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. Fig. 4. Predicted breeding values (best linear unbiased predictions) of the most resistant (lowest symptom expression) 10% of strawberry progeny to Fusarium oxysporum f. sp. fragariae at 14 weeks. Narrow-sense heritability was estimated at 0.49 ± 0

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mixed models and best linear unbiased predictors (BLUP) through the animal model to estimate the additive genetic variance and breeding value of individuals have been outlined by Lynch and Walsh (1998) and Piepho et al. (2008 ). For BLUP estimations

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half-sib levels, needs to be evaluated. This step requires further analysis to predict if a cross will generate the intended variability for the traits of interest. Best linear unbiased prediction has been used in plant breeding for the estimation of

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unbalanced experimental designs. To account for spatial variation between environments, unbalanced data, and pedigree relationships, best linear unbiased predictors of phenotypes are used in place of arithmetic means. Phenotypic data on the scale and scope

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A major objective of the apple (Malus domestica Borkh.) breeding program in Stanthorpe, Australia, is to develop early ripening, high-quality cultivars. The heritability and inheritance of ripening date was investigated. Regression of offspring on midparent harvest dates and estimation of best linear unbiased predictions for parents were used to demonstrate that apple harvest date is highly heritable. Predominantly, additive genetic components of variance are responsible for the variation. Despite the existence of some specific combining ability variance and some non-normal family distributions, the best strategy for a breeder to predict the harvest date of progeny is to calculate the mean harvest date of parents.

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Breeding values (BVs) for four plant (bloom date, fruit development period, fruit density, and blind node propensity) and five fruit (weight, blush, shape, soluble solids, and titratable acidity) traits of 28 peach [Prunus persica (L.) Batsch (Peach Group)] genotypes used as parents in the Texas A&M University peach breeding program were predicted using best linear unbiased prediction (BLUP). Data from seedlings of 108 families developed from 42 peach parents were analyzed by using a mixed linear model, with years treated as fixed and additive genotypes as random factors. The precision of the predictions was high for most parental genotypes, as indicated by the correlations (rTI) between predicted and true BVs and the standard error of the predictions (SEP). In most cases, the higher the number of progeny, the better the agreement between predicted and true BVs for that parent. Parents with observations from more than 30 seedlings had a rTI ≥ 0.90 and smaller SEPs. For all traits analyzed, the lowest precision (low rTI and high SEP) was observed for `Flordaking', whose predicted BVs was based only on pedigree information.

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The effects of long-term genetic improvement are measured by selection response predicted from estimates of narrow-sense heritability. However, changes of population mean must be partitioned into genetic and environmental components-in order to accurately estimate selection response.

A long-term selection experiment for cut-flower yield in the Davis population of gerbera (Gerbera hybrida, Compositae) was conducted for sixteen generations. Breeding value was estimated for individual plants in the population using Best Linear Unbiased Prediction (BLUP). Genetic change was calculated from breeding values of individual plants in each generation. The results of this study indicate: the long-term selection experiment was successful and necessary for genetic improvement. Genetic change over sixteen generations was 33 flowers. Mean breeding values increased monotonously with an “S” shape pattern. Environmental effects fluctuated from generation to generation. Cut-flower yield in the Davis population of gerbera will continuously respond to selection.

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Heritability estimates are useful to predict genetic progress among offspring when the parents are selected on their performance, but they also provide information about major changes in the amount and nature of genetic variability through generations. Genetic and phenotypic correlations, on the other hand, are useful for better planning of selection programs. In this research, seedlings of 39 families resulting from crosses among 27 peach [Prunus persica (L.) Batsch] cultivars and selections were evaluated for date of full bloom (DFB), date of ripening (DR), fruit period development (FDP), flower density (FD), node density (ND), fruit density (FRD), fruit weight (WT), soluble solids content (SS), apical protuberance (TIP), red skin color (BLUSH), and shape (SH) in 1993 and 1994. The data were analyzed using the mixed linear model. The best linear unbiased prediction (BLUP) was used to estimate fixed effects and predict breeding values (BV). Restricted maximum likelihood (REML) was used to estimate variance components, and a multiple-trait model to estimate genetic and phenotypic covariances between traits. The data indicates high heritability for DFB, DR, FDP, and BLUSH, intermediate heritability for WT, TIP, and SH, and low heritability for FD, ND, FRD, and SS. They also indicate year effect as a major environmental component affecting seedling performance. High correlation estimates were found between some traits, but further analysis is needed to determine their significance.

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Thirteen peach [Prunus persica (L.) Batsch] fruit characteristics were investigated for 3 years, 1993, 1994, and 1995, in College Station, Texas, to determine heritability, genetic and phenotypic correlations, and predicted response to selection. Seedlings of 108 families resulting from crosses among 42 peach cultivars and selections were used in the evaluations. A mixed linear model, with years treated as fixed and additive genotypes as random factors, was employed to analyze the data. Best linear unbiased prediction (BLUP) was used to estimate fixed effects. Restricted maximum likelihood (REML) was used to estimate variance components, and a multiple trait model was used to estimate genetic and phenotypic covariances between traits. Genetic and phenotypic correlations ≥0.65 and <0.30 were considered strong or very strong and weak, respectively. Date of ripening, fruit development period (FDP) and date of full bloom had the highest heritability (h2) estimates, 0.94, 0.91, and 0.78, respectively. Fruit cheek diameter and titratable acidity (h2 = 0.31) were the traits with the lowest estimates. Fruit development period, fruit blush, and date of ripening had the highest predicted selection responses, whereas fruit suture, fruit cheek, L/W12 (ratio fruit length to average fruit diameters), and fruit tip had the lowest values. Most genetic correlations were ≥0.30 and were, in general, much higher than the corresponding phenotypic correlations. All four measures of fruit size were genetically and phenotypically very strongly correlated. Important genetic correlation estimates were also observed for date of ripening with FDP (ra = 0.93), date of ripening and FDP with fruit blush (ra = -0.77, ra = -0.72), SS (percent soluble solids) (ra = 0.63, ra = 0.62) and TA (ra = 0.55, ra = 0.64), and SS with TA (ra = -0.56). Direct selection practiced solely for early ripening and short FDP is expected to have a greater effect on correlated traits than direct selection for early bloom and large fruit mass.

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. Linear mixed-effects models were constructed for each of the three sensory traits and the total work variable. Family and direction of cross within family were estimated as fixed effects, yielding best linear unbiased effects; whereas genotype, year, and

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