In 1971, George C. Williams conceived the evolutionary cost of sex as the cost of reducing the genome during meiosis:
“[...] in meiosis, the number of chromosomes and constituent genes is reduced by half. Each resulting gamete, and zygote that is formed by fertilization, will have a sampling of half the genes of the individual that provides the gametes. In the usual mitotic divisions, each resulting cell preserves the entire genome intact. [...] These parthenogenetic eggs would each contain twice as much of the mother's genotype as is present in a reduced and fertilized egg. Other things being equal, the parthenogenetic female would be twice as well represented in the next generation as the normal one. […] Sexual reproduction is analogous to a roulette game in which the player throws away half his chips at each spin. The game is fair as long as everyone behaves in this way, but if some do and some don't, the ones who keep their chips have an overwhelming advantage and will almost certainly win.” (Williams 1971, p. 13)
Here, Williams starts with a 50% vs. 100% genome transmission argument, also known as genome dilution, but at the end the sociobiological notions of cheating slips in.
The following fixed the term cost of meiosis:
“Only Maynard Smith (1971a, b) has attempted to give the short-range problem an exact formulation and to consider the possibility of an individual advantage in sexual reproduction. He concluded that sexual reproduction (except in internalized hermaphrodites) has, roughly, a 50% disadvantage in relation to to asexual reproduction. This corresponds to the 50% loss of genetic material in meiotic oogenesis. There may be other disadvantages, such as the generation of recombinational load, and some possible minor advantages in genetically diverse, rather than uniform progenises, but what might be termed the cost of meiosis must be the overwhelming consideration.” (Williams and Mitton 1973, p. 546)
In 1975, the 50% reduction of the genome becomes a 50% hazard of genes coding for sex (the gene’s eye view) and some qualifications are added:
“Each “sex gene” suffers a 50% hazard per generation, relative to asexual alternatives." (Williams 1975, p. 9)
“The 50% cost of meiosis applies to outcrossed but not to self-fertilizing hermaphrodites.” (1975, p. 10)
“If males assist females in raising the young, the cost of meiosis is reduced (Maynard Smith 1971A), unless it is possible for a female to get a male to help raise parthenogenetic young. The primary task for anyone wishing to show favorable selection of sex is to find a previously unsuspected 50% advantage to balance the 50% cost of meiosis.” (1975, p. 10f)
However, Maynard Smith argued against genome dilution:
“No such immediate two-fold disadvantage is associated with sexual reproduction in organisms with isogametes, as is apparent if one considers the biomass associated with each genome rather than the number of cells. Since sex and meiosis almost certainly preceded anisogamy, this disadvantage of sex need not be taken into account when considering the origin of sex, although it is highly relevant when considering its maintenance in higher organisms.” (Maynard Smith 1974, p. 300)
“Some of the confusion which has arisen over this came, I think, for the phrase ‘the cost of meiosis’. In a species with isogametes there is no necessary twofold cost associated with meiosis, although the time taken to complete the meiosis division might constitute a cost. In a sense, a gene is in a primary oocyte is running a 50% chance of being eliminated in a polar body, and could therefore gain a twofold selective advantage by suppressing meiosis. But I believe that the twofold advantage of parthenogenesis is best seen as the advantage of not producing males.” (Maynard Smith 1978, p. 3)
This cost of males is now the prevalent conception and, in the heads of the peers, the cost of meiosis has been frozen as an argument about genome dilution, no matter how much Williams developed it towards a sociobiological concept (Lively 2010; Lehtonen et al. 2012). Nevertheless, Williams continued to pursue another route that lead him to an increasingly sociobiological conception. That is, 50% vs. 100% transmission turned into coefficients of relatedness (0.5 vs. 1):
“Much of the importance and complexity derives from variation in degrees of relationship arising from sexual reproduction, in which a halving of the chromosome number (meiosis) in eggs and sperm, and subsequent fertilization, are the essential features. Without this chromosome cycle, all the coefficients of relationship would be one or zero (complete genetic identity or total independence) , and much of the complexity of interactions among organisms would presumably disappear.” (Williams 1980, p. 371)
“What would be gained by an individual, in an otherwise sexual population, who cheated by eliminating meiosis and fertilization from its production of an offspring, but remained otherwise the same?” (Williams 1980, p. 372)
“If the fusing gametes are equal, neither parent seems to be subsidizing the reproduction of the other. In a more important sense this conclusion is wrong. Given that one cell fuses with another, we can then ask about the consequences of whether it plays the sexual game (meiosis) in its next cell division, or cheats (mitosis). It then becomes clear that the 50% cost of meiosis is still very much a reality.” (Williams 1980, p. 377)
In a ‘Retrospect on sex and kindered topics’, Williams (1988) reasserts his claim that isogamy still involves a cost of sex and thereby arrives at an entirely sociobiological conception.
