Trivers–Willard hypothesis  

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Kunstformen der Natur (1904) by Ernst Haeckel
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Kunstformen der Natur (1904) by Ernst Haeckel

In evolutionary biology and evolutionary psychology, the Trivers–Willard hypothesis, formally proposed by Robert Trivers and Dan Willard in 1973, suggests that female mammals are able to adjust offspring sex ratio in response to their maternal condition. For example, it may predict greater parental investment in males by parents in "good conditions" and greater investment in females by parents in "poor conditions" (relative to parents in good condition). The reasoning for this prediction is as follows: Assume that parents have information on the sex of their offspring and can influence their survival differentially. While pressures exist to maintain sex ratios at 50%, evolution will favor local deviations from this if one sex has a likely greater reproductive payoff than is usual.

Trivers and Willard also identified a circumstance in which reproducing individuals might experience deviations from expected offspring reproductive value—namely, varying maternal condition. In polygynous species males may mate with multiple females and low-condition males will achieve fewer or no matings. Parents in relatively good condition would then be under selection for mutations causing production and investment in sons (rather than daughters), because of the increased chance of mating experienced by these good-condition sons. Mating with multiple females conveys a large reproductive benefit, whereas daughters could translate their condition into only smaller benefits. An opposite prediction holds for poor-condition parents—selection will favor production and investment in daughters, so long as daughters are likely to be mated, while sons in poor condition are likely to be out-competed by other males and end up with zero mates (i.e., those sons will be a reproductive dead end).

The hypothesis was used to explain why, for example, Red Deer mothers would produce more sons when they are in good condition, and more daughters when in poor condition. In polyandrous species where some females mate with multiple males (and others get no matings) and males mate with one/few females (i.e., "sex-role reversed" species), these predictions from the Trivers–Willard hypothesis are reversed: parents in good condition will invest in daughters in order to have a daughter that can out-compete other females to attract multiple males, whereas parents in poor condition will avoid investing in daughters who are likely to get out-competed and will instead invest in sons in order to gain at least some grandchildren.

"Condition" can be assessed in multiple ways, including body size, parasite loads, or dominance, which has also been shown in macaques (Macaca sylvanus) to affect the sex of offspring, with dominant females giving birth to more sons and non-dominant females giving birth to more daughters.

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