Comparison between estimation of breeding values and fixed effects using Bayesian and empirical BLUP estimation under selection on parents and missing pedigree information

Bayesian (via Gibbs sampling) and empirical BLUP (EBLUP) estimation of fixed effects and breeding values were compared by simulation. Combinations of two simulation models (with or without effect of contemporary group (CG)), three selection schemes (random, phenotypic and BLUP selection), two levels of heritability (0.20 and 0.50) and two levels of pedigree information (0% and 15% randomly missing) were considered. Populations consisted of 450 animals spread over six discrete generations. An infinitesimal additive genetic animal model was assumed while simulating data. EBLUP and Bayesian estimates of CG effects and breeding values were, in all situations, essentially the same with respect to Spearman''s rank correlation between true and estimated values. Bias and mean square error (MSE) of EBLUP and Bayesian estimates of CG effects and breeding values showed the same pattern over the range of simulated scenarios. Methods were not biased by phenotypic and BLUP selection when pedigree information was complete, albeit MSE of estimated breeding values increased for situations where CG effects were present. Estimation of breeding values by Bayesian and EBLUP was similarly affected by joint effect of phenotypic or BLUP selection and randomly missing pedigree information. For both methods, bias and MSE of estimated breeding values and CG effects substantially increased across generations.     

Predicting breeding values and genetic components using generalized linear mixed models for categorical and continuous traits in walnut (<Emphasis Type="Italic">Juglans regia</Emphasis>)

Genetic components for economically important traits in walnut (Juglans regia) were estimated for the first time using historical pedigree and heirloom phenotypic data from the walnut breeding program at the University of California, Davis. The constructed pedigree is composed of ~ 15,000 individuals and is derived from current and historic phenotypic records dating back > 50 years and located across California. To predict the additive genetic values of individuals under selection, generalized linear mixed models (GLMM), implemented with MCMCglmm, were developed. Several repeatability models were established to obtain the best model and predict the genetic parameters for each trait. Repeatability for yield, harvest date, extra-light kernel color (ELKC), and lateral bearing were predicted at 0.82, 0.98, 0.63, and 0.96, respectively, and average narrow-sense heritabilities were 0.54, 0.77, 0.49, and 0.75, respectively. Each individual in the pedigree was ranked by its estimated breeding value (EBV). The genetic trend showed specific patterns for each trait, and real genetic improvement was found over time. The completed pedigree built here, the estimated breeding values, and the ranking of individuals according to their breeding values, can be used to guide future crossing designs in the walnut breeding program and future implementation of genomic selection methods in walnut.     

Optimised parent selection and minimum inbreeding mating in small aquaculture breeding schemes: a simulation study

The effectiveness of low cost breeding scheme designs for small aquaculture breeding programmes were assessed for their ability to achieve genetic gain while managing inbreeding using stochastic simulation. Individuals with trait data were simulated over 15 generations with selection on a single trait. Combinations of selection methods, mating strategies and genetic evaluation options were evaluated with and without the presence of common environmental effects. An Optimal Parent Selection (OPS) method using semi-definite programming was compared with a truncation selection (TS) method. OPS constrains the rate of inbreeding while maximising genetic gain. For either selection method, mating pairs were assigned from the selected parents by either random mating (RM) or Minimum Inbreeding Mating (MIM), which used integer programming to determine mating pairs. Offspring were simulated for each mating pair with equal numbers of offspring per pair and these offspring were the candidates for selection of parents of the next generation. Inbreeding and genetic gain for each generation were averaged over 25 replicates. Combined OPS and MIM led to a similar level of genetic gain to TS and RM, but inbreeding levels were around 75% lower than TS and RM after 15 generations. Results demonstrate that it would be possible to manage inbreeding over 15 generations within small breeding programmes comprised of 30 to 40 males and 30 to 40 females with the use of OPS and MIM. Selection on breeding values computed using Best Linear Unbiased Prediction (BLUP) with all individuals genotyped to obtain pedigree information resulted in an 11% increase in genetic merit and a 90% increase in the average inbreeding coefficient of progeny after 15 generations compared with selection on raw phenotype. Genetic evaluation strategies using BLUP wherein elite individuals by raw phenotype are genotyped to obtain parentage along with a range of different samples of remaining individuals did not increase genetic progress in comparison to selection on raw phenotype. When common environmental effects on full-sib families were simulated, performance of small breeding scheme designs was little affected. This was because the majority of selection must anyway be applied within family due to inbreeding constraints.     

