Abstract
The mechanism by which genetic variability is maintained in natural populations
for quantitative characters is not well understood. Many observations show that
there is a considerable amount of genetic variability in a large population, and unless
the character is closely correlated with fitness the optimum is usually near the mean,
with fitness decreasing as the distance from the mean increases. Probably, Fisher'
was the first to investigate a model in which the fitness was assumed to decrease in
proportion to the squared deviation from the optimum. This model was also used
by Haldane2 and Wright.3 Robertson4 has shown that if genes are maintained by
overdominance, but act additively with respect to a quantitative character, then
the optimum is at the mean and the decrease of fitness is proportional to the squared
deviation from the optimum.
In all these treatments the relation between the mutation rate and the amount of
genetic variability maintained is either ambiguous or left out of consideration. The
purpose of this paper is to propose a new model which enables one to make predictions
about the relations between mutation rate, genotypic variance, and genetic
load or amount of selective elimination involved in the maintenance of genetic
variability.
Assumptions and Mathematical Formulation.-The basic assumptions are:
(1) At every locus involved with the quantitative character under discussion,
mutation can produce an infinite sequence of alleles. Every mutation may produce
a new allele different from the pre-existing ones.
(2) The effect of a new allele on the quantitative character is only slightly
different from the parent allele from which it was derived by a single mutational
step.
(3) The genes are additive with respect to their effect on the quantitative
character.
(4) The optimum phenotype is fixed, and fitness decreases in proportion to the
squared deviation from the optimum.
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