MISC. PUB. 1178, U.S. DEPT. OF AGRICULTURE 



Suppression of Population Held 



With Conditional 



Calculations are presented to show the poten- 

 tial for population suppression by conditional 

 lethal genes that are introduced while the pop- 

 ulation is held in check by partial sterility. 

 Such a method might be more economical and 

 more desirable from the standpoint of avoiding 

 side effects to nontarget organs than that of 

 keeping insects in check with insecticides or 

 other control measures. 



For the calculations, we assume that the level 

 of sterility required could be induced without 

 adversely affecting mating competitiveness, 

 sperm competitiveness, or lifespan. The level of 

 sterility required to hold a population constant 

 depends on the rate of increase between genera- 

 tions. For example, if a population normally 

 increased fivefold per generation, then 80-per- 

 cent sterility in all individuals would prevent a 

 change in numbers. Similarly if a population 

 increased tenfold, then 90-percent sterility of all 

 individuals would prevent a change. Moreover, 

 if a population normally increased fivefold per 

 generation, the 90-percent sterility of all in- 

 dividuals would cause a downward trend in 

 numbers. 



To keep a fully fertile native population in 

 check by overflooding with partially sterile in- 

 dividuals, slightly higher levels of sterility are 

 required in the release strain than when all 

 individuals of the native population are partially 

 sterile. The smaller the release ratio, the higher 

 the level of sterility required. Whether matings 

 between partially sterile males and partially 

 sterile females yield offspring has an important 

 bearing on population trends in the calculations 

 presented here. 



In our calculations the number of individuals 

 released in each generation remains constant, 

 either 198,000 or 396,000; parental generation 

 of the native population consists of 2,000 in- 

 dividuals. Thus the initial ratio of released to 

 native insects is 99:1 or 198:1. However, if the 

 target population increases, the release ratio 

 diminishes, and the population's growth acceler- 

 ates after the Fi generation and vice versa. 



If matings between partially sterile males and 

 partially sterile females produce no offspring, 

 the overall population is held nearly static by 



in Check by Partial Sterility 



Lethal Traits 



the following two sets of conditions: Initial 

 release ratio of 99:1 and 198:1, each with 90- 

 percent sterility and a fivefold increase between 

 generations. However, when matings between 

 partially sterile males and partially sterile 

 females produce offspring commensurate with 

 the level of sterility, the population increases 

 even when the rate of increase is only fivefold 

 and the initial release ratio is 198:1. 



Because of the complexity of the equations 

 involved in arriving at the relative frequency 

 distributions of genotypes and numbers of off- 

 spring, especially with three and four genes, we 

 used a digital computer programed to generate 

 from the Fi genotypic identification and distri- 

 bution of offspring, the F 2 , F 3 , and F 4 genotypic 

 identifications, offspring distributions, and rel- 

 ative frequencies with provisions to weight the 

 computations as dictated by the particular study 

 performed. We programed in PL/l-F and FOR- 

 TRAN IV-G and ran under release 15/16 of OS 

 on an IBM System/360, Model 50G (128K), us- 

 ing three IBM 2311 direct-access storage devices 

 for intermediate storage and an IBM 1403 500- 

 line-per-minute printer for final output. The 

 computer facility is located in the University 

 Computer Center, North Dakota State Univer- 

 sity. 



The method employed in arriving at the final 

 answers on the computer is similar to and is de- 

 rived from a method that might be employed if 

 one were to compute the answers by hand (see 

 Appendix, p. 10) If we have a native insect 

 population consisting of y individuals with a 

 genotypic identification of dd, and if we release 

 a controlled population consisting of x individ- 

 uals with a genotypic identification of DD, we 

 might calculate the Fi generation in the fol- 

 lowing way: 



Let M represent male and F female members. 

 dd (M) X dd (F) 



= y 2 /(x + y) dd males and females 

 DD (M) X DD (F) 



= x 2 / {x + y) DD males and females 

 DD (M) X dd (F) 



— xy/(x + y) Dd males and females 

 dd (M) X DD (F) 



= xy/ (x + y) Dd males and females 



