Hamilton’s Theory

In particular, Darwin was referring to the social insects. Already in those times it was common knowledge that hymenopteran colonies (honeybees, wasps, bumble bees and ants) usually consist of one reproducing queen and a multitude of sterile workers. This particular case of sociality is termed ‘eusociality’. In addition to sterile individuals cooperatively helping the fertile animals raising the offspring, eusociality is characterized by another trait: at least two generations overlap in life stages capable of contributing to colony labor, so that the offspring can assist their parents during part of their life cycle.

The abandonment of reproduction by the worker caste was the huge dilemma to which Darwin devoted an entire chapter in his ‘Origin of Species’. While the omnipresence of exploitation is well in accord with the rule ‘reproduce at the cost of your competitors’ the equally obvious existence of all degrees of altruism up to the complete sacrifice of reproductive success in favor of another organism seemed an insurmountable obstacle. How can individuals without own offspring exist if reproduction and inheritance are the foundation of the whole theory?

Darwin’s own solution was to assume that the colonies formed some sort of super-organisms that compete against each other in a very similar way as individuals do. To perceive animal colonies as super-organisms with their members as rough analogues of cells is a long known and, even today for certain studies, a very useful concept. The idea of family or “group selection” placated Darwin’s contemporaries and was still widely accepted well into the 20^th century. According to this idea, the unit of selection for altruistic alleles of an originally selfish gene would be the colony or deme, not the individual. The altruistic, cooperative allele spreads in the species as colonies without a high occurrence (gene frequency) of this allele become extinct. However, in order for interdemic selection to be effective, one has to assume that there is no migration between the groups and that there is sufficient selection pressure, i.e. the rate of colony extinction is very high. Furthermore, individual selection will always be faster than group selection, as the number of individual organisms is much larger than that of populations and the turnover-rate of individuals is much higher. Thus, group selection can never counteract individual selection. Because of these considerations, group selection was eventually abandoned as the prime explanation for the evolution of cooperation. In its stead, William Donald Hamilton’s (1936-2000) discovered the principle of ‘kin selection’. Hamilton’s theory was published in the Journal of Theoretical Biology in 1964. At the time, it was so innovative that it almost failed to be published and was largely ignored for a decade. When finally noticed, its influence spread exponentially until it became one of the most cited papers in all of biology. It is the key to understanding the evolution of altruistic cooperation among related organisms, such as the social insects. Cooperation among unrelated individuals is beyond the scope of this article and is treated elsewhere (see bibliography and chapter ‘Prisoner’s Dilemma’).

Kin Selection

Why should there be a distinction between cooperation among unrelated individuals and that among related individuals at all? We have learned that genetics is the basis upon which evolutionary change is taking place. Fitness was defined above in terms of successful reproduction, i.e. the number of offspring carrying the selected allele. The more offspring, the “fitter” the parent. Darwin’s “struggle for existence” is a struggle for reproduction. With sexual reproduction, however, only one half of an organism’s genome is transferred into one of his offspring at a time. Therefore, any particular trait - depending on its mode of inheritance – is often transmitted from a parent to its offspring with a probability smaller than one. Thus, in order to transmit as many of one’s genes into the next generation as possible (and hence be evolutionarily successful), an organism has to produce as many surviving offspring as possible in order to maximize the probability of transmitting all its genetic information. This might constitute a difficult task, however, since all its competitors try to do the same. But there are other sources of one’s own genes available: relatives.

Fig. 1: The coefficient of relatedness. In diploid organisms, every parent (top row) transmits 50% of its genetic information to each offspring (middle row). On the average, siblings therefore share half of each parent’s contribution to their genome, adding to a coefficient of relatedness r=0.5. Consequently, cousins share an r=0.125 or r=1/8 (bottom row). Likewise, these cousins are related to their common grandparents by ¼ or r=0.25. One may also say that r is a measure for the probability that any given allele is shared by two individuals.

An ordinary diploid, sexually produced organism shares 50% of its genes with either of his parents. Accordingly, it shares about 50% with its siblings, 25% with its uncles, aunts, grandparents, grandchildren and so forth (coefficient of relatedness, see Fig. 1). Hamilton’s strike of genius was to reformulate the definition of fitness as the number of an individual’s alleles in the next generation. Or, more precisely, inclusive fitness is defined as an individual’s relative genetic representation in the gene pool in the next generation:

                 (1)