The inclusive fitness theory, formalized by Hamilton as the inequality R>c/b, explains that cooperation is favored by natural selection if relatedness is greater than the cost to benefit ratio. R is the relatedness parameter and is expressed as the fraction of genes shared between the altruist and the recipient due to their common descent. This theory has stimulated measures of pedigree kinship and supplied hypothetical explanations for phenomena appearing in eusociality. However, the inclusive fitness theory was questioned due to the rarity of eusociality in evolution and the odd occurrences of it throughout the animal kingdom. This theory is a mathematical approach with many limitations such as not being capable of describing evolutionary dynamics or distributions of gene frequencies. Other limitations include that all interactions must be additive and pairwise, it can only deal with very specific population structures, and when in a limited environment where inclusive fitness theory works, it is identical to the condition derived by standard natural selection, providing no additional biological insight.
An alternative theory to the inclusive fitness theory is the fixed-threshold model projected for the development of the phenomenon in established insect societies. Variation, often genetic, exists in the response thresholds associated with different tasks. According to “The Evolution of Eusociality,” “When two or more colony members interact, those with the lowest thresholds are first to undertake a task at hand.” The activity inhibits their partners, who are then more likely to move on to other available tasks. This theory offers a different approach to explain eusociality but is limited by the specific insect society not found across the animal kingdom. The argument of which theory is right is worthwhile as it will cause new theories to be produced in the search for why eusociality occurs.
For more on eusociality and an alternative theory to eusocial evolution, see Martin, N., C. E. Tarnita, and E. O. Wilson. 2010. “The evolution of eusociality.” Nature 466: 1057-1062.