Inclusive Fitness Theory and the Haplodiploidy Hypothesis
Hamilton’s inclusive fitness theory, the ‘genetical mathematical model’ presented in the 1964 article, explained the conditions favoring the increase in frequency of a gene with altruistic effects in a population (Hamilton 1964a). The so-called Hamilton’s rule roughly summarizes Hamilton’s ideas about the conditions favoring this process (Charnov 1977). In its condensed version, the formula shows that altruism can evolve if: br > c, where r is a measure of the degree of relatedness, the fraction of genes shared by the altruistic actor (let’s say a worker wasp) and the recipient of the altruistic action (let’s say, the brood of the queen wasp they help to raise) as a result of common descent; b and c are respectively the costs to the actor and benefits to the recipient.
According to this rule, under the right circumstances, it is not against Darwinian rules that some individuals direct altruistic behaviors towards their close relatives, who are more likely to share with them the same genes. Talking from a gene’s eye view perspective, a gene with altruistic effects can spread in a population if it favors the fitness of those individuals who bear copies of that same gene. This means that, in order for a gene to transmit copies of itself in a population, it is not necessary that it gets transmitted directly in the offspring of the individuals bearing it. If its bearers helps members in the population that are related to itself, then it indirectly helps the transmission of copies identical to itself in other members of the population. Thus, Hamilton wrote: “The social behavior of a species evolves in such a way that in each distinct behavior-evoking situation, the individual will seem to value his neighbors’ fitness against his own according to the coefficients of relationship appropriate to the situation” (Hamilton 1964b, 19).
In Part II of the 1964 paper, Hamilton presented his famous hypothesis about how inclusive fitness theory might apply to the evolutionary emergence of altruistic behaviors in social insects of the order Hymenoptera (Hamilton 1964b). Insects of this order have an unusual sex determination pattern, so called haplodiploidy, as females are diploid, say they have a double set of chromosomes, whereas males are haploid, say they have only one set of chromosomes. Haplodiploidy entails that females on average share more genes with their sisters than with their own offspring. On average, in case of single insemination and in absence of inbreeding, the amount of genes that a female shares with her own sister is %, whereas the amount of genes that she shares with her own offspring is /. This is why, the haplodiploidy hypothesis is also named the ‘% relatedness hypothesis’ (for instance, West- Eberhard 1975).
The haplodiploidy hypothesis suggests that, the frequent evolution of sterile workers in Hymenoptera might be the result of the unusually high relatedness of hymenoptera sisters due to male haploidy, which leads to all sperm produced by a male being identical. This means that a female may well be able to get more genes into the next generation by helping the queen reproduce, hence increasing the number of sisters she will have, rather than by having offspring of her own. Although it is still unclear how much stress Hamilton put on explanatory power of this hypothesis (Segerstrale 2013), it seemed that the theory of inclusive fitness could provide an explanation of how sterility might have evolved in Hymenoptera by focusing most importantly at the % relatedness between self-sacrificing workers and the brood they attend (Hamilton 1964b).