In this study we consider the effect of re- 

 leasing only partially sterile males with a con- 

 ditional lethal trait determined by a single 

 dominant gene. In all other respects the model 

 used is identical to that of Klassen et al. 7 We 

 assume that the release strain may not be com- 

 pletely homozygous for this gene and that the 

 frequency (q) of the native type allele in 

 the release strain is 0.223606, 0.100000, or 

 0.031622. According to the Hardy-Weinberg 



equilibrium, the respective frequencies (q 2 ) of 

 the native genotypes (dd) in such strains 

 would be 5, 1, or 0.1 percent. For our example, 

 we assume that all Dd and DD insects cannot 

 enter diapause and that they perish during the 

 winter. We also assume that five releases are 

 made to coincide with the overwintered pa- 

 rental, F u F 2 , F :i , and F 4 generations. All com- 

 putations were made by means of a digital com- 

 puter, using the methods of Klassen et al. 7 



RESULTS AND DISCUSSION 



Table 1 shows that when the population in- 

 creases fivefold per generation, a downward 

 trend in numbers can be induced in all cases 

 calculated, including case 16 with releases of 

 12.500 90-percent sterile males per generation. 

 After just one release of 100,000 completely 

 sterile males, theoretical extinction is achieved. 

 Two releases of 50,000 or 25,000 completely 

 sterile males are required to achieve theoretical 

 extinction, and three releases of 12,500 com- 

 pletely sterile males achieve this result. In 

 actual practice the population would be com- 

 pletely suppressed when the density was too 

 low to permit individuals of the opposite sex 

 from meeting. The magnitude of this density 

 would depend on the species and other factors. 

 Complete suppression in a single season may 

 be achieved with lower release ratios and lower 

 levels of sterility in multivoltine populations 

 than in monovoltine or bivoltine populations. 



When the population increases tenfold per 

 generation, a downward trend cannot be in- 

 duced if the released males are only 90-percent 

 sterile. However, with 98-percent sterility, a 

 downward trend can be induced with only 

 12,500 sterile males per release. When 12,500 

 completely sterile males are released per gener- 

 ation, four or five releases are required to 

 achieve extinction compared with three releases 

 of 25,000 completely sterile males, two releases 

 of 50,000 completely sterile males, and one or 

 two releases of 100,000 completely sterile 

 males. 



When the population increases twentyfold 

 per generation, downward trends can be in- 



7 See footnote 5. 



duced by releasing 100,000 or 50,000 98-, 99-, or 

 100-percent sterile males or by releasing 25,000 

 99- or 100-percent sterile males. When 100,000 

 or 50,000 males are released, complete suppres- 

 sion would require two or three more releases 

 of 99-percent sterile males than of 100-percent 

 sterile males. 



When the population increases fortyfold per 

 generation, a downward trend would be in- 

 duced in just three cases: Releases of 100,000 

 99- or 100-percent sterile males and 50,000 100- 

 percent sterile males. With this very high rate 

 of increase, complete sterility would probably 

 be required to achieve complete suppression. 

 Thus table 1 clearly illustrates the need to ad- 

 just the release ratio to the rate of increase and 

 to the level of sterility attainable without seri- 

 ous damage to the males. 



There may be instances when the induction 

 of a high level of sterility impairs the competi- 

 tiveness of males. In order to suppress popula- 

 tions in such instances, we must decide whether 

 the high level of sterility is mandatory. If such 

 is required, we would compensate for impaired 

 competitiveness by increasing the release ratio. 

 By considering cases in table 1 in which the 

 population increases tenfold per generation, we 

 can estimate the effect of impaired competitive- 

 ness. The release of 100,000 50-percent competi- 

 tive insects is equivalent to the release of 50,000 

 fully competitive insects. Similarly 100,000 25- 

 percent competitive insects are equivalent to 

 25,000 fully competitive insects and 100,000 

 12.5-percent competitive insects are equivalent 

 to 12,500 fully competitive insects. 



Table 1 shows that when the rate of increase 

 is tenfold, the release of 100,000 95-percent 



