Estimation of the true additive genetic variance sigma ki = 1 d2i in the presence of linkage disequilibrium.

Accurate estimates of the true additive genetic variance (sigma ki = 1 d2i) of a cross between two pure breeding varieties can be obtained from the additive genetic components of the first three ranks (D1, D2 and D3) when the latter are biased by the presence of linkage. Additive genetic variances of the lower ranks are directly equatable with sigma ki = 1 d2i because they incur minimal bias even when the predominating linkages are strong. More precise estimates of sigma ki = 1 d2i are however obtainable from the asymptotic regression analysis or a weighted least squares analysis. Estimates of sigma ki = 1 d2i when obtained from 784 hierarchically derived F7 families of the V2 X V12 cross of Nicotiana rustica were observed to be considerably larger than the additive genetic variance displayed by the F13 inbreds of the same cross for all the characters that showed significant excess of repulsion linkages. These results lend support to our commonly held view that the prediction procedures generally underestimate the probability of successful recovery of superior recombinant inbreds.

Predicting the properties of first cycle inbreds and second cycle hybrids extractable from two, three and four parent crosses.

Standard biometrical genetical models of Mather and Jinks (1982) when made applicable to the means and variances of the 55 early generations produced by crossing four parents and six F1's in all possible combinations provide estimates of genetic parameters that can be used to predict the distributive properties of the first cycle inbreds and second cycle hybrids which could be extracted from any of these generations. Thus we can predict the inbreeding and outbreeding potentials of each generation in the early stages of a breeding programme and formulate the best breeding strategy for harnessing the full genetic potential of the breeding material and choosing the best end product. The 55 generations provide reliable estimates of the predictors and therefore should be used whenever possible. Simpler experiments consisting of the basic generations of the six single crosses, however, are sufficient for obtaining estimates of the predictors of the inbreds and can be used to predict their properties when information about the second cycle hybrids is not required or the remaining generations are not available. Replacement of the F2, backcross, three way cross and double cross generations with their randomly mated progenies is expected to improve the accuracy of predictions in the presence of a linkage disequilibrium. However, the gains made may not be justified against the costs of the additional breeding and the delay in making the predictions. Extensive experimental testing of the theory of these procedures must await the completion of the current field experiments. In the meantime the limited tests conducted on the material extracted from the Nicotiana rustica varieties V1, V2, V5 and V12 have confirmed the familiar conclusions that the V1 X V5 and V2 X V12 differ in their inbreeding and outcrossing potentials.

Genetical investigations into ß-glucan content in barley.

Random inbred lines produced by doubled haploidy (DH) and single seed descent (SSD) have been used to investigate the genetics of ß-glucan (gum) content in barley (Hordeum vulgare). Genetical analyses indicated that gum content is controlled by a simple additive genetic system. Significant negative genetic correlations were observed between ß-glucan content, thousand grain weight and height in the DH samples. These correlations were much reduced in the SSD samples and would suggest linkage of the genes controlling these characters. The presence of repulsion linkages could be exploited in a barley breeding programme by producing F1 derived DH to generate recombinants with high thousand grain weight and low ß-glucan content. Genetical parameters estimated from DH and F3 samples have successfully been used to predict the number of inbred lines transgressing the parental range for ß-glucan content and bivariate combinations involving ß-glucan.

Predicting the properties of second cycle hybrids produced by intercrossing random samples of recombinant inbred lines.

Distributive properties of the second cycle hybrids that are produced by inter-crossing the recombinant inbreds extractable from the F2 of a cross between two pure breeding lines can be predicted from the early generations of the original cross. Hence the frequency of such hybrids that will outperform the extreme recombinant inbreds or the original F1 can be predicted. Basic generations and triple test cross families provide the most reliable estimates of the predictors and therefore should be used whenever possible although, in the presence of linkage, randomly mated F2's may give improved predictions. Simpler experiments consisting of the parental varieties and their F1 and F2 generations, however, provide all the information that is likely to be necessary for most practical purposes. The predictive power of the new approach is demonstrated on material extracted from the cross of varieties 1 and 5 of Nicotiana rustica. The predictors were estimated from the means and variances of V1, V5, F1 and F2 raised in six environments between 1973 and 1983. The predicted frequencies of second cycle F1's which outperform the extreme recombinant inbred lines derived from this cross are compared with those observed among 190 second cycle hybrids in a diallel between 20 recombinant inbreds derived from the same cross.

