Parental expenditure

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Parental expenditure is a term used by R.A. Fisher in his 1930 book The Genetical Theory of Natural Selection to describe the opportunity cost that parents spend in producing and rearing children. Fisher stated that it is not strictly the the sex ratio (number of males to females) which is held at a constant 50:50 by natural selection. Instead, parental expenditure on children of both genders is what nature maintains at 50:50.

The sex ratio of sexually reproducing animals in the wild is usually 50:50. At first, this seems to make sense, if one considers a monogamous species such as humans. However, in a harem-based system such as that of elephant seals where 4 percent of males account for 88 percent of all copulations, the actual sex ratio of 50:50 seems to produce an excess of males who consume resources but end up leaving no offsprings. Furthermore, these excess males typically weigh about two to three times the weight of females. The puzzle of 50:50 sex ratio in the face of great evolutionary waste troubled Charles Darwin; he wrote that it would be safer to leave this problem for the future. Richard Dawkins in his book, River out of Eden, described how such seemingly wasteful production of males was solved by Fisher's concept of parental expenditure and the gene-centered view of evolution.

First, the 50:50 sex ratio is known to be evolutionarily stable. Every child has exactly one father and one mother. If reproductive success is measured by number of children produced, then the total reproductive success of all living males must equal that of all living females. If the sex ratio remains at 50:50, then males and females enjoy equal average reproductive success per individual. However, in a population of animals, the sex ratio could theoretically change over time, resulting in differences in average reproductive success between males and females. For instance, a sex ratio of 25:50 would make an average males twice as reproductively successful as an average female. Such inequality in reproductive success would give parents (in evolutionary speak) an incentive to produce more boys, assuming that parental expenditure is the same for boys and girls, and that both of them will have equal opportunities at mating in the future. Over time, such negative feedback by parents will bring the sex ratio towards the 50:50 equilibrium. Parents' choice of producing children belonging to the minority gender is said to be an evolutionarily stable strategy.

Secondly, even though the 50:50 sex ratio is established as evolutionarily stable, the harem problems in polygynous species still remains unanswered. Surprisingly, the same logic based on average reproductive success can be applied again to solve this problem, even though males in an elephant seal population have wildly different opportunities at mating. Imagine that 1 out of 10 male seals end up leaving descendants, and the rest 9 do not. This still does not change the average reproductive success for the set of 10 male seals as a whole, because the total reproductive success of males does not change. A parent seal which produces 10 male pups can expect, on average, nine of them to leave no descendants, and one of them to eventually mate with 10 females. As a result, the evolutionarily stable sex ratio in a harem system is still 50:50.

Fisher's theory of parental expenditure posits that it is the parental expenditure on male and female children which is held by nature at a constant 50:50, not the actual sex ratio. For instance, if it takes twice the amount of energy and effort to give birth to a male child compared to a female child, one would expect a sex ratio of 25:50, because for the price (parental expenditure) of one male child, a parent can afford to produce two female children.

The parental expenditures on male and female elephant seals appear to be equal, as the seal population shows a constant 50:50 sex ratio. This seems inconsistent with the massive size difference between males and females, as the much heavier male consumes more resources in order to grow to maturity. But data suggests that male pups and female pups attain equal weight at the time of weaning, indicating that the parental expenditure truly is equal for both male pups and female pups.

Parental expenditure does not explain why nature allows reproductively unsuccessful seals to consume valuable resources, at the expense of the community and the species as a whole. Such questions are answered by the theory of self gene and Dawkins' concept of the utility function. Nature does not try to optimize resource usage for the good of the species. Instead, the gene-centered view of evolution posits that individual genes maximize their own survival by constructing animals and directing their behavior, often with pitiless indifference to how the species as a whole fare.

Further readings

• Stephen Jay Gould (2002) The Structure of Evolutionary Theory. (pages 648-649, 678, and 692 on sex ratio)