Continuously Distributed Factors Affecting Fitness'

UBBY and LEWONTIN (1966; LEWONTIN and HUBBY 1966) have demonstrated the probability that a population of diploid organisms can support more than an estimated 1000 polymorphisms. Their calculations agree with those of KIMURA and CROW (1964) and VAN VALEN (1963) in indicating that such widespread polymorphism cannot be maintained through single locus heterosis without entailing an absurdly high segregational load. The present paper is intended to demonstrate one way in which a high level of polymorphism might be maintained through selection favoring heterozygosis, with a modest segregational load. The segregational load will be considered as a component in the total variance in viability, rather than as a proportion of the population lost through selection. A mathematical model will be presented and several numerical examples will be given. For the sake of simplicity, one aspect of fitness will be treated as if it represented the sum of all as,pects of fitness; this aspect of fitness is zygote to adult viability, which can be treated as a probability. The simplifying assumption is that the genes being considered do not influence the fecundity of fertile adults. Very severe genetic effects, like severe environmental accidents, will result in death under most circumstances. Minor decrements in the probability of survival, such as those due to overdominance and to small fluctuations in the environment, are subject to many modifying factors, and are cumulative in nature. One of the principal factors affecting the expression of minor genetic and environmental effects is the environm'ental opportunity afforded as a result of the density of the population. In most natural populations, the reproductive potential far exceeds the environmental opportunity, and natural selection proceeds by culling to what the habitat can support. In the present model it is assumed that the genetic and nongenetic factors affecting the probability of survival are cumulative in each individual, and that individuals can be ordered in a linear array according to the sum of the factors affecting their survival. Natural selection proceeds by culling a proportion of the zygotes, taking those with the worst combinations of genes, environment and luck. The remainder, with better combinations of genes, environment and luck, survive to reproduce. Thus this is a threshold model. A few more simplifying assumptions must be made. I t is assumed that the probability of homozygosis is the same at each of N polymorphic loci, and that the selective advantage of the heterozygote is the same over any homozygote at