A method for analysing probabilistic models representing an extension of path analysis, and a model of mixed homogamy based on this method were introduced recently (Rao, Morton & Cloninger, 1979; Cloninger, 1980). However, constraints imposed by the method on linear models, or a rationale for and implications of the mixed homogamy model have not been clearly stated.

A mathematical treatment of the extension of path analysis and of the mixed homogamy model is presented in this paper. Constraints on linear models imposed by the extension are obtained. It is demonstrated that the mixed homogamy model, when applied to analysing nuclear families in a population, implies the following mating system in the population: some individuals choose their mates strictly on the basis of group membership, others choose their mates strictly on the basis of phenotype, and no individual chooses a mate on the basis of both group membership and phenotype.

A population with u deleterious mutations per genome per generation is considered in which only those individuals that carry less than a critical number of k mutations are viable. It has been shown previously that under such conditions sexual reproduction is advantageous. Here we consider selection at a locus that determines recombination frequency of the whole genome. The value v = u/ √ k has been found to play the decisive role. When v < 0·35 the direction of selection for recombination may be different for different cases, but the intensity of selection is always very small. The advantage of recombination becomes considerable when v > 0·5, its growth under increasing v being approximately linear. If v > 2 no less than 95% of the progeny are bound to die because of the selection against deleterious mutations. Since this seems to be too great a mutation load, we may assume 0·5 < v < 2·0 for any sexual population if mutation really maintains crossing-over. Results on selection at a locus which controls mutability provide evidence that v is located within the specified interval if the physiological cost of a twofold reduction of the mutation rate is within the range 10–80%. A number of consequences of this hypothesis about the mechanism of selection for sex and recombination are discussed.

From the available electrophoretic data, it is clear that haplodiploid insects have a much lower level of genetic variability than diploid insects, a difference that is only partially explained by the social structure of some haplodiploid species. The data comparing X-linked genes and autosomal genes in the same species is much more sparse and little can be inferred from it. This data is compared with theoretical analyses of X-linked genes and genes in haplodiploids. (The theoretical population genetics of X-linked genes and genes in haplodiploids are identical.) X-linked genes under directional selection will be lost or fixed more quickly than autosomal genes as selection acts more directly on X-linked genes and the effective population size is smaller. However, deleterious disease genes, maintained by mutation pressure, will give higher disease incidences at X-linked loci and hence rare mutants are easier to detect at X-linked loci. Considering the forces which can maintain balanced polymorphisms, there are much stronger restrictions on the fitness parameters at X-linked loci than at autosomal loci if genetic variability is to be maintained, and thus fewer polymorphic loci are to be expected on the X-chromosome and in haplodiploids. However, the mutation-random drift hypothesis also leads to the expectation of lower heterozygosity due to the decrease in effective population size. Thus the theoretical results fit in with the data but it is still subject to argument whether selection or mutation-random drift are maintaining most of the genetic variability at X-linked genes and genes in haplodiploids.

Multilocus recombination frequencies are expressed in terms of pairwise recombination frequencies for paracentric and pericentric intervals. Applications of this theory to mapping and genetic counselling are discussed.

Two male-sterile chromosome anomalies, the insertion Is(7; 1)40H and the tertiary trisomy, Ts(512)31H, were found to be associated with reduced ovarian volumes in immature females. Together with the reciprocal translocation, T(11; 19)42H, in which this effect was described previously, reduced ovaries have been found in all three male-sterile chromosome anomalies investigated so far, suggesting that ovarian involvement is likely to be common in these conditions. Assuming that the smaller ovarian size reflects a reduction in the number of oocytes, it is suggested that male-sterile chromosome anomalies may exert basically similar deleterious effects on meiotic germ cells in males and females, the difference in outcome being due to cell-physiological differences between spermatocytes and oocytes and to the small number of surviving oocytes required for fertility in females.

Two substrains of the inbred mouse strain 101, maintained at Harwell and at Neuherberg, and designated 101/H and 101/E1, differed at five of the eight genetic loci tested and it seems very likely that one of these substrains has been genetically contaminated. The available evidence suggests that 101/E1 is probably the contaminated substrain.

