from here to paternity

Oooh, he’s got his father’s eyes/hands/vacant expression. Such are the comments every new parent has to tolerate. Never mind that three-week-old ricardito looks like your standard generic infant: he apparently has my nose (`nicely rounded’ says the mother-in-law; `bulbous’ sighs the wife).

The degree to which newborn babies resemble their fathers is, of course, interesting from an evolutionary perspective. Males don’t want to invest resources rearing other males’ children, and so looking like your father can be adaptive. The catch is that it’s only adaptive if your father is in fact the male proposing to rear you. It might equally suit philandering bandits (and their female partners) to have children that at most resemble their mother. Empirically the matter seems not to be settled, as a glance here indicates, but it does appear that infants’ likeness to their fathers is not great.

[Aside: I’m not sure how, or even if, such empirical studies account for the fact that any lack of paternal resemblance in the study group can arise for two reasons: first, that kids don’t look like their fathers all that much; second, that their fathers might not be their fathers. ]

Sticking to theory, what range of `strategies’ might we expect to see in macro equilibrium once we take the above forces into account? If we lump mating behaviour in there too, my hunch is that we should observe equilibria where both {adultery, no paternal resemblance} and {fidelity, paternal resemblance} strategy combinations are played. From the male viewpoint, resemblance is only adaptive if one is in danger of being cuckolded by philanderous bandits playing the first strategy pair, while banditry only pays if there are potential cuckolds out there.

This at first seems to predict an `arms race’ along the resemblance dimension. One problem with this idea, though, is that there’s an inherent asymmetry. The philanderer can’t make his offspring resemble the cuckold, since there’s no gene for that; at best, the offspring will look like the mother.

In these circumstances, why wouldn’t a faithful male (also `playing’ the paternal resemblance strategy) leave if there is no such resemblance and his mate’s child resembles her alone? This paper (discussed here) introduces another strategy level, that of deceit and gullibility. It is obviously in the mother’s interest always to tell her mate that the baby looks like him, regardless of the actual paternity. A main result of the paper is that it may be in the mate’s interest to believe her, as long as the probability of deceit is low enough that the expected benefit from sticking around exceeds the expected opportunity cost.

The problem with this story is that `low probability of deceit’ equals ‘low proportion of bandits’. And a low proportion of bandits is just not consistent with stable equilibrium if the non-bandits are gullible and babies do not overly resemble their fathers. Philandery will be highly adaptive, bandits will flourish and gullibility will cease to be adaptive.

Something is missing here. I’ll have to think.


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