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Mathematical formulae for the sampling variances of average heterozygosity and Nei's genetic distance are developed. These sampling variances are decomposed into their two components, i.e. the inter-locus and intra-locus variances. The relationship between the number of loci and the number of individuals per locus to be examined for estimating average heterozygosity and genetic distance is also discussed. The utility of the inter-locus variance of heterozygosity for studying the mechanism of maintenance of genetic variability in populations is indicated.

Techniques which produce C-bands and G-bands in man also produce bands in the chromosomes of die Desert locust. These bands are not confined to the regions of constitutive heterochromatin. The chromosome regions which stain with these techniques form few or no chiasmata during male meiosis. Other factors are implicated in the control of chiasma frequency in the unbanded chromosome regions.

SummaryBlood groups, red cell enzyme variants, haemoglobin and haptoglobin types have been examined in Hindu and Muslim samples from Indore, Madhya Pradesh. Comparison of the gene frequencies with those from other Indian populations demonstrates the extent of genetic diversity in the Indian subcontinent. For those systems where gradients are suggested, the gene frequencies of the present samples appear to agree with those expected from their geographic positions. While the Hindu and Muslim samples are very similar to each other in gene frequency, there are differences in the observed heterozygosity, which appear to reflect the differences in structure of the two populations.

The conditions are found under which the frequency of a new gene altering the recombination fraction between two loci controlling meiotic drive will increase. When the model mimics the recombination reducing effects of a chromosomal rearrangement, such as an inversion or duplication, then the result is that the frequency of the chromosomal rearrangement in the population will increase. This may help explain the presence of inversions and duplications (or insertions) in the segregation-distorter system in Drosophila. In some cases it is found that if the new gene causes any alteration in the recombination fraction between the two loci, the frequency of the gene will increase.

When directional selection for an additively inherited trait is opposed by natural selection favoring heterozygous genotypes a selection plateau may be reached where genetic variance is present. The amount of response when this plateau is reached is a simple function of the selection response in the first generation and the intensity of natural selection. When selection is practiced in small populations, the sizes of the initial equilibrium gene frequencies are at least as important as the intensity of natural selection in determining the probability of fixing desirable alleles.

Experimental perturbations of gene frequency at the esterase-5 locus in Drosophila pseudoobscura were carried out in a series of population cages started with differing numbers of founder chromosomes. Cages founded with few chromosomes showed changes in gene frequency at the allozyme locus. Such changes were less marked in cages founded with a larger sample of chromosomes. These experiments show the importance of linkage disequilibrium in affecting allozyme frequencies, and emphasize the necessity of careful experimental design when studying fitness differences between allozymes in laboratory populations.

The distinction between sexual selection and assortative mating is discussed. It is argued that assortative mating might evolve as a result of sexual selection. Simple models of sexual selection show that stable polymorphisms can be established by alleles with a wide range of additive and dominant effects. In more general models, the sexual selection is determined by female mating preferences depending partly on the frequencies of the preferred genotypes. However, if the mating preferences are directly proportional to the genotypic frequencies, there is no resulting selective effect on the population. When natural selection opposes the sexual selection, the ratio of the proportion of females exercising the mating preference to the natural selective coefficient determines whether a stable polymorphism can be established or not. Semler's experiments show that male sticklebacks who develop the typical red throat colour in the breeding season have a considerable sexual advantage over those who do not develop the colour. But they are at a selective disadvantage from predators. The frequency of the red males fits the model of a recessive gene maintained by a balance of sexual and natural selection.

The previous paper (LANGLEYT,O BARanId KOJIMA 1974) reports that the directional linkage disequilibria, Dw = PABPab-PAbPaB, tend to be negative for data between allozymes and linked to inversions. A and B stand for the two alleles with the greatest frequency in the population. In this paper we show that linkage disequilibrium in this direction is produced at equilibrium when double homozygotes have fitnesses that are a constant fraction of the product of the two component single homozygote fitnesses, a pattern that is frequently observed in experimental data.

