Hamilton’s haplodiploidy hypothesis and the females who do all the work

In this post Nick Davies, who is doing his DPhil between the WCMB and the Foster lab in Zoology, provides some history on the long-standing question of why worker castes in social colonies of wasps, bees, and ants are exclusively female.

“also they put a litle of the Sugar in a porrenger, and that in the midst of a flatter Dish filled with Water: and [...] these Wonderfull Creatures discerning it to be there, (whether by Instinct or Smell I cannot say [...]) they came about the Dish, and at last put forward into the Water, till so many were drowned that they made a Bridge with their Bodies for their fellows, over which they went to and fro till they had carried away the Sugar. This another Knight, his brother, and all the Famelie testified. Which if true, it shews these litle Generous Creatures to be very resolute in Sacrificing their Lives for the Benefit of their Country, and very magnanimous in despising their privat Satisfaction, in comparison of the Advantage of all the Societie, as well as faithfull in their Trust, and of very great and public spirits: being free from that vice wherby men are apt having found a Treasure to appropriat it all by stealth to themselvs, and to envy others the Enjoyment of it.”

— Thomas Traherne (1637–1674), Commentaries of Heaven

Fire ants forming a raft. Source: National Geographic.

The social hymenoptera—ants, bees, and wasps living in tightly regulated colonies where a specialized, sterile worker caste devotes itself to raising its siblings—have long fascinated naturalists. The above anecdote about ants from the 17th-century poet and clergyman Thomas Traherne illustrates one of the defining characteristics of the social hymenoptera: self-sacrifice for the “Advantage of all the Societie”. As with other examples of altruism, these acts can seem, at face value, to contradict what we know about natural selection. If survival of the fittest requires individuals to maximise their own reproductive success, why are these “Wonderfull Creatures” so willing to lay down their own lives in order to help others?

The answer, as we now know, lies in kin selection. Behaviour is influenced by genes, and we normally expect a gene variant that brings harm to its host—say, by increasing curiosity about a natural predator—will not spread through a population. But could a gene that harms its host nevertheless succeed at spreading through natural selection? It turns out that there are a number of ways this can work. One of these ways is kin selection, which relies on the fact that genes tend to be more closely shared between relatives. If there is an altruistic action which greatly benefits an individual’s close relatives, then even if it causes harm to the altruist, a gene encoding that action can still be favoured by natural selection, because the altruist’s relatives have a high probability of also having the gene for the altruistic behaviour, and their fitness is increased by the altruistic individual’s behaviour.

This is how we explain behaviours like alarm calls. If a ground squirrel spots an approaching coyote, and the squirrel has a gene that causes him to emit a loud trill at this sign of jeopardy, the noise may draw the coyote’s attention to him and could well endanger his life. However, if the warning saves the lives of his brother and sister squirrels, many of whom will share the alarm-call gene, they may be more likely than other squirrels in the larger population to survive to reproductive age, thus indirectly passing on the altruist’s alarm-call gene. Crucially, the more closely related a pair of individuals is, the more likely they are to share any given gene; hence the geneticist J. B. S. Haldane’s tongue-in-cheek (and possibly apocryphal) remark, in response to being asked whether he would sacrifice his life to save a drowning brother: “No, but I would to save two brothers, or eight cousins”.

A Belding’s ground squirrel watches for approaching predators. Source: Wikipedia.

As with many 20th-century developments in evolutionary theory, the idea of kin selection can readily be traced back to Darwin. In a famous passage in the Origin of Species (1859), he wrote:

“a well-flavoured vegetable is cooked, and the individual is destroyed; but the horticulturist sows seeds of the same stock, and confidently expects to get nearly the same variety: breeders of cattle wish the flesh and fat to be well marbled together; the animal has been slaughtered, but the breeder goes with confidence to the same family. I have such faith in the powers of selection, that I do not doubt that a breed of cattle, always yielding oxen with extraordinarily long horns, could be slowly formed by carefully watching which individual bulls and cows, when matched, produced oxen with the longest horns; and yet no one ox could ever have propagated its kind.”

(This example is made clearer when we remember that an ox is a castrated bull.)

It was the evolutionary biologist W. D. Hamilton (1936–2000), however, who was largely responsible for formalizing and popularizing kin selection, in the 1960s. He formulated the inequality now known as ‘Hamilton’s Rule’: if a trait costs C units of reproductive success to one individual, but provides B units of benefit to a second individual or class of individuals, who is/are related to the first individual by a relatedness coefficient of r, and the inequality

rB > C

holds, then the trait will be favoured by natural selection. When rB = C, the trait is selectively neutral, and when rB < C, it will be disfavoured. For example, in humans, brothers are related by r = 1/2, whereas cousins are related by r = 1/8. This is why Haldane professed that he was willing to give his own life (a cost of C = 1) to save two brothers (B = 2) or eight cousins (B = 8). In the hymenoptera, kin selection explains why sterile workers might be willing to raise their siblings despite that it seems to provide them with no direct benefit: their altruistic behaviour towards reproductive siblings (drones and queens) indirectly helps pass on their genes.

