Uncertainty and decision making

So.... here is a post about my first biology publication: "how should prey animals respond to uncertain threats?".

I'll summarize very briefly some ideas about gambling, and the Kelly criterion, and then discuss what that has to do with prey animals.

Let's start our discussion by imagining that you and I are going to gamble on coin flips. We will flip a coin, and bet at even odds (so if it's heads, I pay you the amount of the bet, and it it's tails, you pay me that same amount). But, the coin is biased in your favor, so that it comes up heads 55% of the time, and tails 45% of the time. This means that you have a 10% edge on the bet: on average, you expect to get back 110% of the bet, for each bet you make.

If we only do one coin flip, and you want to maximize your expected profit, you would bet everything you have. You might lose, but your expected profit is positive.

Instead, let's consider the case where we keep flipping the coin over and over again, and you try to maximize your long-term profit. In that case, it would be silly to bet all of your money on the first coin flip because, if you lost that one, you would lose the ability to make money on future bets (because you would be broke and not able to keep betting).  Back in the 1950's, J Kelly demonstrated that the best possible strategy in this case is to bet 10% of your money on each coin flip. As your bankroll grows, you bet more. This strategy provides the best balance between betting big (since you expect to make money on each bet, and bigger bets mean more profit), and avoiding going bankrupt (which gets rid of any chance of future profit).

In my paper, I discuss a semi-related problem, which is as follows.

Imagine that you are a deer, in a forest. You spot movement out of the corner of your eye, but you don't know for sure what is causing it. If it's a wolf (or whatever predator), you should run away to avoid being killed, but if it's not a predator (say, just some leaves blowing in the wind), then running away would waste energy, and cost you whatever mating or foraging opportunities were presently available to you.

Now we want to figure out what the deer (you) should do in that situation.

Interestingly, much like in our gambling example, the "correct" decision (the one that would be favored by evolution; the one that allows the deer to have the most offspring in its lifetime) is very heavily influenced by the uncertainty of the outcome. So, even if it might be immediately (on average) advantageous to "risk it", and not flee, when you are uncertain about whether or not a predator is present, the fact that you lose all future mating chances if you are wrong makes the "correct" decision strategy more cautious.

This issue - the influence of uncertainty on prey escape decisions - was not previously understood in the behavioral ecology models, but I am hopeful that future work in this field will be influenced by my result.