A formal theory of group-level adaptation for obligate eusociality

Darwin argued that natural selection leads organisms to appear as if they are striving to maximize their fitness. This idea is readily recognized at the individual cell or body level, but such adaptive design may also manifest at some higher levels of biological organization. Previous work has formalized the idea that social groups can be viewed as adaptive individuals in their own right-i.e., "superorganisms"-under the assumptions that within-group selection is absent and that there is no class structure. However, the original and most common biological use of the term "superorganism" is in reference to insect colonies in which members exhibit striking class structure in the form of reproductive division of labour. Accordingly, although obligately eusocial colonies are regularly conceptualized as having the capacity for colony-level adaptation, current formalisms are unable to support this idea. Here, we develop a formal theory of group-level adaptation for obligately eusocial colonies by establishing mathematical correspondences that connect the dynamics of natural selection-as described by Price's equation-to the mathematics of optimization-wherein the colony is considered a fitness-maximizing agent-under a range of assumptions as to which members of the colony control its phenotype and the degree to which they are genetically related.