To summarize thus far: we can use kin selection to explain why natural selection might favour certain altruistic traits, including why we might expect the production of a self-sacrificing, sterile worker caste to be favoured by natural selection; and kin selection can be formally described by Hamilton’s Rule. But Hamilton put his rule to more subtle use in the paper that introduced it (Hamilton 1964) to explain a striking feature of social insects. In the hymenoptera, colony life does not have a single origin; rather, social lineages evolved from solitary lineages 9 times independently (Ross et al. 2013). Despite these multiple origins, each evolutionarily ‘new’ instance of sociality shares remarkably similar features. One particular such feature involves the sex of workers: the worker castes among all social hymenoptera are always composed exclusively of females. Males, with very few exceptions, are never workers and generally contribute little to colony life. Why has this sex bias reliably recurred?

Female worker honey bees return from foraging. Source: Wikipedia.

W. D. Hamilton theorized that the relatedness term in his famous inequality was responsible. Most animals familiar to us are diploid, which means that both males and females have two sets of chromosomes: one from their mother and one from their father. Full siblings under diploidy will have a relatedness coefficient of r = 1/2, because they each inherit half of their mother’s genes and half of their father’s genes, and so the probability that, at a particular locus, a randomly-selected allele from one sibling and a randomly-selected allele from the other sibling are identical by descent is 1/2. (It is possible to interpret the relatedness coefficient in a number of ways, but this description suffices for our purposes.) Hymenoptera, however, are not diploid but haplodiploid: males are produced from unfertilized eggs and are haploid, with just one set of chromosomes they inherit maternally; females are produced from fertilized eggs, and are therefore diploid, with one set of chromosomes from each parent.

This leads to unusual relatedness relationships between siblings of different sexes. For example, under haplodiploidy, two full sisters have a 3/4 probability of an allele at a given locus being identical, because they inherit their father’s full complement of genes alongside half of their mother’s genes. Therefore, a female is more related to her sisters (r = 3/4) than to her daughters (r = 1/2). (This differs from the case in diploids, where a female is equally related to her sisters and to her daughters, with r = 1/2 in both cases.) Hamilton hypothesized that this could explain the sex bias in hymenopteran worker castes. After all, this means that a female can more efficiently pass on her genes by raising her mother’s daughters than her own, whereas males have no similar reason to favour their siblings over their offspring.

However, under haplodiploidy, a female has only r = 1/4 relatedness to her full brothers, because her brothers don’t inherit any genes from her father at all. So, averaged across both sexes, females are actually equally related to their siblings (brothers and sisters) and offspring (sons and daughters), with an average relatedness coefficient of r = 1/2 in both cases. This realization deflated enthusiasm for Hamilton’s haplodiploidy hypothesis. Nonetheless, despite the lack of theoretical support, it still features prominently in many textbooks, and indeed, even on the relevant Wikipedia pages.

It is important to note that this rare mistake by an exceptionally gifted biologist has no bearing on whether the overall theory of kin selection is ‘true’: Hamilton’s haplodiploidy hypothesis may have fallen out of favour, but kin selection is still the logical conclusion of a gene-centred view of evolution. However, it does seem that relatedness coefficients in and of themselves do not explain why hymenopteran workers are only ever female. Rather, the most plausible theory is that hymenopteran workers are female because of the ancestral pattern of parental care among their solitary ancestors (Bourke & Franks 1995). Social hymenoptera evolved from solitary-living wasps, the females of which provide care to their offspring in the form of food and shelter. In contrast, paternal care in this clade is exceedingly rare. A longstanding observation maintains that sib-rearing behaviours in social hymenoptera look a lot like brood care in solitary hymenoptera, except redirected toward brothers and sisters (e.g., Wheeler 1928). Furthermore, new genetic evidence suggests that maternal care and sib care are controlled largely by the same genes (Amdam et al. 2006; Toth et al. 2007). This simple hypothesis, that females and not males were pre-adapted to perform altruistic sib-rearing, and so it was females who were better suited to the worker role, seems to explain patterns of sex biases in worker castes across all eusocial lineages where brood care is the primary function of workers, not just among the hymenoptera (Ross et al. 2013).

However, it is still possible that haplodiploidy influenced the ancestral pattern of parental care, precisely by predisposing female solitary wasps—and not males—to provide care to their offspring. If it could be shown that haplodiploids are more readily able to evolve maternal care than diploids, haplodiploidy could still have played an evolutionary role in determining the sex of hymenopteran workers. This possibility is the subject of some of my work with Andy Gardner, the results of which I will share here in the near future.

REFERENCES

Amdam, G.V., Csondes, A., Fondrk, M.K. & Page, R.E. 2006. Complex social behaviour derived from maternal reproductive traits. Nature 439: 76–78.

Bourke, A.F.G. & Franks, N.R. 1995. Social Evolution in Ants. Princeton University Press, Chichester.

Hamilton, W.D. 1964. The genetical evolution of social behaviour. I, II. J. Theor. Biol. 7: 1–52.

Ross, L., Gardner, A., Hardy, N. & West, S.A. 2013. Ecology, not the genetics of sex determination, determines who helps in eusocial populations. Curr. Biol. 23: 2383–2387.

Toth, A.L., Varala, K., Newman, T.C., Miguez, F.E., Hutchison, S.K., Willoughby, D.A. et al. 2006. Wasp gene expression supports an evolutionary link between maternal behavior and eusociality. Science 318: 441–444.

Wheeler, W.M. 1928. The Social Insects. Kegan Paul, Trench, Trubner & Co., London.