the mating game

I am back from the neuroscience retreat in Lake Tahoe. I had a lot of fun, and have some new ideas for science. These involve semi-autonomous sensorimotor control systems, and will not be discussed in this blog post.

Both nights of the retreat, the neuro grad students threw a big party for all of us. It was a great opportunity to drink a few beers, and do some networking.

At one of said parties, I was discussing some recent work I did on escape decisions for prey animals with imperfect information, and my colleague inquired about whether or not I had considered the issue of mating opportunities with imperfect information.

That question is the topic of this blog post.

Imagine that you are a lady-deer (doe), and that it's mating season. You will be in heat for 10 days, after which it's too late for you (you have to wait until next year to mate).

Imagine that you get to mate once and only once this mating season and that, each day, you get the chance to inspect one randomly selected man-deer (buck), and choose whether or not to mate with him. Also imagine that you can assess the quality of the man-deer from your interaction, and that not all men-deer are equal (some are better potential mates). What selection strategy can you use to mate with the best possible male, and how does that strategy change as the season progresses?

I think the answer is pretty simple, and we can figure it out by working backwards from the last day. On the last day, you should mate with whatever male you see, because it is your last chance to mate (and even a poor quality mating opportunity is better than none at all, right?!).

On the second-to-last-day, you should mate with the male if he is better than average (in other words, better than the expectation value of quality of the male you will see the next day).

One the third-to-last day, you should mate with the male if he is better than 2/3 of the population. To be more rigorous, I would say "mate if the male is better than the expectation value of the max. quality of two randomly selected males", but the 2/3 rule is fine for our current purposes.

Clearly, with more time left in the mating season, we can afford to be more selective.

Formally, I think the optimal strategy is "mate with the male if they are better than the maximum quality in a group of n randomly selected males, where n is the number of days left in the mating season."

I suspect that this result is both easy to prove, and that it has probably already been done by someone (although I am too lazy to find out whom).

Anyhow, next time you are people-watching at a club, and you see people pairing up with strangers, look at the clock, calculate how long until "last call", and consider the subtle mathematics behind "the mating game."