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It is generally difficult to identify possible effects of selection at a specific locus because of the heterogeneity of the genetic background. Geographical patterns ofEst-6 gene frequencies suggest that there is selection at this locus but selection on loci closely linked to it cannot be excluded. Differences in catalytic properties between allozymes have been shownin vitro; further, several laboratory studies have shown apparent fitness differences between allozymes. Our study used inbred lines highly homogeneous in the genetic background. Four populations were set up fromEst-6s andEst-6F homozygous females inseminated by males of the same genotype at each combination of three factors: temperature (18 and 25°C); methyl malonate (presence or absence); input gene frequencies [p(S) = 0.2 and 0.8]. The populations were sampled periodically for about 28 generations. Methyl malonate was chosen to exert pressure in the enzymatic function of esterase-6. Statistical analyses show that: there are no sex differences; gene frequencies change from input values to those of the first sampling, when only individuals of the first generation are present at 18oC or individuals of the second generation just begin to appear at 25°C; gene frequencies do not change thereafter and Hardy-Weinberg equilibrium is established. The changes in gene frequencies observed in the first generations suggest thatEst-6 can under certain conditions be a target of selection. Such conditions may not, however, occur in natural populations.

It is well established that in crosses betweenAnopheles atroparvus andA. labranchiae, F1 males are sterile while the females are fertile. This paper presents results of backcrossing the F1 females and of further crosses which suggest that the genetic situation causing sterility is the simultaneous presence, in a male, of the Y chromosome of one species and of a gene (or genes) from the X chromosome of the other species.

A quantitative character has been modelled as determined by two diallelic loci and an environmental component. A Gaussian distribution defines the phenotypic expression of each genotype, and the two loci influence, independently of each other, either the mean or the variance of the distribution. Genetic and phenotypic variability attained at equilibrium have been investigated under constant and fluctuating selection regimes, with respect to different genetic determinations and recombination rates between the two loci. The results obtained show that the type of response to constant and variable environments is strictly dependent on the phenotypic effects of the two loci.

In a large random mating population segregating for a pair of allelomorphs with full dominance, the condition that neither allelomorph should disappear is that the arithmetic mean of the fitnesses of recessives in different generations should exceed unity, their geometric mean fall below it.

An equilibrium of a pair of allelomorphs at a sex-linked locus can be stable under natural selection if the fitnesses of the mutant hemizygote and homozygote differ from that of the normal in opposite directions, even if the female heterozygote is less fit than the mean of the homozygotes. But if the fitnesses of the mutant homozygote and liemizygote differ in the same direction from those of the normals, stability demands that the heterozygous female should be fitter than either homozygote. The facts as to human glucose-6-phosphate dehydrogenase are discussed in the light of these findings. In this case it seems likely that there is real heterosis, but this may not be true for most such equilibria found in nature.

Expressions are found for the equilibrium between mutation and selection at autosomal and sex-linked loci, when the mutation rates and the relative fitnesses of mutants differ in the two sexes, and in the presence or absence of inbreeding. They have been found both when mutation precedes selection and when it follows it.

The rare recessive human genes which increase the mortality of inbred human beings may not all be kept in being by mutation. They may include relic genes which were useful in the past but are harmful today. They may also include genes kept in being by greater fitness of the heterozygote at loci where the other homozygote has a lowered fertility rather than a lowered viability.

The logical structure of human relationships is discussed. When the relatives are not inbred their genetical implications can be summarized by four coefficients of relationship, namely Wright’s coefficient of single autosomal relationship, a coefficient of double autosomal relationship, a coefficient of single sex-linked relationship, and one of double sex-linked relationship between women only. A simple symbolism for human relationships is developed. There are 516 possible relationships betweenA andB, not involving an ancestor of either more remote than a grandparent, and not involving incest. Table 1 gives the coefficients of relationship for all of them. 192 are relationships between first cousins. In 66 cases the coefficients may be raised by monozygotic twinning. The effect of relationship on incompatibility between mother and foetus is described. There is a brief discussion of relationships involving incest, and those between second cousins.

Whenqn is a parameter of a population in generationn,qn+1 is often a simple function ofqn. If so,n is an automorphic function ofqn. A simple transformation ofqn permits the expression ofn as an infinite series which often converges quickly, and allows numerical calculation. It is sometimes possible to obtain a very close approximation to the value ofn in terms of logarithms. Examples are given.

Polymorphism may be due to the fact that the fitness of a phenotype diminishes as its numbers increase. The stability of the equilibrium is discussed, and it is shown that under natural conditions instability is unlikely.