Monday, April 27, 2009

The Green Beard of Sex   posted by DavidB @ 4/27/2009 04:45:00 AM

One morning recently I woke up and suddenly thought I had solved the evolutionary problem of sex. About ten minutes later, I realised I hadn't, and went back to sleep. But it may still be worth outlining the 'solution', first because understanding the fallacy in the solution helps clarify the problem itself, and secondly because in some circumstances the solution is not entirely fallacious.

The evolutionary problem of sex is that it is wasteful. Quite apart from the time and effort involved in getting a partner, sexual reproduction seems to involve a major genetic waste. With sex an organism usually only puts half of its genes into each offspring, while the other half is effectively thrown away. Provided the division of genes (at meiosis) is random, the genes which maintain sexual reproduction themselves will only go into half the offspring. If we call a gene that maintains sexual reproduction a prosexual gene, while a gene that causes asexual (clonal) reproduction is antisexual, a prosexual gene will only on average be passed on to half of its posessors' offspring, whereas an antisexual gene will be passed on to all of them.

Of course, this advantage of antisexual genes would be offset if there are twice as many offspring under sexual reproduction as under asexual. This would be expected if the two partners in sexual reproduction contribute equal resources to the production of offspring. This does sometimes happen, as in many single-celled organisms, where the partners exchange material equally, and in some animals where males contribute as much as females to the nutrition and care of offspring. But the latter case is comparatively rare. In most animals and plants, the male contributes little or nothing to the offspring other than bare genetic material. I will call this the standard scenario. In the standard scenario, then, it seems that the female is behaving as a genetic altruist towards the male. A female who is willing to mate with a male is effectively saying 'come and be my genetic parasite'. (I will assume there are separate sexes, though the same arguments could be developed, mutatis mutandis, for the sexual functions of hermaphrodites.)

If we see sexual reproduction as a form of genetic altruism, we can at once classify possible solutions to the problem, drawing on the general theory of altruism. This is the first part of my not-so-brilliant idea. Notably, we have:

Group selection solutions

Sexual reproduction may be disadvantageous to individuals but advantageous to groups, for example by enabling them to evolve faster and avoid extinction. R. A. Fisher thought this was a serious possibility. But apart from all the usual problems of group selection, in the case of sex there is an additional problem. Many organisms (especially among plants) are capable of reproducing both sexually and asexually. It would be easy for them to switch entirely to asexual reproduction, yet most of them continue to reproduce sexually at least some of the time. This implies that in these cases there must be some advantage of sexual reproduction at the individual level.

Direct fitness benefits to the individual

If the individual gains some direct benefit in reproductive fitness, sufficient to offset the cost, then sexual reproduction is not altruistic after all, since it is not on balance costly. Most of the currently favoured solutions to the problem are of this kind; for example, W. D. Hamilton's idea that sex helps individuals resist parasites and pathogens. Some solution or combination of solutions of this kind may well be sufficient, but at present none of them is generally accepted. To explain the prevalence of sexual reproduction the benefit has to be both large and widespread.

Reciprocal altruism

An altruistic act can be beneficial to the individual if it is accompanied or followed by a reciprocal act of equal or greater value. In the case of sex, this would be the case, for example, if hermaphrodites simultaneously take on both male and female sexual roles in mating with each other. This occurs among some slugs, earthworms, etc, but it is obviously not a general solution to the problem. There would also be reciprocity if males contributed equal resources, but the whole point of the standard scenario is that this is uncommon.

Kin selection (inclusive fitness)

Close relatives of an individual carry identical copies of some of the same genes. A gene in the individual which promotes altruism towards relatives therefore gives some benefit to copies of itself. In the case of sex, an individual who mates with a relative mitigates some of the genetic 'cost' of sex, but as far as I can see this would never be enough to offset the cost entirely.

Green Beard Effects

A gene for altruism may be favoured by selection if it benefits another individual who is not related to the altruist, but who carries a copy or copies of the same gene. The problem is how to recognise such an individual, given that genes are not directly observable. The answer is that the gene may have some observable external effect. Richard Dawkins dubbed such an effect a Green Beard. If a gene produces green beards, and altruism towards green beards, such a gene can be favoured by selection. The problem is that such convenient combinations of effects are probably rare. Note that it is not sufficient (as Dawkins is quite clear) for an individual with a green beard merely to act altruistically towards other individuals with green beards: it has to be same gene which causes the altruistic behaviour and the green beard. Of course, pleiotropism (multiple effects of genes) is common enough, but the particular kind of pleiotropism required for a Green Beard Effect would be an unusual coincidence.