A single locus model of extranuclear genomes is developed under the assumption of the complete action of within-generation drift which is caused by random transmission of multiple copy genomes during cell division in a generation. Within-generation drift segregates different copy genomes in a cell into different cells, resulting in homoplasmic cells. Under some conditions, the present model reduces to that for haploid nuclear genomes. A point overlooked in previous models is that the multiplicity also admits of the possibility of selection occurring within a cell or between cells in an individual (within-generation selection). If there is selection mediated by, for instance, differential proliferation of genomes, then a haploid model no longer explains the dynamics of extranuclear genomes. Rather a model analogous to biased gene conversion at a single locus (Nagylaki, 1983; Walsh, 1983) is more appropriate. An application of this model to either the fixation probability or substitution rate of new mutations shows that strictly maternal inheritance does not allow the fullest use of mutations, as it obscures the effect of within-generation selection. But if there is appreciable paternal contribution, within-generation selection could be a strong evolutionary force to which nuclear genomes are never exposed.

Postmeiotic segregation (PMS) of genetic variants occurs when a DNA heteroduplex formed during meiotic recombination goes undetected by repair enzymes and is transmitted unresolved to the meiotic products. PMS provides an alternative explanation for the origin of mosaics now attributed to half-chromatid mutation. In multicellular diploid eukaryotes, PMS could result in mosaic individuals with unusual migration patterns for proteins studied by gel electrophoresis. If the gonade were mosaic, complex progenies containing as many as six phenotypic classes at a single locus could be produced.

In Takahata & Slatkin (Genetical Research 1983, 42, 257–265), two sentences should be read as:

but, in contrast, the configuration of the genome and the mode of transmission both make a large difference (on page 257, lines 11–12 up)

Contribution no. 1528 from the National Institute of Genetics, Mishima, Shizuokaken 411, Japan (on page 264, above REFERENCES).

Selection theory usually assumes an equally probable contribution of each selected individual to a large ‘gene pool’ from which the individuals to be measured in the next generation are sampled. With unequal contributions it is possible to find several sets of values for N (the number of selected individuals) and fi (probability of contribution of the ith individual) such that the same selection intensity is attained. It is suggested that the set of values producing minimum genetic drift should be chosen in order to increase the long-term response without any reduction in the short-term advance.

When males from a strain of Drosophila melanogaster which have multiple copies of the P family of transposable elements integrated into their genome (Bingham, Kid well & Rubin, 1982) (‘P’ strains) are crossed to females of strains lacking those elements (‘M’ strains), the F1 progeny manifest a number of aberrant traits known collectively as hybrid dysgenesis (Kidwell, Kidwell & Sved, 1977). Progeny of the reciprocal cross (P♀ × ♂M) are normal. The dysgenic syndrome is characterized by a high degree of genomic instability caused by enhanced transposition of P elements. Since mutations at visible loci and chromosomal rearrangements are frequently observed in dysgenic hybrids, it was hypothesized that this phenomenon could be used to investigate the effects of transposition on quantitative characters; therefore, the progeny of dysgenic and non-dysgenic crosses were artificially selected for high and low abdominal bristle number. The response to selection, phenotypic variation, and realized heritability were all increased in the dysgenic lines, relative to the non-dysgenic control. It is postulated that these features are the result of P element-induced mutations of loci affecting bristle number, and that future work should lead to the identification of these loci, as well as elucidating the role of transposition in population differentiation for metric traits

The rDNA of five Y chromosome mutants was examined with respect to their insert free (In−) repeat type multiplicity. The In− repeat number of each mutant was correlated with its hemizygous bobbed phenotype and additivity with an X NO bobbed (bb) mutant. Four of these mutants showed a direct relationship between their In− frequency, hemizygous bb phenotype and additivity tests. A fifth mutant, bb1–4, had a sufficient number of In− repeats to ensure viability to the late pupal stage and show additivity; however, the In− repeats genetically behaved as a complete rDNA deletion. Possible mechanisms resulting in the suppression of the bb1–4 In− repeats are discussed.