The rarer-sex effect

Abstract

The study of sex allocation-that is, the investment of resources into male versus female reproductive effort-yields among the best quantitative evidence for Darwinian adaptation, and has long enjoyed a tight and productive interplay of theoretical and empirical research. The fitness consequences of an individual's sex allocation decisions depend crucially upon the sex allocation behaviour of others and, accordingly, sex allocation is readily conceptualized in terms of an evolutionary game. Here, I investigate the historical development of understanding of a fundamental driver of the evolution of sex allocation-the rarer-sex effect-from its inception in the writing of Charles Darwin in 1871 through to its explicit framing in terms of consanguinity and reproductive value by William D. Hamilton in 1972. I show that step-wise development of theory proceeded through refinements in the conceptualization of the strategy set, the payoff function and the unbeatable strategy. This article is part of the theme issue 'Half a century of evolutionary games: a synthesis of theory, application and future directions'.

Keywords: consanguinity; game theory; reproductive value; sex allocation; sex ratio; unbeatable strategy.

Figure 1.

The history of the rarer-sex effect. (a) Charles Darwin first formulated a theory of the rarer-sex effect, focusing upon equalization of the adult sex ratio, in 1871. (b) Karl Gerhard Düsing provided a mathematical analysis, based on number of grandoffspring, in 1883. (c) Corrado Gini clarified aspects of the logic, but ultimately rejected the principle, in 1908. (d) John Austin Cobb (shown here aged 13–14 in 1880) reframed the theory in terms of the sex ratio of newborns, parental expenditure and reproductive value in 1914. (e) Ronald Aylmer Fisher provided a mathematical account of reproductive value in 1927 and 1930. (f) William Donald Hamilton incorporated consanguinity and developed the concept of the unbeatable strategy between 1964 and 1972. Image credits: (a) public domain; (b) Hauke Heinecke; (c) Italian National Institute of Statistics, [7]; (d) Clive Cobb; (e) public domain; (f) Sarah Hrdy.