Tuesday, September 22, 2009

Cause of homosexuality

Evolution has to answer some tough questions, such as how could the human eye evolve (see Appendix 2 below) or why did peacocks evolve to have such a ridiculous (but beautiful) tail (see Appendix 3 below). In many respects evolution is a ruthless driver of efficiencies. But there are some anomalies. For example, why are there so many homosexuals? If there were a gene for gayness, then surely evolution would wipe it out. I'd like to proposes an explanation.


But first let me discuss tennis! ( It will be relevant, I promise)

When a tennis player is about to take a shot, naively we might think that the best strategy would be to hit the ball in such a way as to maximise the probability of it going in, that would be to hit it back gently into the middle of the court. However competitive players almost never do that.

If the player hits the ball harder (faster) then it will increase the probability of the ball going out, but if he were to gently hit the ball, then the opponent will almost certainly take advantage of the weak shot and hit a winner. So the optimal shot involves taking a calculated risk that the ball will go out. ( See Appendix 1 for a plot of some probabilities and expected score)

Now returning to evolutionary psychology: why are there so many gay people? Well, consider the following hypothesis: There are some genes which give people an advantage, such as say ability to recognise emotions in others. But rather than working just as a black and white (i.e. binary) scale, it is much more gray than that and that the genes can also lead to a small possibility (probability) of homosexuality.

Someone who carries these genes can still have an advantage over others who don't even though they expect some percentage of their offspring will be gay. Over all the effect of having the genes is positive.

Well, what could such a set of genes be? Or what quality do they give the people who have the genes. It could be a 'feminine-side'. A man who can express emotions and empathise with others who display their emotions can have an advantage over someone with very limited social skills. However having such genes could also lead to a probability of homosexuality. And so a genetic cause of homosexuality gets passed from one generation to the next in a bundle of genes with net beneficial effect.

The next question is how do we test this hypothesis? Well, in some families all the kids are tall. There is a high correlation in height of siblings. If the hypotheis is true, we would expect a lower correlation of homosexuality between siblings, since the genes are causing a probability of homosexuality and not actually homosexuality, unlike genes which cause height. But the correlation would still be positive.

Appendix 1
Let's look at the strategy of the tennis player in a mathematical way.

Let v be the speed of the ball that player A hits.
Ignoring drop shots for now, we'll consider speeds from the easy shot into the middle of the court up to the very high speeds which are very difficult to keep in.

Let p(v) be the probability that a shot hit with speed v by player A will go in.

Let q(v) be the probability that player B, on the other side of the net, will be able to return the ball again conditional on A's shot, which was hit with speed v, being in.

For both p(v) and q(v), low speeds will give high probabilities, high speeds will see the probabilities dropping towards 0.

For a given shot, we'll award A a score of

-1 when A's shot is out, that happens with probability (1-p(v))

0 when A's shot is in and B returns it successfully, that happens with prob: p(v) * q(v)

+1 when A shot is in and B is unsuccessful in returning it, that happens with prob p(v) * ( 1 - q(v))


We can now work out the expected score when A hits the ball with speed v:

E(S(v)) = -1 * (1 - p(v)) + 0 + 1 * p(v) * ( 1 - q(v))
E(S(v)) = 2 * p(v) - 1 - p(v) * q(v)


Below is a plot of what E(S(v)) might look like against v.



So we can see from the plot above, that to maximise his expected score, player A needs to hit the ball with a speed that will result in there being a reasonably high probability of the ball going out.

In exactly the same way, genes can be advantageous to the carrier, even if it means there is a significant probability of having homosexual offspring as long as they confer some other advantage.


Appendix 2
The evolution of the eye has been well explained. I won't go into the details here except to say that a useful introductory article can be found in wikipedia

Appendix 3
The best explanation I've heard for why peacock's beautiful tails have survived generations of ruthless evolution is that if a peahen were to have a preference for fit males with smaller tails, then her male offspring who have inherited the short tail from their father, would have trouble finding a mate. The cause of their problem would be that their mother had a opinion on which was the best mate that differed from the consensus. So, when choosing a mate, your children will thank you for going with the consensus.

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