A Quantitative Test Of Hamilton's Rule For The Evolution Of Altruism

Discussion

Although Hamilton's original 1964 rule provides a general framework of how natural selection works [17],[27], its theoretical and empirical applications usually involve the limiting assumptions of weak selection and additivity of costs and benefits of fitness components as well as the absence of pleiotropic and epistatic gene interactions [15],[16],[28] (but see [13] for relaxations of some of these assumptions in concrete applications), leading to the conclusion that the rb − c>0 rule should be used with caution when there are pleiotropic, epistatic, and non-additive effects [29],[30]. Interestingly, the genetic architecture of the robots in our system also led to departure from all these assumptions with the exception of non-additivity of costs and benefits of fitness components. However, the occurrence of non-additive (epistatic) effects of mutations at several loci in the genome leads to a situation that is conceptually similar to non-additivity of costs and benefits of fitness components [22]. In both cases, the fitness depends non-additively on gene action, with the interaction involving alleles at two loci on the same genome in the case of non-additive (epistatic) gene effects, and alleles at two homologous loci on two different genomes in the case of non-additivity of costs and benefits of fitness components.

Despite the fact that the assumptions mentioned above were not fulfilled, Hamilton's original 1964 rule always accurately predicted the conditions under which altruism evolved in our system. Whatever the c/b value used, altruism always evolved in populations where r was greater than c/b. This finding is important given that the assumption of weak selection, additivity of costs and benefits of fitness components and absence of pleiotropic and epistatic gene interactions are also likely to be violated in real organisms that also have a complex mapping between genomes and phenotypes.

Another important issue relates to the measure of relatedness. There has been considerable confusion in the literature since relatedness coefficients actually measure more than pedigree coefficients and because different derivations of Hamilton's rule take as their focal trait a variety of different quantities [16],[17],[30]. In the original derivation of Hamilton's rule [1] and many that followed (e.g., [12],[31]), the trait of interest was the genetic value at a single gene position and the regression coefficient of relatedness corresponded to an identity in state relative to the population average [31]. The interest in social evolution where social partners tend to be genealogical kin [1] has led to the use of Wright's F statistics as a measure of relatedness (e.g. [12],[22],[32]). Alternatively, Hamilton's rule has been derived to express the change in the social behavior phenotype (e.g., [16],[22],[33],[34]), often considered as a quantitative trait with many underlying gene positions contributing. In this case the coefficient of relatedness represents a regression of some measure of the individual's genetic value for that trait such as a breeding value [17], p score [16], gene frequency [1],[12], or partner phenotype on its own phenotype value [34].

Interestingly, the simple genetic structure of our groups leads to all these measures of relatedness being identical. In all our experiments groups were started by individuals randomly chosen from the previous generations. The relatedness between these founding individuals is therefore zero as they are not more genetically or phenotypically similar within groups than between groups. Positive within-group relatedness was created by cloning the founding individuals. Thus, positive relatedness was only due to one-generation coancestry and the probability that benefits of altruism being provided to a clone compared to an unrelated individual. Such a breeding system is conceptually very similar to that Hamilton had in mind when trying to explain the evolution of reproductive altruism in social insects where the sterile (altruistic) workers are the offspring of their mother queen (the individual benefitting from the altruistic worker behavior). The relatedness in such a system can also be described in terms of identity by descent [35], which provides an approximation of identity in state for rare genetic variants (see [31] for a recent review). Of interest would be to test in future studies how the evolution of altruism is influenced by more complex population structures where the effect of strong selection may lead to variation in within-genome differences in the covariance between genes in different individuals.

Because the rewards provided by the food items were either assigned to the focal individual who successfully transported it (selfish behavior) or shared equally between all the other group members (altruistic behavior), the fitness effects were additive and there were no synergetic effects. Thus, the cost incurred by an individual sharing altruistically a food item and the benefits to the other group members was not dependent on the recipients' genotypes and the proportion of them being altruistic. The lack of such synergetic effects results in the costs and benefits associated with an altruistic act being independent of the genotypic composition of the groups and the overall level of altruism in the population (i.e., there are no frequency-dependent effects). In natural systems there are frequently synergetic effects and this is one of the main reasons why it is not possible to reliably quantify the cost and benefits associated with altruistic actions (e.g., [15],[16],[36],[37]).

From an empirical perspective, our study is therefore valuable because there have been many tests of Hamilton's rule, but these studies are usually not quantitative due to the impossibility of assessing the costs and benefits of altruistic acts, even in the most simple social systems such as those documented in some bacteria [10],[38], social amoebae [39], or even synthetic microbial systems [36]. Our study also demonstrates that contrary to some misunderstandings [3], kin selection does not require specific genes devoted to encode altruism or sophisticated cognitive abilities, as the neuronal network of our robots comprised only 33 neurons. More generally, this study reveals that a fundamental principle of natural selection also applies to synthetic organisms when these have heritable properties [40].