Today I present the simulation “HamiltonianHandicap” (download), a case of the Handicap Principle. HamiltonianHandicap is one of the more intuitive cases of HP, based on the work of William Hamilton: The advertisement (handicap) costs almost nothing to a healthy male, but is very costly to an ill male. Here is an example given by Richard Dawkins:
[…] think of the spectacularly long tail of a male bird of paradise. […] A common symptom of disease in a bird is diarrhoea. If you have a long tail, diarrhoea is likely to mess it up. If you want to conceal the fact that you are suffering from diarrhoea, the best way to do it would be to avoid having a long tail. By the same token, if you want to advertise the fact that you are not suffering from diarrhoea, the best way to do so would be to have a very long tail.1
The Handicap Principle, when applied to choosing a partner, is similar to Sexual Selection in that both are self-sustaining. The difference lies in the way the self-sustaining loop emerges. In ordinary sexual selection, females first start favoring males with a trait because that trait is advantageous in and of itself, but can keep doing so even when the trait becomes disadvantageous. With the Handicap Principle, females start favoring males with a trait because it communicates their quality (not because it’s disadvantageous — that’s a misunderstanding). Therefore, it is interesting to start with only a small percentage of advertising males and selective females.
In this sim, each animal has the following genes:
- sex
- health (true = healthy, false = sick)
- advertise (true or false)
- partner selection strategy
Health and advertisement are only expressed in males, selection strategy only in females. A female sees whether a male advertises, and if yes, whether he is healthy or (genetically) ill. That is, she sees one of three possibilities. The selection strategy is represented by a vector of length 3, giving a rating to each of those possibilities. When a female selects among several males, she first selects those males to whom she gives the maximum rating, then among those, one at random. Initially, most females have a neutral selection strategy (all males have the same rating), and a small part have random strategies, that is, they can prefer any of the three visible possibilities, or even more than one — some ratings may be equal.
The survival score a male receives depends on both health and advertisement, and all four combinations receive different scores. The highest is for a healthy non-advertising male. A healthy advertising male receives a very slightly lower score — if his score is much lower, he will prefer not to advertise. The reason I didn’t just give him the same score as to a healthy non-advertising male is that in real life, nothing is free. An ill male, of course, has a lower score, and if he advertises, even lower (otherwise that wouldn’t be a handicap).
The survival of females doesn’t depend on health or advertisement — each female receives the survival score of the average male, so that about half the population are females, and all females have equal survival chances.
Instead of Mendelian genetics, here each animal has only one version of each gene, and each child inherits the gene from one of its parents at random. This avoids the asymmetry between the dominant and recessive genes. There is also a small probability of mutation from healthy to ill, intended to keep the advertisement relevant.
Since selection strategies don’t mutate, it’s important to have a large enough number of selective females initially in order to ensure diversity and to be able to watch the different strategies compete. Therefore, either the population or the initial selectors percentage has to be big. I prefer the former: as I said, I’m interested in emergence.
Graphs: health + advertisement selectors are those females that rate healthy advertising males higher or equally to the other two groups. strict h+a selectors are those that give healthy advertising males the strictly highest ratings. In both cases the ratios are among all selective females. As an extra output after the simulation stops, the variable selection contains the strategies of all selective females, and its statistics are printed.
Technical: This time, the code is not Matlab-compatible, so it will only run on Octave with the “gnuplot” toolbox installed. To stop the simulation, press “Enter” in the command window.
Enjoy. If you have any feedback, I’ll be glad to hear it.
1 Richard Dawkins: The Selfish Gene, 30th anniversary edition, page 306, Oxford University Press, 2006.
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