Persistence of accuracy of genomic estimated breeding values over generations in layer chickens

Background

The predictive ability of genomic estimated breeding values (GEBV) originates both from associations between high-density markers and QTL (Quantitative Trait Loci) and from pedigree information. Thus, GEBV are expected to provide more persistent accuracy over successive generations than breeding values estimated using pedigree-based methods. The objective of this study was to evaluate the accuracy of GEBV in a closed population of layer chickens and to quantify their persistence over five successive generations using marker or pedigree information.

Methods

The training data consisted of 16 traits and 777 genotyped animals from two generations of a brown-egg layer breeding line, 295 of which had individual phenotype records, while others had phenotypes on 2,738 non-genotyped relatives, or similar data accumulated over up to five generations. Validation data included phenotyped and genotyped birds from five subsequent generations (on average 306 birds/generation). Birds were genotyped for 23,356 segregating SNP. Animal models using genomic or pedigree relationship matrices and Bayesian model averaging methods were used for training analyses. Accuracy was evaluated as the correlation between EBV and phenotype in validation divided by the square root of trait heritability.

Results

Pedigree relationships in outbred populations are reduced by 50% at each meiosis, therefore accuracy is expected to decrease by the square root of 0.5 every generation, as observed for pedigree-based EBV (Estimated Breeding Values). In contrast the GEBV accuracy was more persistent, although the drop in accuracy was substantial in the first generation. Traits that were considered to be influenced by fewer QTL and to have a higher heritability maintained a higher GEBV accuracy over generations. In conclusion, GEBV capture information beyond pedigree relationships, but retraining every generation is recommended for genomic selection in closed breeding populations.     

Impact of reconstructed pedigrees on progeny-test breeding values in red spruce

Pedigrees reconstructed through DNA marker assigned paternities in polymix (PMX) and open pollinated (OP) progeny tests were analyzed using mixed models to test the effect of unequal male reproductive success and pedigree errors on quantitative genetic parameters. The reconstructed pedigree increased heritabilities in the larger PMX test. Increased heritability resulted from adding the paternities to the pedigree per se, not by correcting the male reproductive bias by specifying the exact pedigree. Removing hypothesized pedigree errors had no effect on quantitative parameters, either because the magnitude of the errors was too small (PMX) or the progeny test was too small to detect variance components reliably (OP). Although there was no advantage in backwards selection, the increased additive variance, heritabilities and accuracy of progeny with assigned paternities in the pedigree, should permit forward selection of offspring with greater genetic gain and complete control of coancestry for future breeding decisions. Some possible breeding population structures with the new genetic information are discussed.     

Impact of reconstructed pedigrees on progeny-test breeding values in red spruce

Pedigrees reconstructed through DNA marker assigned paternities in polymix (PMX) and open pollinated (OP) progeny tests were analyzed using mixed models to test the effect of unequal male reproductive success and pedigree errors on quantitative genetic parameters. The reconstructed pedigree increased heritabilities in the larger PMX test. Increased heritability resulted from adding the paternities to the pedigree per se, not by correcting the male reproductive bias by specifying the exact pedigree. Removing hypothesized pedigree errors had no effect on quantitative parameters, either because the magnitude of the errors was too small (PMX) or the progeny test was too small to detect variance components reliably (OP). Although there was no advantage in backwards selection, the increased additive variance, heritabilities and accuracy of progeny with assigned paternities in the pedigree, should permit forward selection of offspring with greater genetic gain and complete control of coancestry for future breeding decisions. Some possible breeding population structures with the new genetic information are discussed.     

The importance of information on relatives for the prediction of genomic breeding values and the implications for the makeup of reference data sets in livestock breeding schemes

Background

The theory of genomic selection is based on the prediction of the effects of genetic markers in linkage disequilibrium with quantitative trait loci. However, genomic selection also relies on relationships between individuals to accurately predict genetic value. This study aimed to examine the importance of information on relatives versus that of unrelated or more distantly related individuals on the estimation of genomic breeding values.

