In order to control genetically the population of mice maintained as a closed colony, it is necessary to apply the theories of population genetics. Effective population size is one of the most important conceptions in population genetics. In 1938 and later, Wright derived some formula to estimate the effective size of wild animal or plant populations, and in 1957, Nozawa derived a general for.oula shown here as formula (1) and transformed it into a formula for estimation of she effective size of farm animal populations.
The author will now attempt to transform formula (1) into a formula for estimation of the effective size of a closed mice colony. If each male is mated with the same number (C) of female, as is usual in closed colonies of mice ; therefore,
Nf=CNm
kf=km/C
sm=sr=s
If the intra-class correlation coefficient (ρ) is almost zero, as shown in Table 1, and the variance (σ2km) of progenies which are contributed to the next generation by male parents is C times that of the variance (σ2kf) of progenies contributed by female parents, formula (1) can be transformed into formula (2) . In this formula, Nm is the number of male parents, C is the ratio of the number of female parents to the number of male parents, s is the ratio of the number of the breeding members in a generation to that in the next generation, and σ2km is the variance of the number of progenies contributed by the male parents to the next generation. If each male is mated with a female, namely, C=1, formula becomes formula (3), as was derived by Nozawa in 1957. When C=1 and s=1, formula (2) becomes formula (4) Which is Wright's formula.
The effective size of the ICR-JCL mice colony maintained in our Institute was estimated with formulae (1) and (2) as shown in the Table 3. Both estimations almost agree. It shows that the effective size of the ICR-JCL mice colony is between 300 and 400 in each generation, and this effective size is only about one fourth of the number of actual breeding members in this colony. The first reason for the difference between the effective size and the number of breeding members is that each male is mated with six females. The second reason is that the variances (σ2km and σ2kf) of progenies to next generation by male and female parents are larger than that of progenies contributed randomly, because the female parents contribute about five progenies per chance of contributing progenies.
The effective sizes of the population of a colony which has 50 males and various values of C, s and σ2km, are shown in Tables 3 to 7.
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