The truthful signalling hypothesis: an explicit general equilibrium model

Non-random mating involving inheritance of social status

We propose a unified theoretical scheme to calculate genotype frequencies of polymorphic populations with biological and social inheritance. This scheme is used to simulate the effects of social non-random mating on the population's evolution in the general situation of multiple biological gene loci and allele inheritance with natural selection and mutation. We study the case of hemophilia in several diverse situations when there exists non-random mating due to inheritance of social status. This study clearly shows that interaction between the social and the biological gene has significant impact on the population's evolution.

A two-sex life history model of handicap signaling

The males of many species (such as peacocks) develop excessively large traits, which appear to interfere with their agility and hence survival probability. Moreover, it is also observed that females seem to prefer mating males with such clumsy traits. Zahavi (1975) proposed a handicap theory to explain this phenomenon, suggesting that this trait/preference interaction is a way in which strong males can signal their viability by yielding a handicap in terms of a clumsy trait size. This paper presents a two-sex model of selfish genes that generates this particular male-female interaction, and characterizes the conditions behind a handicap equilibrium. We first show the female dominance result of Bateman (1948) in this two-sex model, and then specify the relevant equilibrium conditions, including the incentive compatibility condition for females, the individual rationality condition for males, and the stability condition of population composition. Identifying these conditions helps us understand the various features of the searching/signaling of sex selection in evolution.

Truthful signalling, the heritability paradox, and the Malthusian equi-marginal principle

The article shows that heritable quality differentials are consistent with the Zahavi Handicap Principle (the Truthful Signalling Hypothesis (TSH)). Earlier analyses have assumed non-heritable quality. The crucial innovation is the Malthusian equi-marginal principle: under selection pressures the relative numbers of higher- and lower-quality organisms will change until, in equilibrium, not the average but the marginal levels of quality will be equalized. Assuming kin selection, each male maximizes his own reproductive success and signals until the marginal value of more signalling is zero. We further require evolutionary stability; displacements to higher or lower population sizes must be restored to equilibrium. The article proposes an alternative to Fisher's [1958. The Genetical Theory of Natural Selection. Dover Publications, Inc., New York [Original publication 1929]] and Hamilton and Zuk's [1982. Heritable true fitness and bright birds: a role for parasites? Science 218, 384-387] suggestions. The model is solvable for ranges of parameters that constitute the stable region. We particularly consider the unit signalling costs of the high- and low-quality males, where it has been widely believed that for a TSH equilibrium the former must be lower than the latter. This article confirms our earlier result that this is not a necessary condition for a truthful signalling equilibrium, though the unit signalling costs of the high-quality males cannot be too much larger.

Maynard Smith: amplifying the reasons for signal reliability

One of the many questions to which John Maynard Smith contributed was that of why most animal signals are reliable. He initially rejected the "handicap" argument but gradually accepted it, a process I briefly describe. This episode illustrated his preference for mathematical models over verbal ones, and the generosity with which he could change his mind. Even after accepting that some signals are reliable because of their strategic costs, he argued for a pluralistic approach to signal reliability. Signal complexity was a developing interest when he died. Signals usually involve several components, some of which appear to amplify other signal components. The terms "amplifier" and "index" require more thought to reduce the scope for semantic confusion. I conclude by describing Maynard Smith's fascination with peacocks Pavo cristatus.