Methods

Simulated and real data were used to examine the effects of various degrees of relationship on the accuracy of genomic selection. Genomic Best Linear Unbiased Prediction (gBLUP) was compared to two pedigree based BLUP methods, one with a shallow one generation pedigree and the other with a deep ten generation pedigree. The accuracy of estimated breeding values for different groups of selection candidates that had varying degrees of relationships to a reference data set of 1750 animals was investigated.

Results

The gBLUP method predicted breeding values more accurately than BLUP. The most accurate breeding values were estimated using gBLUP for closely related animals. Similarly, the pedigree based BLUP methods were also accurate for closely related animals, however when the pedigree based BLUP methods were used to predict unrelated animals, the accuracy was close to zero. In contrast, gBLUP breeding values, for animals that had no pedigree relationship with animals in the reference data set, allowed substantial accuracy.

Conclusions

An animal''s relationship to the reference data set is an important factor for the accuracy of genomic predictions. Animals that share a close relationship to the reference data set had the highest accuracy from genomic predictions. However a baseline accuracy that is driven by the reference data set size and the overall population effective population size enables gBLUP to estimate a breeding value for unrelated animals within a population (breed), using information previously ignored by pedigree based BLUP methods.     

The importance of identity-by-state information for the accuracy of genomic selection

Background

It is commonly assumed that prediction of genome-wide breeding values in genomic selection is achieved by capitalizing on linkage disequilibrium between markers and QTL but also on genetic relationships. Here, we investigated the reliability of predicting genome-wide breeding values based on population-wide linkage disequilibrium information, based on identity-by-descent relationships within the known pedigree, and to what extent linkage disequilibrium information improves predictions based on identity-by-descent genomic relationship information.

Methods

The study was performed on milk, fat, and protein yield, using genotype data on 35 706 SNP and deregressed proofs of 1086 Italian Brown Swiss bulls. Genome-wide breeding values were predicted using a genomic identity-by-state relationship matrix and a genomic identity-by-descent relationship matrix (averaged over all marker loci). The identity-by-descent matrix was calculated by linkage analysis using one to five generations of pedigree data.

Results

We showed that genome-wide breeding values prediction based only on identity-by-descent genomic relationships within the known pedigree was as or more reliable than that based on identity-by-state, which implicitly also accounts for genomic relationships that occurred before the known pedigree. Furthermore, combining the two matrices did not improve the prediction compared to using identity-by-descent alone. Including different numbers of generations in the pedigree showed that most of the information in genome-wide breeding values prediction comes from animals with known common ancestors less than four generations back in the pedigree.

Conclusions

Our results show that, in pedigreed breeding populations, the accuracy of genome-wide breeding values obtained by identity-by-descent relationships was not improved by identity-by-state information. Although, in principle, genomic selection based on identity-by-state does not require pedigree data, it does use the available pedigree structure. Our findings may explain why the prediction equations derived for one breed may not predict accurate genome-wide breeding values when applied to other breeds, since family structures differ among breeds.     

Genomic breeding value prediction: methods and procedures

Animal breeding faces one of the most significant changes of the past decades - the implementation of genomic selection. Genomic selection uses dense marker maps to predict the breeding value of animals with reported accuracies that are up to 0.31 higher than those of pedigree indexes, without the need to phenotype the animals themselves, or close relatives thereof. The basic principle is that because of the high marker density, each quantitative trait loci (QTL) is in linkage disequilibrium (LD) with at least one nearby marker. The process involves putting a reference population together of animals with known phenotypes and genotypes to estimate the marker effects. Marker effects have been estimated with several different methods that generally aim at reducing the dimensions of the marker data. Nearly all reported models only included additive effects. Once the marker effects are estimated, breeding values of young selection candidates can be predicted with reported accuracies up to 0.85. Although results from simulation studies suggest that different models may yield more accurate genomic estimated breeding values (GEBVs) for different traits, depending on the underlying QTL distribution of the trait, there is so far only little evidence from studies based on real data to support this. The accuracy of genomic predictions strongly depends on characteristics of the reference populations, such as number of animals, number of markers, and the heritability of the recorded phenotype. Another important factor is the relationship between animals in the reference population and the evaluated animals. The breakup of LD between markers and QTL across generations advocates frequent re-estimation of marker effects to maintain the accuracy of GEBVs at an acceptable level. Therefore, at low frequencies of re-estimating marker effects, it becomes more important that the model that estimates the marker effects capitalizes on LD information that is persistent across generations.     

