Interaction Component Of Variance Research Articles

Study of Some Flax Characters, Genetic Stability and their Relation to Yield

The present study consisted of twelve genotypes of flax which were evaluated over twelve environments (2 seasons (2013/14 and 2014/15), 2 locations (Etay El-Baroud Exp. Sta., El-Beheira Governorate and Ismailia Exp.Station, Ismailia Governorate) and 3 plant density (1000,1250 and 1500 seeds/m2)) These materials were evaluated in a split plot design with three replications at the twelve environments which-mentioned before. The mean square of environments (E) genotypes (G), and E x G interaction for all studied traits revealed highly significant differences, indicating a wide range of variation among genotypes, environments and these genotypes exhibited differential response to environmental conditions. The significant variance due to residual for all characters indicated that genotypes differed with respect to their stability suggesting that prediction would be difficult, which means that mean performance alone (mean yield) would not be appropriate. Interaction component of variance (σ2ge) was less than the genotypic variance (σ2g) for all characters except each of straw weight per plant, plant height and capsules number per plant. This was reflected in high value of heritability and low gap between GCV and PCV values for 1000 – seed weight, fiber percentage, oil percentage, seeds number per capsule, and technical length. These results indicating the possibility of using technical length as selection index for improving straw weight/plant and both of number of seeds per capsule and 1000- seed weight as selection indices for improving seed weight/plant. The criterion, yield stability (YSi) statistic indicated that only one genotype (S.541- D/4) exhibited superiority and stability for all straw characters, in addition to S.435-11/10/3 for each of straw yield/fad, technical length and plant height. Also, S.541- /6 gave high mean performance and stability (YSi) for seed yield/fad, oil yield/fad, 1000- seed weight and oil percentage. Therefore, the two strains (S.541-D/4 and S.435/11/10/3) may be recommended to be included in any breeding program for improving straw yield and its related traits and also, S.541-C/6 for improving seed yield and its related characters. Straw weight/plant was positive and significant correlated with each of technical length, plant height, and seed weight/plant. And also, plant height exhibited positive correlation with technical length. Whereas, seed weight per plant, exhibited positive correlation with both of capsules number/plant and 1000 - seed weight. Whereas, the correlation between oil percentage with both of 1000- seed weight and capsules number per plant was positive. These mean that the possibility of using both of technical length and plant height as selection indices for improving straw weight/plant and both of1000-seed weight and capsules number/plant and as selection indices for improving seeds weight/plant.

GIZA 11 AND GIZA 12; TWO NEW FLAX DUAL PURPOSE TYPE VARIETIES

Sixteen flax genotypes {13 promising lines and 3 check varieties viz., Giza 8 (oil type), Sakha 1 (dual purpose type) and Sakha 3 (fiber type)} were evaluated for straw, seed, oil yields and their related traits under twelve different environments; four locations (Sakha, Etay El-Baroud, Ismailia and Giza Exp. Stations through three successive seasons (2011/12, 2012/13 and 2013/14). These materials were evaluated in a randomized complete blocks design with three replications at the twelve above-mentioned environments. The analysis of variance revealed highly significant differences among genotypes (G), environments (E) and G x E interaction for all studied traits except straw weight per plant, indicating a wide range of variation among genotypes, environments and these genotypes exhibited differential response to environmental conditions. The significant variance due to residual for all characters except both straw weight per plant and oil yield per fad indicated that genotypes differed with respect to their stability suggesting that prediction would be difficult, which means that mean performance alone would not be appropriate. Interaction component of variance (σ2ge) was less than the genotypic variance (σ2g) for all characters, indicating that genotypes differ in their genetic potential for these traits. This was reflected in high heritability and low discrepancy between phenotypic (PCV) and genotypic (GCV) coefficients of variability values for these traits indicating the possibility of using each of long fiber percentage, plant height and technical stem length as selection indices for improving straw weight per plant, as well as, using 1000-seed weight and capsules number per plant as selection indices for improving seed weight per plant. Yield stability (YSi) statistic indicated that S.541-C/3 and S.541-D/10 gave high mean performance and stability for straw, fiber, seed and oil yields per fad in addition to oil percentage, capsules number per plant and 1000-seed weight. Therefore, the two genotypes well be released under the name Giza 11 and Giza 12, respectively. These newly released varieties are of dual purpose type for straw, fiber, seed and oil yield. They may replace the low yielding cultivars Giza 8, Sakha 1 and Sakha 3.