The main part of my not-so-brilliant idea is that sex itself is a green beard. The very fact that an individual is willing to reproduce sexually is a reliable indicator that it carries prosexual genes. Provided the genes are only effective in the homozygote state (in other words, they are recessive to antisexual genes), then any individual who reproduces sexually can be sure that its offspring will receive two prosexual genes, one from each partner, and not just one, so the gene will not decline in frequency. Problem solved!

The Fallacy

To see that there must be a fallacy somewhere, consider a population of fixed size, with separate sexes in equal numbers, exclusively sexual reproduction, and no male contribution to offspring (as in the standard scenario). In such a population each pair will have two surviving offspring, on average one male and one female, who will continue the process in the next generation. Suppose now that a mutation in a female produces an antisexual gene, which causes the female to produce only clonal daughters. Such a female will have two daughters, each daughter will herself have (approximately) two daughters, and so on, all of whom will have antisexual genes. The frequency of antisexual genes in the population will therefore rapidly increase. Since the population is fixed, the number of daughters per asexual mother in each generation will gradually decline, but so will those of sexual mothers, and the asexuals will still squeeze out the sexuals until there are only asexuals, producing one daughter each per generation. This is of course not my example, but a familiar scenario due to John Maynard Smith, which he used to demonstrate what he called the 'twofold cost of sex'.

Since the 'green beard' effect of sex would still apply in such a scenario, but without preventing the elimination of sex, there must be a fallacy somewhere in the green beard idea. As often, it is easier to see that there must be a fallacy than to pin it down. I think the main explanation is that the true cost of sex is not the waste of genes, but the inefficiency of sexual reproduction under the standard scenario. In a stable population each male-female pair produces on average two surviving offspring. Since the male contributes no resources, the female alone evidently has enough resources to produce two offspring. These two offspring in turn mate with two other individuals and the four individuals produce four offspring between them, and so on. In a stable population reproducing sexually the number of surviving offspring is always the same as the total number of parents involved. But if one female has sufficient resources to produce two offspring, she could produce two female offspring by asexual reproduction. In this case each offspring would in turn have two offspring, and in each generation the number of female descendants of the original female will be approximately doubled, subject to the ceiling of the total population. They will always have an advantage over the sexual reproducers, because they are using the available resources twice as efficiently to produce offspring: N offspring per individual, instead of N offspring per couple. The cost of sex really has nothing to do with the division of genes. To dramatise the point, suppose a population reproduces entirely clonally, but with a system of environmental sex determination in which half the offspring are phenotypically males, who are unable to reproduce since the females do not need them. In this scenario there is no division of genes, but there is still an inefficiency in producing males, and any mutant gene which enabled females to produce only female offspring would have a rapid evolutionary success.

This suggests that the evolutionary problem of sex should really be split into two parts, of equal importance:

a) given that males usually contribute no resources, why is sexual reproduction so prevalent?


b) given that sexual reproduction is so prevalent, why do males usually contribute no resources?

The first question is the classic problem of sex, to which so many solutions have been offered.

The second question is relatively neglected, but at first sight seems almost equally problematic. If it so disadvantageous to females to mate with a non-contributing male, why is there not a strong pressure to select males who do contribute? After all, sexual selection is often a powerful and effective force. I suspect that the answer has two main parts. First, in plants and many animals, such as sessile invertebrates, there is physically no way that the male can contribute anything other than his sperm, and for well-known game-theoretical reasons, sperm is usually selected to be small. Second, even in cases where males could in principle contribute resources, they would often have no confidence of paternity, and they would lose more by committing resources to a female than they would gain in access to matings. If the female can obtain parental resources from one male, it will always be in her interest to 'cheat' and get the best available genes from another male if she can. Therefore male parental contributions seldom evolve.


There is of course a large literature on the evolutionary problem of sex, some of which I have read over the years. I wrote most of the above without referring to the literature, but after doing so I looked at a few surveys of the problem, such as John Maynard Smith's chapter in Behavioural Ecology, to check whether I had forgotten something important. I don't think so, but I see that there has been some discussion of whether the 'twofold cost of sex' is best described as a 'cost of meiosis' as a 'cost of producing males'. It seems clear that under the standard scenario there is no cost of meiosis as such, once the 'green beard' aspect is taken into account, whereas there is still a cost of producing males. On the other hand, under some non-standard scenarios there would be a cost of meiosis. To use an example of JMS, suppose a bird species reproduces sexually, with males and females providing equal resources. An antisexual gene in a female would then gain no advantage by suppressing meiosis if at the same time the female stopped mating and therefore no longer obtained resources from a male. But if she could suppress meiosis and still go through the mating process (which is perfectly plausible), she would gain the 'twofold advantage'. In this scenario it would therefore make some sense to talk of a cost of meiosis.

In my brief skim through the literature I did not find any analysis of sex as a form of altruism, or the related idea of sex as a Green Beard, but I dare say it is in there somewhere.