Bayesian prediction of breeding values for multivariate binary and continuous traits in simulated horse populations using threshold-linear models with Gibbs sampling

Simulated data were used to determine the properties of multivariate prediction of breeding values for categorical and continuous traits using phenotypic, molecular genetic and pedigree information by mixed linear-threshold animal models via Gibbs sampling. Simulation parameters were chosen such that the data resembled situations encountered in Warmblood horse populations. Genetic evaluation was performed in the context of the radiographic findings in the equine limbs. The simulated pedigree comprised seven generations and 40 000 animals per generation. The simulated data included additive genetic values, residuals and fixed effects for one continuous trait and liabilities of four binary traits. For one of the binary traits, quantitative trait locus (QTL) effects and genetic markers were simulated, with three different scenarios with respect to recombination rate (r) between genetic markers and QTL and polymorphism information content (PIC) of genetic markers being studied: r = 0.00 and PIC = 0.90 (r0p9), r = 0.01 and PIC = 0.90 (r1p9), and r = 0.00 and PIC = 0.70 (r0p7). For each scenario, 10 replicates were sampled from the simulated horse population, and six different data sets were generated per replicate. Data sets differed in number and distribution of animals with trait records and the availability of genetic marker information. Breeding values were predicted via Gibbs sampling using a Bayesian mixed linear-threshold animal model with residual covariances fixed to zero and a proper prior for the genetic covariance matrix. Relative breeding values were used to investigate expected response to multi- and single-trait selection. In the sires with 10 or more offspring with trait information, correlations between true and predicted breeding values ranged between 0.89 and 0.94 for the continuous traits and between 0.39 and 0.77 for the binary traits. Proportions of successful identification of sires of average, favourable and unfavourable genetic value were 81% to 86% for the continuous trait and 57% to 74% for the binary traits in these sires. Expected decrease of prevalence of the QTL trait was 3% to 12% after multi-trait selection for all binary traits and 9% to 17% after single-trait selection for the QTL trait. The combined use of phenotype and genotype data was superior to the use of phenotype data alone. It was concluded that information on phenotypes and highly informative genetic markers should be used for prediction of breeding values in mixed linear-threshold animal models via Gibbs sampling to achieve maximum reduction in prevalences of binary traits.     

Response to genomic selection: The Bulmer effect and the potential of genomic selection when the number of phenotypic records is limiting

Background

Over the last ten years, genomic selection has developed enormously. Simulations and results on real data suggest that breeding values can be predicted with high accuracy using genetic markers alone. However, to reach high accuracies, large reference populations are needed. In many livestock populations or even species, such populations cannot be established when traits are difficult or expensive to record, or when the population size is small. The value of genomic selection is then questionable.

Methods

In this study, we compare traditional breeding schemes based on own performance or progeny information to genomic selection schemes, for which the number of phenotypic records is limiting. Deterministic simulations were performed using selection index theory. Our focus was on the equilibrium response obtained after a few generations of selection. Therefore, we first investigated the magnitude of the Bulmer effect with genomic selection.

Results

Results showed that the reduction in response due to the Bulmer effect is the same for genomic selection as for selection based on traditional BLUP estimated breeding values, and is independent of the accuracy of selection. The reduction in response with genomic selection is greater than with selection based directly on phenotypes without the use of pedigree information, such as mass selection. To maximize the accuracy of genomic estimated breeding values when the number of phenotypic records is limiting, the same individuals should be phenotyped and genotyped, rather than genotyping parents and phenotyping their progeny. When the generation interval cannot be reduced with genomic selection, large reference populations are required to obtain a similar response to that with selection based on BLUP estimated breeding values based on own performance or progeny information. However, when a genomic selection scheme has a moderate decrease in generation interval, relatively small reference population sizes are needed to obtain a similar response to that with selection on traditional BLUP estimated breeding values.

Conclusions

When the trait of interest cannot be recorded on the selection candidate, genomic selection schemes are very attractive even when the number of phenotypic records is limited, because traditional breeding requires progeny testing schemes with long generation intervals in those cases.     

