Trivers-willard rules for sex allocation : When do they maximize expected grandchildren in humans?

We present a quantitative model of sex allocation to investigate whether the simple "rules of thumb" suggested by Trivers and Willard (1973) would really maximize numbers of grandchildren in human populations. Using demographic data from the !Kung of southern Africa and the basic assumptions of the Trivers-Willard hypothesis, we calculate expected numbers of grandchildren based on age- and sex-specific reproductive value. Patterns of parental investment that would maximize numbers of expected grandchildren often differ from the Trivers-Willard rules. In particular, the optimum parental behavior is sensitive to population dynamics, type of parental investment, and, most important, relative ages of sons and daughters. It is doubtful whether a parent blindly following the simple Trivers-Willard rules would maximize numbers of expected grandchildren, on average. In addition, we show that sex-specific infanticide will almost never achieve the goal of maximizing expected numbers of grandchildren.