilibrium is also important for modeling these kinds of interactions. Nash equilibrium is the set of strategies such that no individual needs to change strategies as long as conditions remain constant. In other words, when one individual's decision makes the other's decision obvious to maximize benefit, we have a Nash equilibrium.

Now that we understand these concepts*, let's try a practice problem (source: International Biology Bowl '22-'23 Advanced Open Exam, q10):

*maybe we don't yet. If this is the case, check out the linked resources. Their explanations are better than mine.

Let's evaluate each statement.

A - If one individual chooses action T, it's best for the other to also choose T. Same scenario for H. It doesn't help anyone to choose different actions. Thus, no individual needs to change strategies, and the decision is obvious. Thus, (T, T) and (H, H) are Nash equilibria. True.

B - From the table, we can see that when one decides to sTeal, and the other decides to sHare, the sTealer has a higher gain (3) than the sHarer (2). Thus, when a population only sTeals, they will outcompete one that only sHares. False. (Note: to read an unlabeled matrix, assume the "x-coordinate" is the one on the horizontal axis of labeling.)

C - The best decision for everyone to make is to do the same thing as everyone else. This yields maximal benefit to all. Thus, both sharing is the ESS. True.

D - If (T, T) is replaced with (1, 1), then the best scenario would be to both share, which yields a benefit of (3, 3). So, this is the new ESS as this is the singular most favorable decision.

So, yeah. That was the basics of game theory, Nash equilibria, & ESS. This was kind of a mess, so please let me know if I screwed up somewhere. I enjoyed learning about this, and I hope you did too! That said, here's some more stuff to read/watch:

Vaishnavi Kolluru
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