The conditions for a stable polymorphism and the equilibrium gene frequency in an infinite population are compared when there is spatial or temporal environmental heterogeneity for the absolute dominance model. For temporal variation the conditions for stability are more restrictive and the equilibrium gene frequency is often at a low gene frequency. In a finite population, temporal environmental heterogeneity for the absolute dominance model was found to be quite ineffective in maintaining genetic variation and is often less effective than no selection at all. For comparison, the maximum maintenance for temporal variation is related to the overdominant model. In general, cyclic environmental variation was found to be more effective at maintaining genetic variation than where the environment varies stochastically. The importance of temporal environmental variation and the maintenance of genetic variation is discussed.

A brief analysis is presented for the effects of gene flow upon genetic differentiation within and between populations generated by mutation and drift. Previous results obtained with the "island" model are developed into a form that lends itself to biological interpretation. Attention is focused upon the effective local population size and the ratio of the genetic identity of two genes in different populations to that of two genes in the same population. The biological significance of this ratio, which is independent of population size, is discussed. Similarities between the results of this model and those of the "stepping-stone" model are noted.

Summary Correlations between sibs and between parent and offspring are considered for autosomal and sex-linked polymorphisms at loci which affect fitness, and at loci where dominant genes lower fitness. The practical implications of natural selection on estimation of such correlations are discussed, with reference to the mode of action of selection. It is shown that, where fitness is affected by a sex-linked locus, parenkoffspring correlations in fitness can exist.

The presence in the cells of a single organism of a number of distinct and separable proteins with the same or very similar enzyme activities is now a well recognized phenomenon. Such multiple forms of an enzyme occurring in a single individual are generally referred to as isozymes or isoenzymes. This term was first proposed (1) in 1959, and since then has been widely adopted in the biochemical and genetical literature. It has proved to be a convenient term in practice because it does not imply unless qualified, any specific molecular relationship between the several protein species that may be observed to have similar enzyme activities (2). In fact, as an increasing variety of examples of the phenomenon have been identified, it has become apparent that different sorts of molecular relationships are involved in dif­ ferent cases. The subject was reviewed in considerable detail in the extensive series of papers given at a symposium (3) of the New York Academy of Sciences on "M ultiple molecular forms of enzymes" and published in 1968. In the present article we propose to consider some of the more recent work and will confine ourselves to studies that have been carried out on humans. Even so, the literature in this area has become so voluminous that we have found it neces­ sary to restrict the discussion to a limited series of examples. These have been chosen because of their special relevance to human genetics and because they illustrate some of the developments that have taken place and some of the new problems that have emerged in recent years. The elucidation of the nature of a particular isozyme system often in­ volves a combination of both biochemical and genetical methods of analysis. As an increasing number of different systems have been progressively in­ vestigated by such methods it has become apparent that isozymes may be generated in cells in a variety of different ways, and that in the case of any particular enzyme more than one kind of cause may be operating. From the genetical point of view it is convenient to consider the various possible causes of isozymes under three heads (4) as follows: (1) Multiple gene loci. There may be two or more separate gene loci in­ volved in determining the structures of a set of isozyme proteins, each locus coding for the aminoacid sequence of a distinctive polypeptide chain. The

Primitive populations seem favorable for studies of genetic structure, especially of isolation by distance in an array of subpopulations. Recent developments in this field are discussed, using pairs of phenotypes, inbreeding coefficients in pedigrees, isonymy, gene frequencies, and even anthropometrics. Of methods to study selection, only specific disease associations appear applicable to primitive populations. Inbreeding and outcrossing effects demand greater precision than has yet been attained in primitive groups. Some of the stated objectives of international biological programs lie far beyond the scope of present methodology.

