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Allendorf is the most important factor for the successful reintro- duction of insects for biological control. In addition, Frankham and Loebel (in press) have shown rapid ad- aptation to captivity in Drosophila The pUIpose of this paper is to demonstrate the ef- fects of equalizing progeny number on adaptation to captivity. A single-locus genetic model developed by King ( 1965) is used to examine the effects of equalizing family size on the efficacy of natural selection as mea- sured by changes in allele frequency. Model Haldane (1924) defined "familial selection," which oc- curs when the number of survivors in each family is equal but when differences in relative survival exist be- tween genotypes within families. He demonstrated that the rate of elimination with familial selection is half that expected with ordinary selection for mildly deleterious recessive alleles. I follow the treatment of King ( 1965), which extended Haldane's treatments to other types of dominance relationships between alleles. (I am in- debted to Dr. James F. Crow for pointing out the rele- vance of King's paper.) Consider a single autosomal locus with two alleles at frequencies p (allele 1) and q (allele 2) in a random- mating population. Allele 2 is favored in captivity by natural selection through relative survival. The breeding structure consists of equal-sized full-sib families with each male and female parenting a single family. The same number of parents for the next generation will be produced by each family. For example, in a con- stant-size population, two progeny from each family will become breeding adults. The differential survival of the three genotypes will have an effect only within families that segregate for two or three genotypes. The survival advantage of allele 2 results in deviations from expected Ada.ptaJion to Captive Breeding 417 Mendelian proportions in the three segregating m~ting types. The production of progeny genotypes from the six possible mating types is shown in Table 1. It is neces- sary to work with genotypic frequencies because Hardy- Weinberg proportions do not hold with familial selec- tion. The frequencies of genotypes 11, 12, and 22 are D, 2H, and R; their relative viabilities within families are a, b, and c The frequency of allele 1 is D + H, and the frequency of allele 2 is H + R The genotype frequencies after one generation of fa- milial selection will then be the following (King 1965): Dn+l = d + 4Ha (a ~ b + a +:, + c) (2) ( D 2H R ) Hn+l = DR + 2Hb a + b + a + 2b + e + b + e (3) (4) _2 (H ~) Rn+l - R + 4He a + 2b + e + b + c Results and Discussion Changes in Allele Frequency The effect of equalizing family size in captivity on nat- ural selection can be examined by comparing allele fre- quency changes as predicted by the equal family size model to the change expected in the general selection model (Crow & Kimura 1970: 182, Equation 5.2.13). An initial frequency of 0.01 for the allele that is favored in captivity seems to be a reasonable value for exploration. Lower allele frequencies usually cannot occur in the founding population because of the limited number of founders. Much higher allele frequencies are unex. Table 1. Mating frequencies and proportion of progeny contributed to the next generation with familial selection (King 19(5). ~" Parental Suroiving progeny genotypes genotypes Frequency 11 12 22 11 11 D2 D2 11 12 4DH 4DH (a : b) 4DH(a:b) 11 22 2DR 2DR 12 12 4H2 4H2 (a + 2: + c) 8H2 (a + :b + c) 4Hz (a + 2: + c) 12 22 4HR 4DH (a : b) 4DH ( ~) a+b .' .,;'.., 22 22 R2 R2 f,' ~~::l l~. Total: 1 Dn+l 2/{n+ 1 Rn+l :i", Conservation Biology