Whitey Bulger Caught, and the Trivers Willard Hypothesis

Apropos this, a timely repost:

This may or may not be a recent photograph of fugitive Whitey (James) Bulger of Boston's Winter Hill Gang. Most of you won't know who Whitey Bulger is. He is actually on the FBI's ten most wanted list. He may have been spotted in Italy last Spring, and the FBI is just now asking for assistance from anyone who knows where he might be. (That's not gonna work.)

Whitey was top dog in Boston's Winter Hill gang. His brother was a Senator for the Commwealth of Massachusetts, and served as Senate President for several years.

It is said that Whitey was an FBI informant, and that his handler, FBI Special Agent John Connolly, tipped Whitey off that he was about to be indicted on racketeering charges. No problem. Whitey had left stashes of cash in safe deposit boxes all around the world, in preparation for the day he had to go on the lam. So he took off in 1995, and the FBI has not been able to catch up. Special Agent Connolly is pulling a ten year vacation in the stir.

I remember when Whitey disappeared, and ever since then, I've used him almost annually in lecture material describing the Trivers-Willard hypothesis. It goes like this:

This may or may not be a recent photograph of Robert Trivers, of the Trivers-Willard Hypothesis. The Trivers-Willard model (I prefer to call it a "model" rather than a "hypothesis" because it is not specific enough to really be a hypothesis ... it's a model that generates lots of hypotheses) states that selection should favor the ability to differentially bias investment in offspring by sex if the two sexes have differential variances in reproductive success, and if there is any way to predict offspring rank. That's a bit thick, so it requires some examples and further explanation. Maybe a story about a mobster would help..

OK, so an example: Red deer (also known as Elk) give birth to one offspring (max) per year. Males compete for access to or to be chosen by females. So, only a small percentage of male red deer mate in a given year, a significant percentage may never mate at all, and a very small percentage sire many many little red deer. Male red deer have a high variance in reproductive success. If you tried to predict how many offspring a given randomly chosen male would have, knowing nothing at all, your best guess would be the average number of offspring red deer have in an average lifetime. But you would be wrong almost every time because the actual number is highly variable. Male red deer have high variance in RS.

Females, on the other hand, have a pretty standard number of offspring. There is not much competition among them, they can always find a male to mate with, etc. If you needed to guess how many offspring a particular randomly chosen female red deer would have in a life time, you could guess the average, and you would be right on or very close. Female red deer have low variance in RS.

So, male and female red deer have differential variance in RS. Males high, females low.

If a female red deer could somehow "predict" the likelihood of her offspring getting to mate, i.e., if she could tell if any offspring she had in the present year (male or female) would be average vs. high ranking, then selection should favor the evolution of a mechanism to actually give birth to the appropriate sex offspring (thus biasing investment in one sex or the other). It turns out that she can. A female red deer that is herself average or lower-quality (thin, ill, injured) is likely to give birth to an offspring that will be either low ranking or average. But if the mother-to-be red deer is high ranking, she is likely to give birth to an individual who will grow up to be high ranking.

Under these conditions, she should have a female offspring if she's average or low ranking, but a male if she's high ranking. And that, it turns out, is what red deer actually do.

That should be clear. But in case it isn't, let's take it down do real life, and bring in the gangsters.

You check the mail this afternoon, and there is a letter from a law firm you have never heard of. It says that your Great Aunt Tillie (whom you've also never heard of) just died, and left you with $1,000 in her will. The check is enclosed.

This may or may not be a recent photograph of a male red deer. Holy crap. Found money! What are you going to do with it? So you and your close advisors (your roommates, your cat, etc.) discuss it and you narrow it down to two choices. Choice A and Choice B.

Choice A is to go to your broker and buy $1000 worth of a nice, relatively safe mutual fund. The fund will buy and sell reliable blue chip stocks, thus spreading the risk over several companies, and over time you can expect to get a return of 50 bucks a years, easy.

Choice B is to buy 1000 one dollar lottery tickets. Your chances of winning are slim, but if you do, you will win 87 million dollars.

So, what do you do? The obvious sane choice is to buy the mutual fund.

But what if your cousin is Whitey Bulger? Whitey Bulger, as head of the Winter Hill Gang, is said to have owned the director of the Commonwealth Lottery agency.The connection between Whitey Bulger and the Lottery has never been proven. They don't have a shred of evidence. He was, however, indicted for 21 counts of RICO-Murder. It is said that one of the things that tipped off authorities about this is that some of his relatives were winning the lottery a little more often than they should have. So, say your cousin is Whitey Bulger, and last time you saw him (at a family wedding) he told you ... "hey, if you ever want to take a "chance" on the lottery, let me know ... I can make that work for you..."

So now, you have two choices.

Choice A: Invest in a mutual fund and gain a return of 50 bucks a year (that's dollars, not elk); and

Choice B: Buy 1000 PowerBall tickets and have a great deal of certainty of winning 87 million dollars.

What would you do?

In case it isn't already clear. the baby male elk is a lottery ticket, the baby female elk is a mutual fund, but the female can guess pretty accurately if the lotter ticket (male offspring) will pay off. Because the elk's cousin is Whitey Bulger. See?