A genetical analysis of diversity and asymmetry in finger ridge counts.

The genetics of asymmetry and diversity of finger ridge counts in man has been examined by jointly regressing the individual counts of each hand on to the mean values summed over left and right hands in a sample of twins. The resulting asymmetry terms are largely under environmental control but with a small significant genetic component. The diversity items show a larger degree of genetic control with a suggestion of dominance or additive X additive epistasis.

The monozygotic twin half-sib method for analysing maternal effects and sex-linkage in humans.

The influence of maternal effects and sex-linked loci upon the statistics derived from an analysis of the families of monozygotic twins (the so called MZ half-sib design of Nance and Corey, 1976) is examined. If, as in the published analyses, the progeny sexes are considered jointly, maternal effects and sex-linkage may be confused. In the absence of sex-linkage a comparison of maternal and paternal half-sib covariances will often be a more powerful test for maternal effects than the conventional comparison of maternal and paternal parent-offspring covariances. If the progeny sexes are considered separately the analysis of sex-linkage presents no fundamental problems.

A modified triple test-cross analysis to test and allow for inadequate testers.

When the population under investigation consists of highly inbred lines the full triple test-cross of Kearsey and Jinks (1968) supplemented by the selfed progenies of the population allows unambiguous and independent tests for epistasis and the adequacy of the pure-breeding testers, L1 and L2. This can also be achieved by supplementing the simplified triple test-cross of Jinks, Perkins and Breese (1969) with the selfed progenies of the L1i and L2i families. If the L1 and L2 testers prove to be inadequate due to the presence of common loci, modifications of the analyses are proposed which correct the resulting biases in the genetical components of variation.

The consequences of using inadequate testers in the simplified triple test-cross.

The genetical consequences of common alleles in the L1 and L2 testers of a simplified version of the triple test-cross which is applicable to populations of inbred lines are examined. The test for epistasis under these circumstances becomes ambiguous and can spuriously detect non-allelic interactions when they may not exist although it still provides a test for epistasis and the adequacy of the testers simultaneously. The tests of significance and the estimates of additive variation are biased to an extent related to the dominance and dominance x additive effects of the common loci while the significance and estimates of dominance variation are deflated because they reflect the dominance effects at the non-common loci only. The covariance of sums and differences is also underestimated for the same reasons. These expectations are illustrated by analysing the 190 simplified triple test-crosses that could be extracted from a 20 x 20 diallel set of crosses between pure-breeding lines of Nicotiana rustica.

Joint scaling tests.

It is shown that a joint scaling test developed by Tan (1974) is closely related to the widely used standard Cavalli joint scaling test (described by Mather and Jinks, 1971) which was not referred to in Tan's paper. With the numbers of individuals per generation observed in practice, the two tests give essentially similar results. The Cavalli procedure also provides estimates of genetical parameters and is more readily extended to a wider range of situations.

Variation in a natural population of Schizophyllum commune. Variation within the extreme isolates for growth rate.

Two extreme dikaryotic idolates chosen from a large sample of a localised population of Schizophyllum commune exhibited a considerable amount of genetical variation for growth rate at the near ambient temperature of 20 degrees C and at the higher temperature of 30 degrees C. The potential variation within these extreme isolates were greater than the variation observed in the whole sample. Regression analysis of the variation in growth rate of the dikaryotic progeny of the extreme isolates on that of their component monokaryons showed that the nature of gene action was not the same in these two stages of the life cycle. The simple additive-dominance model of gene action was adequate to explain the variation in growth rate in both of the extreme isolates at both of the temperatures. The small deviations from this model could be accounted for by unequal gene frequencies due to small sample size although a low incidence of non-allelic interactions could not be rule out. Directional dominance for growth rate was detected in both isolates at the more normal temperature and it was opposing in direction in the two isolates. In the slow growing isolate the dominance was for faster growth and in the fast growing isolate it was for slower growth. This is expected for a character which displays overall ambi-directional dominance if isolates with more extreme growth rates than those recovered in the population sample are eliminated by stabilising selection. The dominance is temperature dependent being ambi-directional in both isolates at the higher temperature. Environmental heterogeneity, the buffering effects of directional dominance and genotype-environment interactions and opposing selective forces operating on the monokaryotic and dikaryotic stages of the life cycle are possible contributory factors to the considerable free and potential variability displayed in this small, localised population.

