Estimation of genetic parameters in barley (Hordeum vulgare L.)

Summary Four different sets of partial diallels were analysed for their relative efficiencies for estimating the genetic parameters in barley: (1) partial diallel with 12 parents, each involved in only 5 crosses; (2) partial diallel with 12 parents, each involved in only 3 crosses; (3) partial diallel with 8 parents, each involved in only 5 crosses; and (4) partial diallel with 8 parents, each involved in only 3 crosses. In partial diallel experiments, the estimates of gca effects were higher than in those of full diallel. Ranking pattern of the parents on the basis of gca effects in partial diallels deviated considerably from the ranking in full diallel. With decreasing s per parent, the deviation in ranking was also more. This clearly suggests the unsuitability of partial diallel analysis for screening high general combiners. Selection of best cross combinations is also not possible because only a sample of crosses (s out of n) is analysed under partial diallel so that there is every possibility of the best cross being excluded from the sample. In general, overdominance was exhibited, indicating that there is ample scope for heterosis breeding in barley.     

Estimation of genetic parameters in barley (Hordeum vulgare L.)

Summary Four exotic and four indigenous strains of barley were used for making diallel crosses. The sets of parents and crosses making full, half and quarter diallel were analysed in a randomized block design for plant height, number of effective tillers, ear length, grain yield per plant, 100 grain weight and number of grains per ear.The three alternatives of diallel were similar with respect to the estimates of degree of dominance, general combining ability and specific combining ability, indicating that all these three methods of diallel were equally efficient. However, as the number of entries are minimum in quarter diallel, it would be economical in terms of cost, time and labour to estimate genetic parameters by this method. Average degree of dominance was found in the range of overdominance. The ranking of parents on the basis of their array mean was similar to the ranking based on gca effects. Similarly, the ranking of crosses on the basis of per se performance was similar to the ranking based on sca effects. This suggests that the selection of best general combiner or best cross combinations may be easier and more effective through array mean for per se performance rather than through high gca and sea effects, respectively. From among 56 crosses, IB-226 X X C-164 was the one which showed superiority for maximum number of characters followed by AB-12/59 X PTS-57. High sea effect for plant height, ear length, grain yield, 100 grain weight and number of grains per ear was the result of cross between parents having high X low general combining ability, indicating additive X dominance type of gene interaction. For number of effective tillers, high sca was produced by low x low general combiners, indicating dominance x dominance gene interaction.Part of a Ph. D. thesis submitted by senior author to Haryana Agricultural University, Hissar.     

Dual Designs and Their Application in Genetical Experiments

The dual of incomplete block designs has been studied with th́eir applications in genetical experiments. Partial diallel crosses (PDC) of type I have been constructed using balanced incomplete block (BIB) designs, partially balanced incomplete block (PBIB) designs and their dual designs. Simplified analysis of PDC has been presented using the dual property of these designs. List of optimal PDC having simple analysis has been given.     

Combining ability in the F1 and F2 generations of diallel cross in hexaploid wheat (Triticum aestivum L. em. Thell)

The F(1) and F(2) progenies of a ten-parent diallel cross (excluding reciprocals) of hexaploid wheat (Triticum aestivum L. em. Thell) were analyzed for combining ability for quantitative and quality traits. The results indicated significant differences among the parents for general combining ability (gca) and crosses for specific combining ability (sca) for all the characters studied. The gca and sca components of variance were significant for all the traits. However, the gca component of variance was predominant indicating the predominance of additive gene effects for the traits studied. Among the parents Durgapura 65, HD 2285, Lok-1, Raj 1972 and HD 2329 were the best general combiners for grain yield and average to high combiners for tillers per plant, grain yield per spike, grains per spike and 1000-grain weight. The best specific crosses for grain yield were Sonalika x WH 157, HD 2428 x Durgapura 65, Durgapura 65 x Sonalika, HD 2428 x Lok-1 and CPAN 3004 x Raj 1972. The parent Raj 1972, Lok-1 and HD 2285 were the best general combiners for grain yield and protein content, however, Raj 3077 was the best general combiner for protein content. The most suitable specific crosses for protein content were HD 2329 x HD 2285, HD 2428 x Raj 1972 and CPAN 3004 x WH 157. Most of the specific crosses for grain yield as well as protein content involved high x average, average x average and average x poor general combiners. To ensure further increase in grain yield along with high protein, combinations of desirable yield components is advocated. Inclusion of F(1) hybrids showing high sca and having parents with good gca, into multiple crosses and/or bi-parental mating, or diallel selective mating could prove a worthwhile approach for further improvement of grain yield in bread wheat.     

