According to the Trivers-Willard hypothesis, females of polygynous mammal species can adaptively modify offspring sex ratio, which would provide them evolutionary benefits in terms of a higher number of grand-offspring. In red deer (Cervus elaphus), a species where the reproductive success of males is significantly more variable than that of females, mothers that are in good condition are expected to have a male-biased offspring sex ratio but only in a population below carrying capacity. We aimed at testing the Trivers-Willard hypothesis on a low-density population of red deer in large woodlands of north-eastern Poland. The overall foetal sex ratio did not differ from parity. The mother’s probability of having male offspring increased with her body mass independently of age and population density. Such condition-based adjustment of the offspring sex ratio in female red deer from a low-density population conforms to the Trivers–Willard hypothesis. However, full support of Trivers–Willard predictions would require further investigations comparing survival and reproductive output of male and female offspring.
For the actual science of this story, you should definitely read the paper and contact the authors if you have any questions.