Estimating the number of genes in a polygenic system by genotype assay.

A new method, genotype assay, is described for estimating k the number of genes or more strictly the number of effective factors responsible for variation of a continuous kind. The central feature is the determination of the proportion of individuals in the Fn generation of a cross between two pure breeding lines that are heterozygous at, at least, one locus by an assay of their Fn+2 grand progeny families. The observed proportion is then equated to a theoretical expectation which is a function of the number of genes involved. Expectations generalised to cover any generation n for experimental designs in which every Fn individual is assayed by comparing two Fn+2 grand progeny families have been derived for two limiting cases; one in which all genotypic differences are expressed as phenotypic differences and the other where the expression is minimised by imposing the maximum and relational balancing out of the contributions of individual gene loci. Equating the observed proportion of heterozygotes to these expectations therefore, leads to an upper and a lower estimate of k corresponding with these two limiting conditions. The reliability and sensitivity of the estimates depends primarily on n the generation chosen for study, the number of individuals (m) assayed from that generation and the number of individuals (l) raised in each Fn+2 grand progeny family. The two variables m and l being the principal determinants of the variances of the family means set the lower limit to the size of the gene effects that can be detected. The method is illustrated by assays of the F3 and F5 generations of two crosses between conditioned lines of Nicotiana rustica for three characters. The estimates are, without exception, as great as or greater than those obtained by alternative procedures. They show large, consistent increases between the F3 and F5 that cannot be traced to greater sensitivity of the latter generation and hence are presumably genuine.

The efficiency and optimal size of triple test cross designs for detecting epistatic variation.

The triple test cross and two of its associate designs have been compared for their theoretical and practical efficiency in detecting epistatic variation. The comparisons are made on the basis of optimal experimental sizes required for each of these tests to detect a modest level of epistasis significantly (P less than or equal to 0-05) and with a reasonable certainty (95 per cent). The experimental sizes are determined for various combinations of heritability, dominance ratio and gene association and for both duplicate and complementary epistasis. Two versions of the test epistasis designed by Kearsey and Jinks (1968). Test 1a and Test 1b, do not differ much in their theoretical efficiency for detecting epistasis and the optimal experimental sizes required by them to detect non-allelic interactions significantly are largely impraticable except when dominance and heritability are high and the degree of association is 50 per cent or more. Both the tests require much smaller experiments to detect duplicate epistasis than complementary epistasis of the same magnitude and this difference is more pronounced for lower levels of heritability and dominance. The theoretical efficiency of Test 2 (given by Jinks, Perkins and Breese, 1969), however, does not vary with the type of epistasis but the sensitivity of the test is inversely related to the degree of gene association between the tester parents. The practical implications of the present investigation are discussed and the validity of some of the most important theoretical predictions and assumptions are tested on a triple test cross involving 80 inbred lines of Nicotiana rustica.

Effect of gene dispersion on estimates of components of generation means and variances.

The components of generation means that measure gene action and interaction at homozygous loci have expectations that depend on the degree of association or dispersion of alleles of like effect at different loci. With anything less than complete association, estimates of these components do not necessarily reflect the relative directions, magnitudes or kinds of gene action or interaction present. To illustrate these expected consequences, the F1, F2 and backcross generation of two contrasting crosses between pairs of inbred lines of Nicotiana rustica have been raised in which the same alleles are segregating at the same loci but for loci contributing to variation in final height the alleles of like effect are predominantly associated in one cross and predominantly dispersed in the other. The simultaneous analysis of the data from the two crosses show all the expected effects of the differences in the degree of association or dispersion. In the dispersion cross the effects of gene action at homozygous loci are underestimated and the interaction between homozygous loci is not detected at all. The large directional dominance component that is common to both crosses is in fact no greater than the additive component once the deflating effect of dispersion is removed, thus ruling out the presence of overdominance. No effects of association or dispersion on the components of variation could be detected nor would any be expected unless there were differences in the predominant linkage phase between the two crosses. Large and predictable effects on estimates of the number of effective factors are, however, demonstrable.