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The two-fold cost of sex explains why it might not be so advantageous to be a sexually reproducing organism.

John Maynard Smith (1978) asked us to imagine a population of sexually reproducing individuals, in which a mutation occurs, allowing a female to reproduce asexually. He also makes two assumptions:

1. The number of offspring a female makes is independent of her mode of reproduction.
2. The probability that an offspring will survive to reproduction is independent of whether that individual was produced sexually or asexually.
Finally, keep in mind that the offspring of a sexual mother are half male and half female., while the offspring of an asexual female are all female.

There will be no average differences in the number of offspring between the mothers, but in the second generation, the two-fold cost of sex becomes apparent. Each daughter produced by the asexual female produces her own daughters. The sexual female, however, has only half as many daughters as the asexual female (because her other offspring were sons.) So while these daughters produce as many offspring as the daughters of the asexual, there are only half as many around to do it. This difference will become magnified each generation. This idea can be illustrated as:

```
Generation           Sexuals            Asexuals            Fraction of
population that are
asexual

1                F x M                  F                   1/3

|                    |
v                    v

2           F x M    F x M      F    F    F    F            1/2

|        |        |    |    |    |
v        v        v    v    v    v

3           F x M    F x M      F    F    F    F            2/3
F x M    F x M      F    F    F    F
F    F    F    F
F    F    F    F

```
So given this logic, asexual reproduction seems to be twice as good as sexual reproduction, and ought to quickly dominate in a sexual population. Yet it clearly has not totally taken over, so something is amiss. If the conclusion of our logic is violated, than it must be that one of our assumptions is incorrect. The first assumption, that the number of offspring which females can produce is independent of mode of reproduction might be violated in species in which males care for offspring. While there are a few cases where female fecundity seems to be limited by male parental care, in most species males provide nothing more than their genes. So the second assumption is probably the place to look.

Before I go on, I should note that in the long run, an asexual population might be doomed to extinction because it is unable to purge its unfit genotypes. (This is Muller's ratchet.) But despite this potential fate, the short term advantage of asexual reproduction should lead it to take over the population. The problem is to discover if there are short-term advantages to sexual reproduction.

If the second assumption has been violated, it means that asexual offspring should be less likely to survive and reproduce. (In other words, they should have lower fitness.) Sexual recombination helps to purge a population of deleterious mutations, so this may play a role. This can only work in the short run if the rate of deleterious mutations is high, and synergistic epistasis effects these mutations. Many others have proposed that sex is advantageous is rapidly changing environments, because it creates novel genotypes which may be more fit in the new environment.

Is there any evidence for these proposed mechanisms? The role of sex in purging deleterious mutations is consistent with evidence on mutation rates, but has hardly been tested. There is considerably more evidence for the advantage of sex in heterogeneous habitats. For example, many plants have genotypes which perform best in different microhabitats. A novel genotype may be able to exploit resources which are unused by other individuals. Experiments with certain grass species have shown that individual plants have higher fitness if grown in competition with different genotypes than with their own genotypes. This suggests that by producing novel genotypes, sex is beneficial in habitats which are heterogeneous.

Another widely cited example of the advantage of sex in heterogeneous habitats is from the geographic distribution of sexual and asexual organisms. In both plants and animals, asexual organisms are more common at high latitude and high altitude. In general, these areas are very harsh physically, but have less complex biota. It may be that sex is adaptive in complex environments, which are constantly changing. In these cases, novel genotypes are required to deal with the continuously shifting pressures of predators, parasites and competitors.

Given how wide spread sexual reproduction is, there must be some benefit to overcome the two-fold cost of sex. The ability to produce novel genotypes and the ability to purge deleterious mutations probably play a role as well. We don't have all of the answers yet, and further theoretical work, as well as experimental testing of these ideas, will be required to determine what factors overcome the two-fold cost of sex.

For more on this topic, see a good textbook on evolution, such as the following two, from where much of this discussion was drawn:

Freeman, S. and Herron, J.C. (1998) Evolutionary Analysis. Prentace-Hall Pp 191-203

Futuyma, D.J. (1998) Evolutionary Biology. 3rd Ed. Sinauer Associates. Pp 606-612.

Or see:

Maynard Smith, J. (1978) The Evolution of Sex Cambridge University Press.

I think that this is a difficult topic, and I fear that my write up is somewhat myopic. Please /msg me with questions so that I can improve it.