SUMMARYComparison, by electrophoretic methods, of eel samples from Iceland, Scotland and Germany confirmed previous reports of uniformity in haemoglobin types. When liver esterases were examined, significant differences in the frequencies of phenotypes in the ‘fast’ zone of the electropherogram were found between samples from Germany and samples from Iceland and Scotland. The frequencies of transferrin phenotypes in Icelandic and Scottish eels differed significantly from those of French and American eels.It follows that regional differences in gene frequencies probably exist within the speciesAnguilla anguilla. The implications for the ‘atlantic eel problem’ are briefly discussed.

SUMMARYIn a two-dimensional stepping-stone model of finite size, if a pair of alleles happen to segregate in the whole population, marked local differentiation of gene frequencies can occur only if migration between colonies is sufficiently rare so thatNm< 1, whereNis the effective size of each colony andmis the rate at which each colony exchanges individuals with four surrounding colonies each generation. On the other hand, ifNm≥ 4, the whole population behaves as if it were panmictic and the allelic frequencies become uniform over the entire distribution range unless mutation is unusually high. Tendency toward local differentiation is much weaker in two-dimensional than in one-dimensional habitats.

In some populations of the salamander Plethodon cinereus , two polymorphic esterase loci are in linkage disequilibrium. Short-term stability of the linkage disequilibrium is demonstrated by an age class analysis. Long, perhaps very long, term stability is suggested by its distribution. This stability and concordant geographic variation in allelic frequencies imply selective origin and maintenance. Data on the frequencies of two color morphs suggest that formation of the linkage disequilibrium is dependent on the genetic background.

The interaction of random gene drift and selection was studied by computer simulation for two quantitative traits, which were considered to approximate stature and skin color differences in human populations. The expected effects of gene drift, fixation of alleles and reduction of genotypic and phenotypic variances, were found in the simulation. Stabilizing selection, which seems to be the type of selection operating on these traits, was found to increase the effects of gene drift. Since there seems to be no evidence of reduction in phenotypic and presumably genotypic variability in small human populations, the applicability of these simple genetic models to human traits raises problems for which several possible solutions exist.

SUMMARYIn a population of Drosophila melanogaster started from an inbred wild-type strain the recessive second chromosome lethal studied had shown overdominance which after many generations was lost. In the present study the persistence of this lethal was tested in three series each of five populations. The genetic backgrounds of the different series of populations were obtained from (a) the inbred strain, (b) the above original population after the overdominance had been lost, and (c) a population started from the same inbred strain and where another lethal had shown overdominance which subsequently had been lost. The lethal was overdominant in the (a) background but detrimental to the heterozygous carriers on the other backgrounds. The detrimental effect of the lethal was stronger in the (b) background than in the (c) background. The varying behaviour of the lethal is possibly due to different adapted background genotypes and/or different degrees of heterozygosity of the gene pools.

A high and low selection line were formed by individual selection of females on the basis of their recombination. In the high line, recombination between Gl and Sb was increased from 14.8 percent to about 30 percent in twelve generations, when a plateau was apparently reached. Realized heritability was 0.12. The absence of a response to selection for low recombination is attributed mainly to genetic random drift, and partially to directional dominance and directional gene frequencies. Natural selection was found to act against increases of recombination above a level of about twenty percent in the measured interval. High recombination tended to be recessive to low recombination. In both selected lines and unselected stocks, intervals proximal to the centromere tended to have a higher recombination variance than distal intervals.

Hemoglobin A(2) (alpha(2)delta(2)) in New World primates represents about 1/160 to 1/16 of total hemoglobin and, by virtue of this low proportion, is presumed to be functionally unimportant. Nonetheless, A(2) exhibits genetic polymorphism by electrophoresis in three out of five genera, whereas the major component, hemoglobin A (alpha(2)beta(2)), is electrophoretically invariant. Moreover, in four genera, including man, the evolutionary accumulation of mutations has been greater in delta than in beta Such findings suggest that both polymorphism and evolutionary changes can accrue to an effectively functionless and thus selectively nearly netutral gene.