Improving accuracy of breeding values by incorporating genomic information in spatial-competition mixed models

Climate change and the increasing demand for sustainable energy resources require urgent strategies to increase the accuracy of selection in tree breeding (associated with higher gain). We investigated the combined pedigree and genomic-based relationship approach and its impact on the accuracy of predicted breeding values using data from 5-year-old Eucalyptus grandis progeny trial. The number of trees that can be genotyped in a tree breeding population is limited; therefore, the combined approach can be a feasible and efficient strategy to increase the genetic gain and provide more accurate predicted breeding values. We calculated the accuracy of predicted breeding values for two growth traits, diameter at breast height and total height, using two evaluation approaches: the combined approach and the classical pedigree-based approach. We also investigated the influence of two different trait heritabilities as well as the inclusion of competition genetic effects or environmental heterogeneity in an individual-tree mixed model on the estimated variance components and accuracy of breeding values. The genomic information of genotyped trees is automatically propagated to all trees with the combined approach, including the non-genotyped mothers. This increased the accuracy of overall breeding values, except for the non-genotyped trees from the competition model. The increase in the accuracy was higher for the total height, the trait with low heritability. The combined approach is a simple, fast, and accurate genomic selection method for genetic evaluation of growth traits in E. grandis and tree species in general. It is simple to implement in a traditional individual-tree mixed model and provides an easy extension to individual-tree mixed models with competition effects and/or environmental heterogeneity.     

Persistence of accuracy of genome-wide breeding values over generations when including a polygenic effect

Background

When estimating marker effects in genomic selection, estimates of marker effects may simply act as a proxy for pedigree, i.e. their effect may partially be attributed to their association with superior parents and not be linked to any causative QTL. Hence, these markers mainly explain polygenic effects rather than QTL effects. However, if a polygenic effect is included in a Bayesian model, it is expected that the estimated effect of these markers will be more persistent over generations without having to re-estimate the marker effects every generation and will result in increased accuracy and reduced bias.

Methods

Genomic selection using the Bayesian method, ''BayesB'' was evaluated for different marker densities when a polygenic effect is included (GWpEBV) and not included (GWEBV) in the model. Linkage disequilibrium and a mutation drift balance were obtained by simulating a population with a Ne of 100 over 1,000 generations.

Results

Accuracy of selection was slightly higher for the model including a polygenic effect than for the model not including a polygenic effect whatever the marker density. The accuracy decreased in later generations, and this reduction was stronger for lower marker densities. However, no significant difference in accuracy was observed between the two models. The linear regression of TBV on GWEBV and GWpEBV was used as a measure of bias. The regression coefficient was more stable over generations when a polygenic effect was included in the model, and was always between 0.98 and 1.00 for the highest marker density. The regression coefficient decreased more quickly with decreasing marker density.

Conclusions

Including a polygenic effect had no impact on the selection accuracy, but showed reduced bias, which is especially important when estimates of genome-wide markers are used to estimate breeding values over more than one generation.     

Genomic prediction in CIMMYT maize and wheat breeding programs

Genomic selection (GS) has been implemented in animal and plant species, and is regarded as a useful tool for accelerating genetic gains. Varying levels of genomic prediction accuracy have been obtained in plants, depending on the prediction problem assessed and on several other factors, such as trait heritability, the relationship between the individuals to be predicted and those used to train the models for prediction, number of markers, sample size and genotype × environment interaction (GE). The main objective of this article is to describe the results of genomic prediction in International Maize and Wheat Improvement Center''s (CIMMYT''s) maize and wheat breeding programs, from the initial assessment of the predictive ability of different models using pedigree and marker information to the present, when methods for implementing GS in practical global maize and wheat breeding programs are being studied and investigated. Results show that pedigree (population structure) accounts for a sizeable proportion of the prediction accuracy when a global population is the prediction problem to be assessed. However, when the prediction uses unrelated populations to train the prediction equations, prediction accuracy becomes negligible. When genomic prediction includes modeling GE, an increase in prediction accuracy can be achieved by borrowing information from correlated environments. Several questions on how to incorporate GS into CIMMYT''s maize and wheat programs remain unanswered and subject to further investigation, for example, prediction within and between related bi-parental crosses. Further research on the quantification of breeding value components for GS in plant breeding populations is required.     

