The analysis of caste ratios and their effect on colony efficiency can be approached by linear programming models. In the formulation offered here, account has been taken of certain general features of organization and behavior peculiar to insect societies; selection was assumed to be at the colony level; and the optimization goal was given as the maximum production of new queens and males by a mature colony whose size has an upper limit characteristic of the species. Even in their elementary form, the linear models here produced some interesting new conclusions, among which are the following: 1. Different kinds of contingencies, for which distinct behavioral responses are evolved (e.g., invasion by enemies, larval hunger, nest fouling), will be met by the colony as a whole in such a way that each kind of contingency causes about the same amount of reduction in average queen production. 2. Castes, including both physical variants and temporal behavioral stages, will tend to be proliferated in evolution until there is one and only one distinct caste specialized to meet each contingency. 3. The weight of workers belonging to a given caste at a given moment will increase in evolution according to the frequency and importance of the contingency to which it is specialized. 4. Under most, but not all, circumstances, it is of advantage to the colony progressively to increase the degree of specialization of each caste. 5. The more specialized the caste becomes, and in general the more efficient it becomes, the less will be its representation in the colony. This inverse relation between ability and numbers, which is a consequence of selection at the colony level, is the direct opposite of what would be predicted from selection at the level of the individual organism. 6. Proliferation of castes should be countered by those contingencies whose changes in frequency through time are poorly autocorrelated and paced so as to be difficult to track genetically. Certain changes in the environment can result in a caste being dropped, a result that at first seems paradoxical. This is due to the fact that, even though the caste is still the best one to handle a contingency that continues to be important, its presence nonetheless results in lowered efficiency of the colony as a whole. 7. The more specialized a caste has become, the less likely it is to be dropped from the optimal mix due to fluctuation in the environment. This, too, is the opposite of what would be expected if selection were operating at the level of the organism rather than at the colony level. 8. Certain empirically determined qualities of physical castes in ants and termites are consistent with the result of this ergonomic theory and, for the moment at least, seem best explained by it.
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Edward O. Wilson (1968) studied this question.