I hope you have yesterday’s post “out of your system.” I will admit here that I don’t know if I was particularly intelligible, but the prose and formalism of Hamilton’s paper isn’t exactly the picture of transparency. I find his later works much more intelligible; I suspect part of it has to do with the fact that Hamilton was responding and extending a tradition of evolutionary genetic modeling which reached back to R. A. Fisher and continued into the 40s and 50s. Reading a paper in 2008 which presupposes familiarity with a corpus of work from nearly three generations in the past can be a bit confusing; Hamilton’s later papers, especially on the evolution of sex, were more “forward looking,” and so the reference points allow a more secure mooring in familiar landscapes. I elided over some technical details and artificialities in Hamilton’s mathematical treatment; but truly very little of that is necessary to comprehend The genetical evolution of social behaviour II. Whereas The genetical evolution of social behaviour I was an abstract treatment where inclusive fitness was deduced from a priori assumptions; part II is a review of the empirical literature which allows one to explore the boundaries and viability of the theory through induction. Therefore the main hurdle toward comprehension of the details of this section has more to do with requisite lack of familiarity with the literature in entomology and ethology than a low level of mathematical fluency. The first part of the paper requires thinking hard, while the second part demands knowing widely. I will admit here that my familiarity with the literature is not what it should be for a hard-headed assessment, though I have read works from Hamilton’s heirs in this field in that attempt and upd to date analysis of insect societies through the inclusive fitness paradigm. My exposition will mostly be descriptive as I attempt to communicate the essential points of the paper’s review of the data up that point in history.
First, a way to formalize J. B. S. Haldane’s quip in regards to the sacrifice one would be willing to commit for the sake of one’s relations:
k > 1/mean (r), here k is the ratio of gain to loss, and r is the coefficient of relationship.
In other words, imagine that you have a coefficient of relationship of 1/2 with an individual. This would usually be a sibling. The inverse of 1/2 is 2, which means that your gain:loss ratio in terms of inclusive fitness must exceed 2 for the genetically controlled behavior to be favored to increase in frequency. One could extend the model vertically as well, if a child or a parent could increase the fitness of their offspring or their parent into the future by a factor of 2 then a sacrifice of their own life might be justified. Usually we conceive of this as a parental sacrifice since the reproductive value of the offspring is usually potentially higher at that point in their life; but there’s no theoretical reason that in long-lived species offspring could not sacrifice their lives for their parents if that would entail in the production of numerous future siblings. In any case, in this section Hamilton reviews studies which suggest that post-reproductive individuals may behave far more altruistically toward their relations than earlier on in their lifespan, the rationale being that altruism is the only way that they can increase their inclusive fitness once their own ability to procreate ceases. This is the logic behind the grandmother effect for humans & post-menopausal females.
But these ultimate evolutionary parameters are shaped by the manifestation of proximate behaviors and morphologies. For example for inclusive fitness to have great relevance some level of discrimination and population viscosity in movement and spatial clustering is critical. Organisms with complex hierarchies, distinctive morphologies and the cognitive ability to engage in discernment of relation from non-relation are the ideal targets of these sorts of dynamics. But even without heightened powers of perception Hamilton points out that altruism via inclusive fitness is likely to emerge in populations with viscous dynamics of dispersion. That is, there is some correlation between genetic variation and spatial variation; one’s relatives remain near. This obviously reduces the cognitive requirements in terms of discernment and also the chance of false positive actions of altruism. Viscous populations due to lack of mobility and dispersion load the die structurally so as to favor the spread of altruism inducing genes, while panmictic populations should favor more selfish variants, which after all would be experience increase at the expense of non-relatives (or, more precisely what Hamilton would term “replica copies”). In terms of proximate behaviors Hamilton cites research which shows that birds which are territorial seem to be less aggressive with each other during ritual combat when they resemble each other in plumage. His logic is that birds which resemble each are more likely to be related, and so when violent conflicts erupt the gains in fitness must be great so as to compensate the loss to a relative. In contrast, between non-relatives the impact upon inclusive fitness is less important as one is less likely to be reducing the fitness of replica copies of genes identical by descent. Further illustrations from birds and insects are used to show how important physical cues are for social organisms; and how hostile they may be toward a perceived “outsider.” Interestingly, Hamilton also notes that the more hyper-social bees are those where the workers are most aggressive and so likely to sacrifice their own lives by stinging; in contrast, only moderately social bees tend to be less aggressive and milder. The implication here is that lower coefficient of relationships across the hive and weaker sociality entail a diminished tendency to risk life and limb for hive-mates.