A general mixture model approach for mapping quantitative trait loci from diverse cross designs involving multiple inbred lines

Most current statistical methods developed for mapping quantitative trait loci (QTL) based on inbred line designs apply to crosses from two inbred lines. Analysis of QTL in these crosses is restricted by the parental genetic differences between lines. Crosses from multiple inbred lines or multiple families are common in plant and animal breeding programmes, and can be used to increase the efficiency of a QTL mapping study. A general statistical method using mixture model procedures and the EM algorithm is developed for mapping QTL from various cross designs of multiple inbred lines. The general procedure features three cross design matrices, W, that define the contribution of parental lines to a particular cross and a genetic design matrix, D, that specifies the genetic model used in multiple line crosses. By appropriately specifying W matrices, the statistical method can be applied to various cross designs, such as diallel, factorial, cyclic, parallel or arbitrary-pattern cross designs with two or multiple parental lines. Also, with appropriate specification for the D matrix, the method can be used to analyse different kinds of cross populations, such as F2 backcross, four-way cross and mixed crosses (e.g. combining backcross and F2). Simulation studies were conducted to explore the properties of the method, and confirmed its applicability to diverse experimental designs.     

Identification of superior parents in a potato breeding programme

Summary An incomplete diallel cross was used to study components of genetic variation in potatoes for a range of characters after early and late harvest. The progenies were also used to evaluate five predictors of progeny performance, namely the mean seedling performance, the mid-parent value and the means of the selfed progenies, of the diploid progenies and of the test-cross progenies. For almost all characters, the general combining ability effects were predominant, although the specific combining ability effects present were greater at late than at early harvests. The seedling performance for tuber yield, number of tubers and average tuber weight did not show any relevant relationship to the field performance. The midparent value provided, in general, satisfactory predictions of the mean progeny performance obtained in the diallel, except for ware tuber yield. The selfed and the diploid progenies did not improve the prediction of progeny means compared to the mid-parent value. The predictions based on the test-crosses surpassed those of the mid-parent value, particularly for tuber yield at ware potato harvest. Methods to identify superior parents are discussed.     

Combining ability and parental evaluation in five selected clones of sugarcane (Saccharum sp. hybrids)

Summary Five Hawaiian commercial sugarcane (Saccharum sp. hybrids) clones were crossed in a full diallel. Four morphological characters were studied in the progeny: number of millable stalks per plant, stalk diameter, stalk length, and sucrose content. A fifth character, plant volume, was calculated from stalk number, stalk diameter and stalk length. The five selected parental clones were treated as fixed variables in the analysis. General combining ability (gca) was significant for all five characters; specific combining ability (sca) was significant for stalk diameter, stalk length, and plant volume. The variance for gca was large in all progeny populations. However, the variance for sca was large in the progeny of only some clones and/or for some individual characters. Parents were evaluated on the basis of their general combining ability: clone H49-3533 had high gca for sucrose content, while clone H53-5356 had high gca for plant vigor.Published with the approval of the Director as Journal Series Paper No. 455, Experiment Station, Hawaiian Sugar Planters' Association.     

Analysis of genetic effects of major genes and polygenes on quantitative traits I. Genetic model for diploid plants and animals

A genetic model was proposed to simultaneously investigate genetic effects of both polygenes and several single genes for quantitative traits of diploid plants and animals. Mixed linear model approaches were employed for statistical analysis. Based on two mating designs, a full diallel cross and a modified diallel cross including F₂, Monte Carlo simulations were conducted to evaluate the unbiasedness and efficiency of the estimation of generalized least squares (GLS) and ordinary least squares (OLS) for fixed effects and of minimum norm quadratic unbiased estimation (MINQUE) and Henderson III for variance components. Estimates of MINQUE (1) were unbiased and efficient in both reduced and full genetic models. Henderson III could have a large bias when used to analyze the full genetic model. Simulation results also showed that GLS and OLS were good methods to estimate fixed effects in the genetic models. Data on Drosophila melanogaster from Gilbert were used as a worked example to demonstrate the parameter estimation. Received: 11 November 2000 / Accepted: 2 May 2001     