SIMULTANEOUS SELECTION FOR HIGH YIELDING AND STABILITY OF SOME ECONOMIC KENAF CHARACTERS

The materials used for the present study consisted of fourteen kenaf genotypes (G) which were evaluated over six environments (three at Ismailia Governorate, two at Giza Governorate and one at El-Beheira Governorate) through three successive seasons (2009 to 2011). in Egypt. The analysis of variance revealed highly significant differences among genotypes, environments and G x E interaction for all studied traits, indicating a wide range of variation among genotypes, environments and these genotypes exhibited differential response to environmental conditions. The significant variance due to residual for all characters indicated that genotypes differed with respect to their stability suggesting that prediction would be difficult, which means that mean performance alone would not be appropriate. Interaction component of variance (σ2ge) was less than the genotypic variance (σ2g) for all characters. This means that genotypes differ in their genetic potential for these traits. The observed narrow range between phenotypic and genotypic coefficients of variability with high heritability in broad since for fiber percentage . Also, fiber weight per plant, technical stem length and plant height showed similar results, indicating possibility of using these three yield traits in selection criteria with giving more weight for fiber weight per plant and technical stem length for improving green stalk yield per plant in turn fiber yield. The criterion, yield stability (YSi) statistic indicated that S.105/2 and S.113 were proved to be superior in yield and stability for all characters studied as well as three genotypes, S.96/20, Giza3 and S.8 were stable for most characters studied. Therefore, the two genotypes (S.105/2 and S.113) maintained mean performance advantage across nearly all the environments sampled by maintaining high level for the above-mentioned traits and they are recommended to be released as commercial stable high yielding cultivars and/or to be incorporated in kenaf breeding program for producing stable high yielding lines. Phenotypic correlation coefficients among green stalk weight with other related characters of kenaf, indicated that, plant height, technical stem length, and fiber percentage are the major components contributing to green stalk weight per plant. Therefore, selection for these traits will improve green stalk weight per plant and in turn fiber yield in kenaf.

Mapping multiple genes for quantitative or complex traits.

Models for complex and quantitative traits that involve multiple, possibly interacting, genes are described. Methods of linkage analysis are developed that utilize special features of these models, and their power is compared with that of simple genome scans that ignore these special features. Our calculations show that for family-based nonparametric linkage analysis in human genetics, in contrast to experimental genetics, there are limits to the increase in power that can be achieved by correctly modeling gene-gene interactions. In particular, the noncentrality parameter of likelihood-based statistics to detect single gene effects involves both single gene and interaction components of variance, so even when the interaction components of variance are relatively large, the incremental power from a statistic designed to detect both single gene and interaction effects is often quite modest. We carry out our analysis with the assistance of a parameterization that allows us to compute score statistics, noncentrality parameters, and Fisher information matrices reasonably explicitly.

A retrospective early test ofPinus sylvestrisseedlings grown at wide and dense spacing

Stored seeds from 30 open-pollinated families that had been field tested for 28 years provided a retrospective opportunity to assess the efficiency of early testing in Scots pine (Pinus sylvestris L.). Seedlings height at the end of first (HGP1), second (HGP2) and third growth period (HGP3), and in the third growth period, leader length (LEADER3), basal stem diameter (DIA3), number of stem units (NSU3), mean stem unit length (MSUL3), aboveground fresh weight (AGFWT3), stem dry weight (STDWT3), and shoot and needle dry weight (SHNDWT3) were studied under wide and dense spacing. Families differed at the 1 or 0.1% level of probability. Differences between spacing were significant at the 0.01% level of probability for all traits measured in the third growth period. Families interacted significantly with spacing for HGP2, HGP3, LEADER3, AGFWT3, SHNDWT3 and MSUL3. Interactions were due to rank changes and the interaction component of variance varied from 26 to 96% of the family variance. Estimates of hi2over wide and dense spacing ranged between 0.23 ± 0.11 (HGP2) and 0.51 ± 0.14 (NSU3). Spacing did not alter the variance structure, hi2for each trait under wide or dense spacing were similar. However, spacing affected the phytotron-field genetic correlations. The average of 80 genetic correlation estimates was 0.52 under wide spacing and 0.29 under dense spacing. Averaged over eight field traits, the efficiency of indirect juvenile selection for the field traits indirect-direct selection percentage ranged from -15% for NSU3 under dense spacing to 99% for HGP3 under wide spacing.

Rainfed lowland rice breeding strategies for Northeast Thailand.: I. Genotypic variation and genotype × environment interactions for grain yield

