Monday, March 27, 2006

Sober, Arbuthnot and Fisher

This is the third part of my discussion of this paper, by Elliott Sober on the Design Argument.

Sober writes that John Arbuthnot noted in 1710 that there was a difference between birthrates of sons and daughters. He cites R.A.Fisher's 1930 analysis, in applying natural selection to this observation, as follows:
Arbuthnot could not have known that R.A. Fisher (1930) would bring sex ratio within the purview of the theory of natural selection. Fisher’s insight was to see that a mother’s mix of sons and daughters affects the number of grandoffspring she will have. Fisher demonstrated that when there is random mating in a large population, the sex ratio strategy that evolves is one in which a mother invests equally in sons and daughters (Sober 1993, p. 17). A mother will put half her reproductive resources into producing sons and half into producing daughters. This equal division means that she should have more sons than daughters, if sons tend to die sooner. Fisher’s model therefore predicts the slightly uneven sex ratio at birth that Arbuthnot observed. (p.5)
This seriously baffled me – perhaps one of the well-informed commenters can help. Obviously, this is specifically addressed to sex ratios in human reproduction. Sex determination in humans comes from an X or Y chromosome in the sperm cell. To the best of my knowledge, the mother has no way of determining what sperm cell fertilizes an egg – either consciously or biologically.

Furthermore, if we are looking at grandoffspring, then surely there are much more important things to look at in biological terms than the age at which offspring die. For example: fertility rates; comparative rates of homosexuality/heterosexuality for the two genders (if such things are genetically coded, as we are told – if 10% of males are genetically homosexual and 5% of females are homosexual, and 5% differences in life expectancy have a natural selection effect, then one would assume that expected sexuality would have natural selection implications for the relative frequency of male and female offspring); comparative ages at which offspring become sexually active and cease being sexually active; and so on.

The analysis also implies that the death rates of different sex offspring are biologically hard-coded. Not only is there a mysterious mechanism present that results in a bias towards male offspring, but this mechanism works by somehow knowing about mortality rates.

The huge question that this proposition raises is: HOW??? If this comes about through natural selection (which, incidentally, I don't have a real problem with – I find Arbuthnot's argument unsatisfying as well), then what on earth is the mechanism?

What are the options?
  • Fisher was completely right – the mother does invest equally in sons and daughters. This seems unlikely to me. If the mother has any control over the gender of her offspring, then I am pretty sure this has only become apparent in the last few years, and certainly could not have been known about in the 1930's. If the mother can't control the gender of her offspring, then in what sense can she be said to be investing equally in sons and daughters? (Please note that when I say “control the gender of her offspring” here, I am not talking about a conscious act. I am talking about her biological relevance to the gender of her offspring.)

  • Fisher was right, but for the wrong reasons. The mother does have some subtle influence over the gender of her offspring – perhaps there are biological or hormonal influences that determine a non-even gender distribution. If this is the case, then what are these influences? If they aren't yet known, then this isn't an example of natural selection explaining something. It is an example of a natural selection “just-so” story that may or may not prove to be the case at some stage in the future.

  • Fisher was a bit wrong. Maybe instead the father has some subtle influence over the gender – perhaps there is an uneven distribution of X and Y sperm cells. But then the father hardly “invests reproductive resources” in his offspring – he may invest other things (although the modern consensus for a long time has been that the father isn't really necessary beyond providing a gamete), but reproduction doesn't tie him up for a significant proportion of his life. If there is an effect on the father, then it should be more significant for the mother.

    Perhaps the gender distribution is hard-coded somehow into the species – but if so, what is the evolutionary basis for this? The neodarwinian paradigm insists that it ought to be DNA. If so, how? If it isn't known, then again we have a supposed natural selection “explanation” that is lacking a mechanism.

  • Fisher was completely wrong, and Arbuthnot was right. There is no natural selection basis for the different frequencies of male and female. Note that I would be most unhappy at this stage to completely jettison Fisher's approach. It makes sense to continue searching for a biological basis for the difference in frequency between boys and girls. To argue that, because I am a proponent of ID, I am somehow more happy with the dead end that Arbuthnot proposes, would be completely wrong.

  • But the fact is that a natural selection story could be made up which would accommodate any observation about frequencies of sex distribution. Supposing female children were much more common than male children: this would work from a natural selection point of view because men are able to impregnate many women. Supposing male children were more common than female children: this would work from a natural selection point of view because it would allow females a greater say in the fitness of the father of their children. And so on.

    The story isn't important – either in these cases, or in Fisher's case. What is important is the science that supports it. Fisher's supposed refutation of Arbuthnot's argument is apparently completely lacking in a mechanism – it simply doesn't square with what we know today about reproduction and evolution. And yet, here it is, being presented in refutation of an argument from design. If there is no mechanism, then it has no less, or more, power than Arbuthnot's argument which asserts that the distribution is a sign of divine involvement.