Sex-ratio optimization with helpers at the nest

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Abstract
In many cooperatively breeding animals, offspring produced earlier in life assist their parents in raising subsequent broods. Such helping behaviour is often confined to offspring of one sex. Sex-allocation theory predicts that parents overproduce offspring of the helping sex, but the expected degree of sex-ratio bias was thought to depend on specific details of female and male life histories, hampering empirical tests of the theory. Here we demonstrate the following two theories. (i) If all parents produce the same sex ratio, the evolutionarily stable sex ratio obeys a very simple rule that is valid for a general class of life histories. The rule predicts that the expected sex-ratio bias depends on the product of only two parameters which are relatively easily measured: the average number of helping offspring per nest and the relative contribution to offspring production per helper. (ii) If the benefit of helping varies between parents, and parents facultatively adjust the sex ratio accordingly, then the population sex ratio is not necessarily biased towards the helping sex. For example, in line with empirical evidence, if helpers are produced under favourable conditions and parents do not adjust their clutch size to the number of helpers, then a surplus of the non-helping sex is expected.