The magnitude and nature of genotype-by-environment (G × E) interactions for grain yield, days-to-flower and plant height of rainfed lowland rice in Northeast Thailand were examined using random F 7 lines from seven crosses developed by the Thai breeding program. A total of 1116 lines and checks were evaluated in a multi-environment trial conducted across three years (1995–1997) and eight sites. The G × E interaction was partitioned into components attributed to genotype-by-site (G × S), genotype-by-year (G × Y) and genotype-by-site-by-year (G × S × Y) interactions. The G × S × Y interaction was the largest G × E interaction component of variance for all three traits. There was little G × S interaction for grain yield and days-to-flower. The G × S interaction was significant for plant height, but was the smallest component of variance for that trait. The G × Y interaction component of variance was significant for all three traits, but was small relative to the genotypic component for days-to-flower and plant height. For grain yield the G × Y interaction component was comparable in size to the genotypic component. Partitioning the genotypic and G × E interaction components of variance into among-cross and within-cross components indicated that there was significant variation both among and within the crosses for each trait. The relationships between the three traits differed among the crosses and the environments. A major factor contributing to the large G × S × Y interactions for grain yield was the genotypic variation for days-to-flower in combination with environmental variation for the timing and intensity of drought. Some of the interactions associated with timing of drought were repeatable across the environments sampled in the multi-environment trial, and to some extent the environments were characterised on the basis of whether there was pre-flowering, intermittent, or terminal drought. There was genotypic variation for grain yield after taking into consideration the influences of timing of drought in relation to plant development. Three of the seven crosses involved the Thai cultivars KDML105 and RD6 as parents. These crosses produced an array of progeny with lower yield than the Thai cultivars, suggesting it would be difficult to improve on the yield of these cultivars. In contrast three of the remaining four crosses, which did not have a Thai cultivar as a parent, produced progeny that had higher yield than KDML105 and RD6 indicating that yield of rainfed lowland rice could be improved above that of the these popular cultivars.

Genetic Study of Non‐Ear Characters in Maize

AbstractSeventy three populations of maize (Zea mays L.) were grown for two years at two locations in Spain in order to study the heritability and constancy of the non‐ear traits days to silking, days to anthesis, plant height, ear height, and leaf number.The differences among populations were highly significant in the individual analyses, as well as in the combined analyses for all the traits.The interaction components of variance were in general small. Broad‐sense heritabilities ranged from 0.844 to 0.869. Constancies were high, in all cases above 1.0.It is concluded that the non‐ear trails studied can be confidently used in a numerical classification of populations of maize.

On estimating the interaction component of variance from unbalanced data†

Simple explicit formulae are given for the direct computation of variance component estimates for interaction in the general unbalanced case, by Henderson's Method 3, under two different restriction sets imposed on the parameters. Generalizations are considered for the presence of empty cells, and for higher order interactions. Simple rules are given for the incorporation of this estimation method into existing general computer programs

Estimation of components of variance for partially cross-classified data in a factorial arrangement of treatments

A procedure is presented for obtaining estimates of components of variance for the main effects and interaction in a two-way factorial arrangement of treatments with only partially cross-classified data (sometimes referred to as unbalanced data in a two-way crossed classification model with interaction). The procedure entails the use of two hierarchical analyses of variance in which each main effect is first treated as classes and then as subclasses. The estimation of the variance component for each main effect results from the solution of two simultaneous equations with values used obtained directly from the hierarchical analyses. The interaction component of variance can be obtained from the variance components for main effects. An example is presented for the purpose of illustrating the procedure. Interpretation of the interaction variance component estimated by the method is limited due to the absence of some of the subclasses.

Inbreeding in Two Populations of Zea mays L.1

Inbreeding effects on five characteristics of two Zea mays varieties were estimated. Seven inbred subpopulations, ranging from F = O to 9/16, of each variety were obtained by using double‐double (8‐line) pedigrees. Environmental error and genotype‐by‐environment interaction components of variance were not significantly affected by the level of inbreeding. The regression of performance on expected inbreeding was linear for yield, number of days to tassel, ear height, and plant height. If epistatic effects are contributing to the variability in these two populations they must be of the type which lead to a linear relationship between average performance and inbreeding. Inbred progenies derived from sets of inbred lines were analyzed separately. Variability in response to inbreeding among such sets of genetic material was detected.

Designs for the simultaneous estimation of functions of variance components from two-way crossed classifications

SUMMARY The paper deals with the estimation of the parameters of a variance component model for two-way crossed classifications with replication. Estimates are needed for row, column and interaction components of variance, and also for the ratios of these variances to the error component of variance. A balanced design with k(k > 2) observations for all subclasses may sometimes be considered extravagant for the purpose. Alternative designs in which duplicates are taken from a selection of subclasses and a single observation is taken from each of the rest, are proposed in the paper. A simple method of analysing these schemes is suggested, and some numerical results on the efficiency of these designs are presented.

Variance and Covariance Components in Part Lactation Milk and Fat Records

Summary The monthly test-day milk and fat records of 1,526 Holstein cows in 232 herds artificially sired by 145 different sires were analyzed to obtain estimates of sire, herd, sire by herd, and error components of variance for the ten test days and for the sum of ten test days and to obtain estimates of sire, herd, sire by herd, and error components of covariance between the monthly records and between the monthly records and the sum of ten test-day records. Although the variances of the estimates of interaction components of variance are not known, the results of the analysis indicate that the sire by herd components of variance are approximately zero. This would suggest that the sire by herd components of covariance are also negligible. It is felt, however, that more data should be analyzed, in order to substantiate or negate these results, since the number of records in the present analysis is small.