Next, Hamilton moves to the question of clones; i.e., asexual lineages. Obviously here the coefficient of relationship, r, should be 1. So why no obligate altruism and sociality? First he notes that many “asexual” species do exhibit sexual tendencies upon closer inspection, or at least sexual lineages. Second, new mutational varieties will have a 0 coefficient of relationship on that locus initially, so selfish variants would quickly infest populations. Over time the asexuality would serve to induce an upper bound as selfish morphs fix within populations, but Hamilton’s argument is that in many clonal species these epiphenomal sweeps sum up to an overall tendency of pure altruism to always being kept at bay. Finally, he notes that though he neglected mutation as adding new variation to a population, and so reducing the r, in fast reproducing clonal lineages this may not be appropriate. So the lack of altruism may be a function of the fact that these lineages’ r is constantly diverging on the loci of interest.
At this point I’m going to skip over Hamilton’s treatment of colonial fungi and what not because I’m not interested in that! Let’s shift to eusocial insects, especially hymenoptera. Hamilton focuses on this taxon because of its ubiquity, both in numbers and in species, and genetic peculiarities which might make it especially susceptible toward the development of altruism. So what’s the big deal? Haplodiploidy. Basically males are haploid and only inherit from their mother (no prior male fertilization required). Because of male haploidy if a male inseminates a female (drone to queen) all the daughters, who are diploid, with have an r of 3/4. Why is this? Females have two copies of each gene, so there is a 1/2 chance of contribution of one or other of the allele, so from the maternal side that female offspring will exhibit variation. In contrast, on the father’s side he has only one copy to contribute, so this means that on the paternal side all the female offspring will be identical by descent. While the sisters exhibit an r of 3/4 in relation to each other, they exhibit an r of 1/2 with their mother. The inference from this is that they would exhibit a relationship of 1/2 with their own daughters! This means that they are more closely related to their siblings than they are to their own offspring; and that likely loads the genetic die to favor the development of sociality so that the sisters can collaborate to allow their mother, the queen, to continuously produce more closely related sisters (take a “gene’s eye view” and you’ll see why this would occur, if the behavior is controlled by one allele that allele will maximize the production of its own copies). But there’s a complication here: many queens are fertilized by multiple drones. If all the males contribute equally then then the expected coefficient of relationship is:
r = 1/2 ( 1/2 + 1/n)
In other words, as you increase n, the number of drones, the r will converge upon 1/4, which is the relationship between a female and her drone “brother.” How does Hamilton handle this? He allows that other factors and constraints besides kin selection are at work; the choices available to a worker are not existent within a vacuum, and evolutionary and ecological trajectories can not be reversed or changed at the drop of a hat. Kin selection may be a sufficient condition to enable eusociality, but may not be necessary to perpetuate it. A species where queens were initially inseminated by only one male, or where one male is overwhelmingly dominant in the contribution to the next generation, might be a favorable condition for the emergence of cooperation. But subsequent to this if later evolutionary conditions give rise to a tendency toward multiple inseminations which reduce r across sisters the proximate behavioral tendencies which enforce altruism and increase total fitness may result in the continuation of eusociality. Of course, one assumes that selfishness could creep into the system, and Hamilton notes that such trends do exist in colonies where workers may attempt to produce offspring furtively.
Next Hamilton addresses some paradoxes in terms of the framework of his theory. He notes that termite colonies are not haplodiploid, have workers of both sexes as well as an attendant to a queen, the king. In Hamilton’s opinion other reasons proffered for the origin of eusociality in termites are satisfactory, indicating that he does not believe that kin selection dynamics of the sort alluded to above with hymenoptera are necessary preconditions for this sort of hive cooperation. When it comes to groups of hymenoptera with multiple queens, such as varieties of wasps, Hamilton notes that upon closer study the reality is that as colonies develop quite often reproductive individuality remains, or that in the architecture of the residence the various reproductives and their daughters remain segregated. In other words, common residence may be expedient and necessary to initiate reproduction, but the full blown behavioral tendencies of eusociality never seem to manifest in their grand forms that we see among honeybees or most ants.
There are some further comments on parent-offspring conflict, surveys of the behaviors of various hymenoptera genuses, but that is the general outline of the paper. I will finish with a few quick comments. As I said, I’m not that familiar with the most current research on entomology, but I will say two things. First, Hamilton’s work is very well respected. Second, many workers disagree on his emphasis in regards to the drivers of eusociality even within haplodiploid insects. The emergence of genomic fingerprinting cheap enough to roughly calculate mean r within colonies had meant that hypothetical relationships are no longer so hypothetical, and in many cases are closer to the lower values than the higher. This perhaps is one reason that E. O. Wilson feels that it is time to resurrect group selection and the analogy of the superorganism. Exciting times.
HAMILTON, W. (1964). The genetical evolution of social behaviour. II. Journal of Theoretical Biology, 7(1), 17-52. DOI: 10.1016/0022-5193(64)90039-6