EXPERIMENTAL STUDIES OF THE EVOLUTIONARY SIGNIFICANCE OF SEXUAL REPRODUCTION. III. MATERNAL AND PATERNAL EFFECTS DURING SEEDLING ESTABLISHMENT

To determine whether genetic differences in fitness components exist among seeds and seedlings in a natural population, weighed propagules of six parents of Anthoxanthum odoratum from a reciprocal diallel cross were planted into the parental source population, a mown field. Seed families of maternal genotypes differed in germination success, while paternal families showed no detectable differences. Differential germination success could not be attributed to propagule weight. Seed families ranked differently in germination percentage in different blocks. No survivorship differences among parental seed families could be detected. There were significant cross × block × germination and cross × block × survivorship interactions; different crosses performed better or worse in different blocks. In some cases, crosses sired by different fathers within a maternal seed family differed in germination or survivorship, suggesting that natural selection may be capable of discriminating among juvenile genotypes within a maternal family despite the presence of large overall maternal effects. These results indicate that seedling establishment may differ according to genotype and that microsite heterogeneity may maintain genetic variation in juvenile traits in natural plant populations.     

Diallel cross analysis of body weight in subspecies of mice.

A complete 4 x 4 diallel cross of CF#1 (C), C57BL/6NCrj (B) C3H/HeNCrj (H) and Yonakuni wild mice (Y, Mus musculus molossinus yonakuni) has been conducted to estimate the effects of sex, degree of heterosis, general combining ability (gca), specific combining ability (sca), maternal ability, and reciprocal cross on body weight at 1 (Wk1), 3 (Wk3), 6 (Wk6) and 10 (Wk10) weeks of age. A least squares analysis was performed on 828 mice and all sources of variation showed significant effects (P < 0.01) on body weight but not sex at Wk1 (P > 0.05). Males were heavier than females (P < 0.01) at Wk3, Wk6 and Wk10. C and Y were the heaviest and lightest in body weight, whereas H and B were intermediate. Differences in body weight were observed between linebred and linecross at all ages studied: 6.57%, 10.22%, 8.70% and 5.89% heterosis for the respective ages. The degree of gca and maternal effects can be ranked as C > H > B > Y. Crossing between C and H had greater sca than other combinations at all ages studied, whereas B x Y had the smallest. Mean body weight of the offspring from two-line reciprocal cross differed according to their dam. A relatively large proportion of additive genetic effects in contributing to the variation in offspring body weight was indicated.     

A comparison of four experimental designs for the estimation of heritability

Summary The partial diallel cross, the complete diallel cross, and the designs known as North Carolina Experiments 1 and 2 are compared for their usefulness in estimating heritability. It is first shown that reliable values for the sampling mean and variance of heritability estimates are obtained from approximate expressions based on the moments of the chi-square distribution. These expressions are then applied to determine the optimum experimental designs for a range of situations.The main basis for discrimination is the amount of information per unit, defined as i = 1/(N var( ²)), where ² is the estimate of the heritability h ² and N is the number of units in the experiment, either individuals or families.The two parameters considered were the heritability of individuals and the heritability of full-sib families, and for each of these the partial diallel cross was the most preferred, followed in decreasing order of preference by design NC2, the complete diallel, and design NC1.It is first shown that there is no optimum number of parents for a partial diallel cross or male parents for designs NC1 and NC2. The number of crosses per parent for a partial diallel or dams per sire for designs NC2 and NC2 should generally be six or less. Any expansion should be in the direction of using more parents in the case of the partial diallel, or more male parents in the case of designs NC1 and NC2. For the two heritability parameters considered in this study it is inefficient to increase the number of replicates beyond two.     

