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.