Theory of Control of Insect Populations by Sexually Sterile Males

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Abstract
The theory of control of insect populations by the release of sexually sterile populations or by treating field populations is examined by establishing basic premises and deriving algebraic equations. The effect of multiple mating is shown to depend on the fertility of females mated to both sterile and fertile males. The effect of release of males alone will be the same as release of both males and females when the released females are sterile; the effect of release of females alone will depend on the number of times males can mate. If a population is seasonally cyclic, the timing of initial releases will have no effect on the number of sterile adults or the time required for extermination, but the initial reduction will be greater and the population before extinction will be lowered if releases are started when the increment of increase is least. The increment of increase of a population and the factors determining the increment are important in determining plant capacity and cost of control. When the cost of the rearing plant, the cost of operation, and the number of generations required to reach extinction are considered, we appear to have an optimum size of plant and rate of release; higher rates of release are costly and save little time. Sterilization of the males in a natural population is a more effective method than the release of sterile populations if both males and females are killed or sterilized. The relative efficiency of different treatments of the 2 sexes in the field depends on the mating ability of the males, the proportion of the 2 sexes that survive treatment, and the fertility of the survivors.

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