With estimates of the fitnesses of the genotypes and selection by incompatibility for the ABO locus which seem reasonable given the state of knowledge, a computer model has been developed to replicate the clines of the A and B genes in Europe. With a fitness change in the BB and BO genotypes of as little as 0.5%, the differences in the frequencies in East and West Europe can be maintained at equilibrium. Appreciable changes in the amount of migration does not affect the equilibrium frequencies in the two areas significantly, while with no selection through incompatibility the equilibrium frequencies were changed about 5%.

The dynamics of gametic frequency change have been analyzed in two experimental plant populations. Individual plants were scored for their genotype at four enzyme loci, and four-locus joint gametic frequencies were estimated from the genotypic data over generations. Striking correlations developed in allelic state over loci, including correlations between nonlinked loci, as these populations evolved. Furthermore, the same pair of four-locus complementary gametic types came into marked excess in the late generations of both populations. The results demonstrate that natural selection acted to structure the genetic resources of these populations into sets of highly interacting, coadapted gene complexes. They also provide evidence, at the level of the gene, that selection operating on correlated multilocus units is an important determinant of population structure.

SUMMARY The model of Cavalli-Sforza and Edwards was used to investigate the gentic relationships of thirty-seven Yanomama villages. Using gene frequency data from eleven genetic systems (MNS, P, Rh, Duffy, Kidd, Diego, Lewis, haptoglobin, Ge, PGM, and acid phosphatase), three hierarchical levels of analysis were carried out. The first level involved in the construction of a gentic network, based on genetic distance between villages, for each of three historically defined clusters of villages. Upon comparing the results with ethnohistory there was shown to be a good agreement between the historical development of a cluster and its genetic network. At the second level of analysis a genetic network was constructed in similar fashion for nineteen villages of the Western Yanomama subgroup, including the three village clusters previously analysed. At this level the integrity of the village clusters was largely maintaine, exceptions being due to specific socio-political events that resulted in changes of the composition of the village gene pool. The highest level resulted in the construction of a network for all thirty-seven villages which showed three of the five geographically defined tribal subgroups as distinct entities. The result of these analyses indicate that the model of Cavalli-Sforza and Edwards can under certain circimstances be used when the requirements of the midel arenot met, and furthermore that the rate of divergence of human populations may approach a steady state at the level of major tribal subgroupings.

The mathematical model of evolution of dominance proposed by Fisher and Wright, and expanded upon by Ewens and others is subjected to a more thorough examination. The model is treated as a bonafide two locus system of a major and modifying locus involving mutation, selection and recombination. In the usual case we confirm Ewens' conclusion to the effect that in the final stages the rate of evolution is essentially algebraic. Further, we establish the role of linkage in determining the rate of evolution. Specifically we show that in both the initial and final stages of the process the looser the linkage the faster the progress towards complete dominance. Other models pertaining to evolution of dominance are briefly discussed. These include cases where the modifying locus possesses pleiotropic viability effects. The relationship to the models for dominance emanating from mimicry situations are also mentioned.

SUMMARYThe ‘neutral mutation theory’ holds that most amino acid substitutions in evolution are selectively neutral. The known pattern of variation in human haemoglobins can only be made consistent with this theory if the human species has passed through a bottleneck of numbers in the recent past. If this theory is true, estimates of the necessary size and duration of this bottleneck can be made. A theory is developed which leads to an estimate ofYg, n, the number of alleles present in a population which arise betweengandngenerations ago, and hence to the estimatewhereuis the neutral mutation rate andNethe effective population size, for the probability that a population contains no such alleles. Using data on haemoglobins, this gives an approximate upper limit to the time elapsed since the bottleneck in human numbers. Either such a bottleneck occurred, or the neutral mutation theory is false; data on other proteins will enable a choice between these possibilities to be made.