Combining ability for the traits of stem branching and plant height in linseed lines

Combining ability for the traits of stem branching and plant height has been studied in ten pure lines of flax under complete and incomplete diallel crosses. High heritability of the traits "plant height", "the number of lateral stems" and "the number of lateral shoots" and essential role of genes with dominant effects of interaction in genetic control of the traits of stem branching and plant height have been shown. On the basis of combining ability indexes the ways for usage of certain genotypes and crossing combinations in flax breeding were defined. As a result of individual selection from hybrid combinations some new complexes of habit traits and agriculturally valuable plant characteristics were obtained.     

作物杂种后代基因型值和杂种优势的预测方法

本文提出了利用作物亲本和F_1预测杂种后代基因型值和杂种优势的统计分析方法.该方法运用加性-显性遗传模型,分析双列杂交试验资料,用MINQUE(1)法估算方差分量以及预测遗传效应值.由加性和显性效应预测值可进一步预测F_1,F_2,BC_1,BC_2,等不同世代的基因型值,在预测F_1群体平均优势和群体超亲优势的基础上,可以推导出其它各世代的杂种优势.提出了预测杂种后代保持超亲优势世代数的简单公式,根据杂交组合F_1群体平均优势和双亲相对遗传差异,便可预测该组合能在生产上直接利用的世代数.以棉花六个品种完全双列杂交试验资料为例,分析了各组合F_1和F_2的基因型值、超亲优势和保持5％超亲优势的世代数.     

Genetic analysis of agronomic characters in chickpea

Summary Twenty-eight diallel trials over 8 years and two locations were analysed to estimate genetic variances for agronomic characters of chickpea (Cicer arietinum L.). The data were analysed according to Method 4 and Model I of Griffing (1956). Days to flowering, plant height, and seed size were found to be predominantly under additive inheritance and were highly predictable. Both additive and non-additive genetic components were important for seed yield, number of branches, pods per plant, and seeds per pod. Although both general combining ability (gca) and specific combining ability (sca) varied significantly with generation, components of gca mean squares were invariably much larger than gca x generation interaction components, indicating that either the F₁ or the F₂ generation can be used to estimate the gca components effectively. Combined diallel analysis of F₂s over locations revealed the importance of combining ability x location interactions and emphasized the need for testing over more than one location for the precise estimation of combining ability. The implications of these findings and those reported earlier in the literature on the breeding strategies/methods for the genetic improvement of agronomic characters in chickpea are discussed.ICRISAT journal article no. 1199     

Genetic aspects of resistance to cocoa swollen-shoot virus in Ghana

The inheritance of resistance in cocoa to infection with cocoa swollen-shoot virus was studied in seed inoculation experiments with progenies of Upper Amazon, Trinitario and West African Amelonado parents. In an eight parent diallel cross grown in two seasons and in six male × female factorial experiments, general combining abilities were much more important than specific combining abilities. The diallel cross revealed significant maternal effects but there was little evidence of specific reciprocal differences. Estimates of general combining abilities corresponded with expectation and were positively correlated with maternal effects, the latter indicating that tester parents should be used as males. The results from scaling tests with hybrids between selections from the River Nanay (a Peruvian tributary of the River Amazon) and Amelonado fitted a model with additive resistance; there was no evidence of dominance. Attempts to obtain stronger sources of resistance by hybridisation and selection were unsuccessful. In three crosses the resistance of individual seedlings was compared with that of the parents using test crosses but no evidence of transgressive segregation was obtained. In further experiments seedings of two hybrids between contrasting parents were heavily inoculated with virus so that few healthy survivors remained. Test crosses showed that these survivors and randomly selected seedlings of the same parentage did not differ as resistance sources.     

Estimating effects of a single gene and polygenes on quantitative traits from a diallel design

A genetic model is developed with additive and dominance effects of a single gene and polygenes as well as general and specific reciprocal effects for the progeny from a diallel mating design. The methods of ANOVA, minimum norm quadratic unbiased estimation (MINQUE), restricted maximum likelihood estimation (REML), and maximum likelihood estimation (ML) are suggested for estimating variance components, and the methods of generalized least squares (GLS) and ordinary least squares (OLS) for fixed effects, while best linear unbiased prediction, linear unbiased prediction (LUP), and adjusted unbiased prediction are suggested for analyzing random effects. Monte Carlo simulations were conducted to evaluate the unbiasedness and efficiency of statistical methods involving two diallel designs with commonly used sample sizes, 6 and 8 parents, with no and missing crosses, respectively. Simulation results show that GLS and OLS are almost equally efficient for estimation of fixed effects, while MINQUE (1) and REML are better estimators of the variance components and LUP is most practical method for prediction of random effects. Data from a Drosophila melanogaster experiment (Gilbert 1985a, Theor appl Genet 69:625–629) were used as a working example to demonstrate the statistical analysis. The new methodology is also applicable to screening candidate gene(s) and to other mating designs with multiple parents, such as nested (NC Design I) and factorial (NC Design II) designs. Moreover, this methodology can serve as a guide to develop new methods for detecting indiscernible major genes and mapping quantitative trait loci based on mixture distribution theory. The computer program for the methods suggested in this article is freely available from the authors.     

