POTENTIAL FOR GENETIC SUPPRESSION OF INSECT POPULATIONS 



that determine the conditional lethal traits. The 

 algebraic expressions (table 1, Appendix) en- 

 abled us to calculate the fraction {ir) of the 

 affected population that was destroyed by one 

 or more lethal traits and to calculate the sup- 

 -ion of the affected population relative to a 

 native population not subjected to population 

 control measures. 



If a strain homozygous for more than one 

 conditional lethal gene is released into a popula- 

 tion of native insects, these genes will become 

 distributed throughout the population in an 

 almost random manner by the F3 generation, 

 barring linkage . intensities of less than 50 

 crossover units. Therefore we may approxi- 

 mately calculate the fraction of the population 

 that would be suppressed following a single 

 release of a strain bearing several conditional 

 lethal traits. If the frequency of individuals 

 without lethal trait 1 is A and the frequency 

 without lethal trait 2 is B, then the frequency 

 of individuals without either lethal trait is AB. 

 Therefore the frequency of individuals with one 

 or both lethal traits is 1-AB, or the fraction of 

 the population suppressed. 



The suppression of the population must be 

 calculated in relation to the uncontrolled native 

 population. Let there be y native insects that 

 increase 0-fold each generation. Then the num- 

 bers of insects in the parental, Fi, F2, and F„ 

 generations are 



y, 2/0, yQ 1 , and y0 n 

 Similarly if x insects with conditional lethal 

 traits are released into a population of y native 

 insects, then the numbers of insects in the 

 parental, Fi, F 2 , and F n generations are 



. 1 y)0, (x - y)0 2 , and (x + y)0 n 



In the /;th generation the conditional lethal 



traits are expressed in a fraction (w) of the 



affected population. The number of survivors is 



(1— w) (x + y)0 D 



Then the relative survival is 



(1 — w) (x + y) -r- y 



x 

 The release ratio X (X = — ) required to 



y 



obtain 98- to 99.9-percent suppression in the 

 Fi and F 3 generations was calculated (table 2) 

 for conditional lethal traits determined by one 

 dominant (dom.) gene, two autosomal (auto.) 

 genes with additive effects, three autosomal 



genes with additive effects, and three autosomal 

 genes with additive effects plus one dominant 

 sex-linked (s.l.) gene. 



The numbers in parentheses in table 2 are the 

 genotypic values of the survivors. For example, 

 2 auto. (3, 4) indicates the trait is determined by 

 two independent autosomal genes with equal 

 and additive effects and the conditional lethal 

 trait will not be expressed in individuals pos- 

 sessing three or four native-type alleles. Simi- 

 larly 3 auto. + 1 s.l. (6-9) indicates that the 

 trait is determined by three independent auto- 

 somal genes with equal and additive effects plus 

 one sex-linked dominant gene with an effect 

 equal to three dominant autosomal alleles. The 

 survivors possess the native-type sex-linked 

 allele and at least three native-type autosomal 

 alleles, or they may lack the native-type sex- 

 linked allele but possess all six native-type 

 autosomal alleles. These calculations were made 

 with an IBM System/360, Model G50 computer, 

 as explained in the next section. 



If the release strain is homozygous for only 

 one conditional lethal trait that expresses itself 

 in the Fi generation, the degree of suppression 

 obtained cannot exceed that obtained with ordi- 

 nary dominant lethal mutations. However, if the 

 genes for conditional lethal traits become ran- 

 domly distributed within the population before 

 they are expressed, the degree of suppression 

 may increase significantly if the trait is under 

 polyfactorial control (table 2). If the condi- 

 tional lethal trait is determined by a single 

 dominant gene, the degree of suppression cannot 

 vary between generations. 



When two conditional lethal traits are com- 

 bined into a single population, release ratios 

 varying from two to five are adequate to obtain 

 98-percent suppression if the traits are ex- 

 pressed in the F3 generation; similarly release 

 ratios of three to 14 will yield 99.9-percent sup- 

 pression in the F3 generation (table 2). When 

 three conditional lethal traits are combined into 

 a single population, release ratios of one or two 

 will yield 98-percent suppression in the F3 gen- 

 eration, and ratios of two to five will yield 

 99.9-percent suppression. Although these values 

 are approximations, they were sufficiently en- 

 couraging to undertake the more precise cal- 

 culations presented in the following sections. 



