What did Trivers and Willard really predict?

Abstract

Correspondence: J. Carranza, Catedra de Biologia y Etologia, Facultad de Veterinaria, Universidad de Extremadura, 10071 Caceres, Spain (email: carranza@unex.es) The issue raised by Trivers & Willard (1973) on the ‘natural selection of parental ability to vary the sex ratio of offspring’ has produced many publications. Probably no other case exists in behavioural ecology where a couple of pages have sired so many studies. With so many descendants, however, mutations are likely to emerge. One main problem is that the Trivers–Willard (TW) hypothesis was a verbal argument and hence semantic interpretations are possible. For instance, TW wrote that ‘females in better condition tend to invest in males’. This may be interpreted in different ways, regarding either the way of allocating the investment or the nature of the comparison, as follows: (1) females in better condition tend to produce bigger (or costlier) male offspring than female offspring or they tend to produce bigger (or costlier) males than females in poor condition; (2) females in better condition tend to produce more male offspring than female offspring or they tend to produce more males than females in poor condition. Furthermore, these statements may lead to complementary ones such as: (1) females in poor condition tend to produce bigger female than male offspring or they tend to produce bigger females than other females; (2) females in poor condition tend to produce more female than male offspring or they tend to produce more females than other females. One needs only to read the original TW paper carefully (or subsequent reviews discussing it: e.g. Frank 1990; Godfray & Werren 1996; Hardy 1997) to see that some of these interpretations are not in concordance with Trivers and Willard’s ideas. I do not intend to review the TW hypothesis comprehensively here, although a simple graphical model may help to put these thoughts into a framework. Figure 1a represents the hypothetical relationship between the fitness return of a female or a male offspring and the amount of care it receives (r). I believe this represents the conditions of the TW model, and I