“I do not agree with Felsenstein that there would be no cost of meiosis without the prior evolution of anisogamy. At the least I would suggest that the modeling Felsenstein has in mind is not the most instructive that can be devised. I have already published some arguments to this effect (Williams, 1980), but will try another here. Perhaps it is just a matter of time before someone discovers (or invents in the laboratory) an all-male species. It makes diploid sperm that inseminate eggs of a related species and give rise to diploid nuclei that exclude the egg pronuclei. [...]
The point of the story is that any male of any species that refrains from such egg piracy is paying a cost of meiosis as a direct result of the haploid and cytologically cooperative behavior of its sperm. [...]
It should be noted that while a cost of meiosis is readily recognizable in my all-male species, a cost of males is not, at least not as an aspect of selection at the individual level.” (Williams 1988, p. 294)
Williams’s reference to Felsenstein, here, means a chapter in the same volume that denies a problem with the evolution of sex beyond recombination (Felsenstein 1988, p. 74). In a comment on the previous post, Felsenstein dismissed Williams's idea of androgenesis (that's the term under which such egg parasitizing all-male species are nowadays studied) on the assumption that producing diploid sperm is twice as costly as producing haploid sperm. As meiosis takes time and energy in order to reduce the diploid genome, this seems to be an unlikely assumption. Moreover, the cost for producing sperm should in absolute units be a tiny fraction of the cost of sex. Therefore, even if the assumption was correct, paying twice the cost for making diploid sperm would not cancel the advantage of saving the cost of sex.
IMHO, Maynard Smith defined the cost of sex at the individual level and Williams (1980, 1988) at the cellular level of gametes. Morphologically different sperm and eggs do not exist in isogamous species and hence the cost of males does not exist either. The cost of cooperation among unrelated gametes, the cost of not cheating, also exists in out-breeding isogamous species.
References
- Felsenstein J (1988) Sex and the evolution of recombination. In: RE Michod and BR Levin (eds) The evolution of sex. Sinauer Associates, Sunderland, MA
- Lively CM (2010) A review of red queen models for the persistence of obligate sexual reproduction. J Heredity 101: S13-S20
- Lehtonen J, Jennions MD, Kokko H (2012) The many costs of sex. Trends Ecol Evol, in press
- Maynard Smith J (1974) Recombination and the rate of evolution. Genetics 78: 299-304
- Maynard Smith J (1978) The evolution of sex. Cambridge Univ Press, Cambridge
- Williams GC (1971) Introduction. In: Williams GC (ed) Group selection. Aldine Transactions, New Brunswick, NJ
- Williams GC (1975) Sex and evolution. Princeton Univ Press, Princeton, NJ
- Williams GC (1980) Kin selection and the paradox of sexuality. In: Barlow GW and Silverberg J (eds) Sociobiology: beyond nature/nurture? Reports, definitions and debate. AAAS Selected Symposium 35, Westview Press Inc., Boulder, Colorado
- Williams GC (1988) Retrospect on sex and kindered topics. Pp. 287-298 in: Michod RE and Levin BR (eds) The evolution of sex: an examination of current ideas. Sinauer Associates, Sunderland, Massachusetts
- Williams GC, Mitton JB (1973) Why reproduce sexually? J. theor. Biol. 39: 545-554