General and specific combining ability from partial diallels of radiata pine: implications for utility of SCA in breeding and deployment populations

Variances for general combining ability (GCA) and specific combining ability (SCA) and the relationship between mid-parental GCA and SCA effects were estimated for tree diameter (DBH) from a series of 20 sets of 6×6 half-diallel mating experiments in radiata pine, planted at ten sites across Australia. Significant SCA variance for DBH was almost equal to GCA variance for the combined analysis of all ten sites. The importance of SCA variance varied among sites, from non-significant to SCA variance accounting for all genetic variation among full-sib families. Significant SCA × site interaction was detected among the ten sites. A significant and positive correlation between mid-parental breeding values and best linear unbiased predictions of the SCA effects was observed. About a quarter of extra genetic gain is achievable through use of SCA variance if selection is based on the best breeding values. To fully exploit genetic gain from SCA variance in a deployment population, positive assortative matings are required for the best parents. It is estimated that the additional deployment gain of 46.0% for ten sites combined, or 52.9% for four sites combined that had significant GCA as well as SCA effects, were achievable relative to gain from GCA only, if all SCA variance within this breeding population was exploited. For a breeding population, selection for breeding values may be sufficient due to positive correlations between breeding values and SCA values. For a deployment population to capture more SCA genetic gain, it is preferable to make more pair-wise mating for parents with higher breeding values.Communicated by O. Savolainen     

Best linear prediction of breeding values in a forest tree improvement program

Summary Best Linear Prediction (BLP) was used to predict breeding values for 1,396 parents from progeny test data in an operational slash pine breeding program. BLP rankings of parents were compared to rankings of averaged standard scores, a common approach in forestry. Using BLP rankings, selection of higher ranking parents tends to choose parents in a larger number of more precise progeny tests. The trend is the opposite with standard scores; higher ranking parents tend to be those in fewer, less precise tests. BLP and a related methodology, Best Linear Unbiased Prediction (BLUP), were developed by dairy cattle breeders and have not been used widely outside of animal breeding for predicting breeding values from messy progeny test data. Application of either of these techniques usually requires simplifying assumptions to keep the problem computationally tractable. The more appropriate technique for a given application depends upon which set of assumptions are better for the given problem. An assumption of homogeneous genetic and error variances and covariances, generally made by animal breeders when applying BLUP, was inappropriate for our data. We employed an approach that treated fixed effects as known and treated the same trait measured in different environments as different traits with heterogeneous variance structures. As tree improvement programs become more complex, the ease with which BLP and BLUP handle messy data and incorporate diverse sources of information should make these techniques appealing to forest tree breeders.     

The effect of genomic information on optimal contribution selection in livestock breeding programs

Background

Long-term benefits in animal breeding programs require that increases in genetic merit be balanced with the need to maintain diversity (lost due to inbreeding). This can be achieved by using optimal contribution selection. The availability of high-density DNA marker information enables the incorporation of genomic data into optimal contribution selection but this raises the question about how this information affects the balance between genetic merit and diversity.

Methods

The effect of using genomic information in optimal contribution selection was examined based on simulated and real data on dairy bulls. We compared the genetic merit of selected animals at various levels of co-ancestry restrictions when using estimated breeding values based on parent average, genomic or progeny test information. Furthermore, we estimated the proportion of variation in estimated breeding values that is due to within-family differences.

Results

Optimal selection on genomic estimated breeding values increased genetic gain. Genetic merit was further increased using genomic rather than pedigree-based measures of co-ancestry under an inbreeding restriction policy. Using genomic instead of pedigree relationships to restrict inbreeding had a significant effect only when the population consisted of many large full-sib families; with a half-sib family structure, no difference was observed. In real data from dairy bulls, optimal contribution selection based on genomic estimated breeding values allowed for additional improvements in genetic merit at low to moderate inbreeding levels. Genomic estimated breeding values were more accurate and showed more within-family variation than parent average breeding values; for genomic estimated breeding values, 30 to 40% of the variation was due to within-family differences. Finally, there was no difference between constraining inbreeding via pedigree or genomic relationships in the real data.

Conclusions

The use of genomic estimated breeding values increased genetic gain in optimal contribution selection. Genomic estimated breeding values were more accurate and showed more within-family variation, which led to higher genetic gains for the same restriction on inbreeding. Using genomic relationships to restrict inbreeding provided no additional gain, except in the case of very large full-sib families.     

