Model 8 shows the calculated ratio on the first day during the F-. emergence period, 

 and on the 5th, 10th, 15th, and 20th days. It is assumed that the rate of emergence is 

 constant, although considerable variation would no doubt occur in actual field populations. 

 The sterile male population is also assumed to be constant at a level of 300 per acre. 



It should be noted that the theoretical ratio of sterile to fertile insects would be 

 240:1 on the first day after treatment, and 12:1 by the 20th day, if the sterile male popu- 

 lation is maintained at 300 per acre. No mortality is calculated for either the naturally 

 emerging population or the released males. Theoretically, reproduction would be re- 

 duced by more than 99 percent on the first day and 92 percent on the 20th day. The 

 average ratio of sterile to fertile insects would be 24:1, which would represent a 96- 

 percent overall control of reproduction. Actually, the theoretical effect would be 

 slightly higher, if we allowed for a 3-day preoviposition period, which was not done in 

 the model. The use of such a regime of sterile males would seem to take full advantage 

 of the biology and population dynamics of the insect. The impact of 96-percent control 

 of reproduction during the F^ period should be substantial, even allowing for a five-fold 

 increase rate for those that reproduced successfully during this period. If only 4 percent 

 of the F-|^ population of 50 boll weevils reproduced successfully, and these produced five 

 times the number of progeny, the total F natural population would be 10 per acre. 



If the F^ boll weevils emerged uniformly during the 20-day period, this would 

 mean a daily emergence of 0. 5 boll weevil per day. However, the boll weevils accumula- 

 ting during the F-. period could overlap the F generation. Theoretically, sufficient 

 numbers of fertile males would accumulate by the end of the F emergence period to 

 reduce the sterile to fertile ratio to 12:1. It would seem advantageous, therefore, to 

 employ one additional insecticide treatment on the last day of the F emergence period 

 to destroy all adults, both fertile and sterile, and immediately release more sterile 

 males to compete only with the emerging F^ boll weevils. In this model, a projected 

 release of 200 sterile males per acre would theoretically be adequate to assure no re- 

 production of the few F emerging boll weevils. According to the model, the average 

 ratio of sterile to fertile insects would be 80:1 during the Fo emergence period. The 

 maximum ratio would be 800:1 on the first day of the F emergence period, and the 

 minimum would be 40:1 on the last day. No reproduction would be expected during the F 

 generation, and theoretical elimination would be achieved on the basis of the populations 

 on 1 acre of cotton. 



Model 9 projects the estimates for a representative population on 1, 000 acres of 

 cotton using the basic information developed in model 8. Model 9 also includes the 

 estimated trend of a normal, untreated population and a population subjected to a full- 

 season program of insecticide treatments only. It is assumed that insecticide treat- 

 ments directed against the F^ and Fq generations will be only 90 percent effective 

 instead of 95 percent, as projected for the overwintered population. It is generally 

 agreed by entomologists that as cotton grows larger it becomes more difficult to achieve 

 levels of control comparable to those obtained when the cotton is smaller. It is possible, 

 too, that the increase rate is higher during the Fg and Fq generations because infested 

 squares are less subjected to desiccation by direct sunshine. 



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