Augmented Partial Diallel Design for Estimating Combining Ability of Parents

The Augmented Partial Diallel Cross (APDC) represents an intermediate position between the Complete Diallel Cross (CDC) and the Partial Diallel Cross (PDC) in which one or more primary lines are crossed with all the other lines but the lines of secondary interest form a PDC system. The method of sampling adopted for crosses of secondary lines is from arrangement of secondary lines on circumference of a circle. The mathematics for analysis of such APDC has been given systematically. The efficiency of estimates of general combining ability (g.c.a.) effects obtained from APDC has been compared with that of Pederson's estimator and CDC. It is observed that there are four types of variances for g.c.a. effects where as for comparing specific combining ability (s.c.a.) effects there are large number of variances indicating that the design is totally unbalanced for s.c.a. comparisons.     

Analysis of genetic control of mating behavior in screwworm (Diptera: Calliphoridae) males through diallel crosses and artificial selection

Summary The mode of genetic control of male screw-worm (Diptera: Calliphoridae) mating behavior was examined using diallel cross and artificial selection. Diallel crosses showed strong dominance effects, with hybrids being uniformly more successful in copulation than their more inbred parental strains. Weaker additive and reciprocal effects were also noted. Environmental (replicate) effects were highly significant. Regression of array variances and covariances indicated that epistatic interactions or unequal allele distribution during gametogenesis may have occurred and that high courtship propensity polygenes show dominance over low propensity genes. Artificial selection on males from outbred strains from Guatemala and Belize resulted in a decreased number of mating attempts for lines selected for reduced activity, but mating attempts in lines selected for high mating activity did not increase. A combination of inbreeding during the selection cycles as well as selection for recessive traits would explain this response. The two types of experiments were in general agreement, indicating significant dominance and environmental influence on male mating behavior with weaker additive and possible maternal effects.     

Accuracy of genomic selection to predict maize single-crosses obtained through different mating designs

Key message

Testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II.

Abstract

Even though many papers have been published about genomic prediction (GP) in maize, the best mating design to build the training population has not been defined yet. Such design must maximize the accuracy given constraints on costs and on the logistics of the crosses to be made. Hence, the aims of this work were: (1) empirically evaluate the effect of the mating designs, used as training set, on genomic selection to predict maize single-crosses obtained through full diallel and North Carolina design II, (2) and identify the possibility of reducing the number of crosses and parents to compose these training sets. Our results suggest that testcross is the worst mating design to use as a training set to predict maize single-crosses that would be obtained through full diallel or North Carolina design II. Moreover, North Carolina design II is the best training set to predict hybrids taken from full diallel. However, hybrids from full diallel and North Carolina design II can be well predicted using optimized training sets, which also allow reducing the total number of crosses to be made. Nevertheless, the number of parents and the crosses per parent in the training sets should be maximized.

     

A comparison between the full diallel cross and the simplified triple-test cross

Summary The simplified triple-test cross (sTTC) is a mating design that, because of its economic use of the experimental material as compared with other designs, seems very attractive. In theory, its power is almost equal to that of more elaborate designs such as the diallel cross. To evaluate the merits of both designs in a genetic analysis of mouse behavior, the results of a previous replicated 4×4 diallel cross (Crusio and van Abeelen 1986) were reanalyzed as a sTTC. We found that, at least with the fairly low number of strains employed, the sTTC analysis is clearly inferior to the diallel cross. This finding, in combination with some theoretical considerations, leads to the conclusion that the sTTC design is not a very useful one for such studies.