The mathematical formula that proves couples should NOT have sex on their first date” proclaimed a Daily Mail headline from last week. You’d have thought I would jump all over a story like this, much like I did for Blue Monday yesterday. The reason I’ve taken a few days to think about this post is because here we have a “formula” story with a difference – it’s actually science.
In a paper appearing in the Journal of Theoretical Biology entitled Duration of courtship effort as a costly signal, researchers Robert M. Seymoura and Peter D. Sozoud use a branch of mathematics called game theory to model a “courtship encounter” between a male and a female.
If you saw The Dark Knight last summer then you’ve seen game theory in action. In a re-working of a classic game theory problem, Heath Ledger’s Joker has rigged two ferries with explosives. On one, the good citizens of Gotham. On the other, a prison-load of thugs and criminals. The Joker, maniac that he is, gives the detonators of each ship to the other ship – so that the citizens can choose to blow up the criminals, and vice versa. He informs them that if they killer their counterparts in the next 30 minutes they will be spared, otherwise he’ll just blow up both ships.
Game theory informs us that the best strategy is for one ship to blow up the other – but of course, this means that both ships will be destroyed anyway, just as the Joker planned. Thankfully, dramatic forces (and Batman) intervene before anyone is harmed. If you want to know more about the maths behind it, a decent explanation is here, but my point is that game theory is a genuine branch of mathematics, and not some crackpot PR nonsense.
The game considered in this paper consists of a male and a female (of any species) engaging in courtship. As time goes on, both parties pay a “cost” for participating in the game. In a human context, this might be a man paying for dinner, whilst the woman he is dating suffers a “cost” to her time – i.e., she might be wasting the evening with an unsuitable mate when she could be finding someone more to her liking. The model also takes into account other species however, for example a male bird singing to a female.
The game ends either when one of the two quit playing (give up to try with someone else) or the female accepts the male as a mate. It is also assumed that males are either “good” or “bad” from the female’s perspective, but she isn’t able to tell good from bad directly. It is only when the pair mate that the female receives a positive payoff from a “good” mate, or a negative payoff from a “bad” one.
The research shows that when the game plays out, a “good” male will participate longer than a “bad” male, allowing the female to weed out a suitable mate: the longer they hang around, the more likely it is that the male will be “good”. Now, this is quite far off from the Daily Mail headline, but the point is that in this case the science is sound. The authors admit that their generalised species model probably doesn’t fit well with humans, especially in a society where contraceptive is readily available. What this research provides is a possible explanation for the evolution of lengthy courtships in many species, including humans. It may not be earth-shattering, but it is science.
R SEYMOUR, P SOZOU (2009). Duration of courtship effort as a costly signal Journal of Theoretical Biology, 256 (1), 1-13 DOI: 10.1016/j.jtbi.2008.09.026