Efficiency of including first-generation information in second-generation ranking and selection: results of computer simulation

Using computer simulation, we evaluated the impact of using first-generation information to increase selection efficiency in a second-generation breeding program. Selection efficiency was compared in terms of increase in rank correlation between estimated and true breeding values (i.e., ranking accuracy), reduction in coefficient of variation of correlation coefficients (i.e., ranking reliability), and increase in realized gain, with best linear unbiased prediction (BLUP). The test populations were generated with varying parameters: selection strategy (forward vs backward selection of parents); number of parents (24∼96); number of crosses per parent (1∼8); heritability (0.05∼0.35); ratio of dominance to additive variance (0∼3); ratio of additive-by-site to additive variance (0∼3); and ratio of dominance-by-site to additive variance (0∼3). The two selection strategies gave distinct results. When parents of the second-generation crosses had been selected via backward selection, adding first-generation information markedly increased selection efficiency. Conversely, when parents had been selected via forward selection, first-generation information provided little increase in efficiency. The amount of increase depended more on heritabilities in both generations and less on dominance and genotype–by–environment effects. Including first-generation information helped more when there were many parents and few crosses per parent in the second generation. Only in the case of extremely low first-generation heritabilities was there no benefit to adding first-generation information in terms of improved ranking reliability and accuracy.     

Comparison of ancestral and current-generation inbreeding in an experimental strawberry breeding population

Progenies from first-generation self, half-sib, full-sib, and cross fertilizations were generated to evaluate the magnitude of inbreeding depression for vegetative and production traits in strawberry. Tests were conducted to determine the linearity of trait mean depression with inbreeding rate (F) over this range of inbreeding values, as an indication of the presence of non-additive epistasis. A control population, for which a similar range of coancestry had accumulated over several cycles of breeding and selection, was also generated to compare the consequences of ancestral and current-generation inbreeding. Trait means for crosses among current-generation half-sibs, full-sibs, and selfs were 2–17%, 3–12%, and 14–45% lower than for unrelated crosses among the same set of parents, respectively. Linear regression of progeny means on current generation F was significantly negative for all traits and explained 17–44% of the variance among progeny means. Mean depression was largely linear over the range of inbreeding rates tested in this population, indicating the absence of epistasis for the traits evaluated. Conversely, (F) regressions of progeny means on pedigree inbreeding coefficients, where coancestry had accumulated over several cycles of breeding and selection, were uniformly non-significant and explained 0–10% of the variance among cross means. Further, multiple regression of progeny means for current-generation relatives on pedigree F failed to improve fit significantly over regression on current-generation F alone for all traits. Together, these results suggest that pedigree inbreeding coefficients are poor predictors of changes in homozygosity when populations are developed through multiple cycles of breeding and selection. They also imply that inbreeding depression will be of minor importance for strawberry breeding populations managed with adequate population sizes and strong directional selection.     

Efficiency of potato breeding using FDR 2n gametes for multitrait selection and progeny testing

Summary The objective of this research was to compare the efficiency of the 4x×2x breeding scheme with the traditional 4x×4x method with respect to potato improvement. The basis for such a comparison was the parental value of four 2x and four 4x male parents from the International Potato Center (CIP) as measured by multitrait selection and progeny testing. The 2x parents produced 2n pollen by parallel spindles at anaphase II, which is genetically equivalent to a first division restitution (FDR) mechanism. Both 2x and 4x parents were crossed with four common 4x female parents. Thus, 32 families were evaluated over 2 years at four Peruvian locations. A selection index which considered tuber yield, tuber number, average tuber weight and specific gravity was used for multitrait selection. Three FDR 2x parents had better selection index scores than the 4x parents over the four locations. Estimates of broad-sense heritability for total yield using different number of replications and locations were calculated by using the variance components. The 4x × 2x breeding scheme was found to be better than the traditional 4x × 4x method since fewer replications and locations are required to evaluate tuber yield in 4x × 2x progenies than in 4x × 4x progenies. The FDR 2x parents were also better material than the 4x parents for testing combining ability for tuber yield of the 4x progenitors. This could be the result of the mode of FDR 2n pollen formation. The pollen of FDR 2x parents is more heterozygous, but more homogenous than n pollen from 4x parents.Paper from the Laboratory of Genetics. Research supported by the College of Agricultural and Life Sciences; International Potato Center; USDA-CRGO-88-37234 3619, and Frito-Lay, Inc., USA