Transcriptome-based strategies for identifying aluminum tolerance genes in popcorn (Zea mays L. var. everta).

Aluminum (Al) toxicity limits crop production worldwide. Although studies have identified genes associated with Al tolerance in crops, a large amount of data remains unexplored using other strategies. Here, we searched for single substitutions and InDels across differentially expressed genes (DEGs), linked DEGs to Al-tolerance QTLs reported in the literature for common maize, and investigated the alternative splicing regulated by Al3+ toxicity. We found 929 substitutions between DEGs in Al-tolerant and 464 in Al-sensitive inbred lines, of which 165 and 80 were non-synonymous, respectively. Only 12 NS variants had deleterious predicted effect on protein function in Al-tolerant and 13 in Al-sensitive. Moreover, 378 DEGs were mapped in Al-QTL regions for the Al-tolerant and 213 for the Al-sensitive. Furthermore, Al stress is primarily regulated at the transcriptional level in popcorn. Important genes identified, such as HDT1, SWEET4a, GSTs, SAD9, PIP2-2, CASP-like 5, and AGP, may benefit molecular assisted popcorn breeding or be useful in biotechnological approaches. These findings offer insights into the mechanisms of Al tolerance in popcorn and provide a 'hypothesis-free' strategy for identifying and prioritizing candidate genes that could be used to develop molecular markers or cultivars resilient to acidic soils.

A simulation-based assessment of the efficiency of QTL mapping under environment and genotype x environment interaction effects.

The objective of this simulation-based study was to assess how genes, environments, and genotype x environment (GxE) interaction affect the quantitative trait loci (QTL) mapping efficiency. The simulation software performed 50 samplings of 300 recombinant inbred lines (RILs) from a F2, which were assessed in six environments. The RILs were genotyped for 977 single nucleotide polymorphisms (SNP) and phenotyped for grain yield. The average SNP density was 2 cM. We defined six QTLs and 190 minor genes. The trait heritability ranged from 30 to 80%. We fitted the single QTL model and the multiple QTL model on multiple phenotypes. The environment and complex GxE interaction effects led to a low correlation between the QTL heritability and power. The single- and across-environment analyses allowed all QTLs be declared, with an average power of 28 to 100%. In the across-environment analysis, five QTLs showed average power in the range 46 to 82%. Both models provided a good control of the false positive rate (6%, on average) and a precise localization of the QTLs (bias of 2 cM, on average). The QTL power in each environment has a high positive correlation with the range between QTL genotypes for the sum of the additive, environment, and GxE interaction effects (0.76 to 0.96). The uncertainty about the magnitude and sign of the environment and GxE interaction effects makes QTL mapping in multi-environment trials unpredictable. Unfortunately, this uncertainty has no solution because the geneticist has no control over the magnitude and sign of the environment and GxE interaction effects. However, the single- and across-environment analyses are efficient even under a low correlation between QTL heritability and power.

Popcorn (Zea mays L. var. Everta) haploids identified by Navajo phenotype and ploidy level.

For popcorn, obtaining and identifying haploids are still challenging steps. We aimed to induce and screen haploids in popcorn using the Navajo phenotype, seedling vigor, and ploidy level. We used the Krasnodar Haploid Inducer (KHI) in crosses with 20 popcorn source germplasms and five maize controls. The field trial design was completely randomized, with three replications. We assessed the efficacy of induction and identification of haploids based on the haploidy induction rate (HIR) and false positive and negative rates (FPR and FNR). Additionally, we also measured the penetrance of the Navajo marker gene (R1-nj). All putative haploids classified by the R1-nj were germinated together with a diploid sample and evaluated for false positives and negatives based on vigor. Seedlings from 14 females were submitted to flow cytometry to determine the ploidy level. The HIR and penetrance were analyzed by fitting a generalized linear model with a logit link function. The HIR of the KHI, adjusted by cytometry, ranged from 0.0 to 1.2%, with a mean of 0.34%. The average FPR from screening based on the Navajo phenotype was 26.2% and 76.4% for vigor and ploidy, respectively. The FNR was zero. The penetrance of R1-nj ranged from 30.8 to 98.6%. The average number of seeds per ear in temperate germplasm (76) was lower than that obtained in tropical germplasm (98). There is an induction of haploids in germplasm of tropical and temperate origin. We recommend the selection of haploids associated with the Navajo phenotype with a direct method of confirming the ploidy level, such as flow cytometry. We also show that haploid screening based on Navajo phenotype and seedling vigor reduces misclassification. The origin and genetic background of the source germplasm influence the R1-nj penetrance. Because the known inducers are maize, developing doubled haploid technology for popcorn hybrid breeding requires overcoming unilateral cross-incompatibility.

Population size in QTL detection using quantile regression in genome-wide association studies.

The aim of this study was to evaluate the performance of Quantile Regression (QR) in Genome-Wide Association Studies (GWAS) regarding the ability to detect QTLs (Quantitative Trait Locus) associated with phenotypic traits of interest, considering different population sizes. For this, simulated data was used, with traits of different levels of heritability (0.30 and 0.50), and controlled by 3 and 100 QTLs. Populations of 1,000 to 200 individuals were defined, with a random reduction of 100 individuals for each population. The power of detection of QTLs and the false positive rate were obtained by means of QR considering three different quantiles (0.10, 0.50 and 0.90) and also by means of the General Linear Model (GLM). In general, it was observed that the QR models showed greater power of detection of QTLs in all scenarios evaluated and a relatively low false positive rate in scenarios with a greater number of individuals. The models with the highest detection power of true QTLs at the extreme quantils (0.10 and 0.90) were the ones with the highest detection power of true QTLs. In contrast, the analysis based on the GLM detected few (scenarios with larger population size) or no QTLs in the evaluated scenarios. In the scenarios with low heritability, QR obtained a high detection power. Thus, it was verified that the use of QR in GWAS is effective, allowing the detection of QTLs associated with traits of interest even in scenarios with few genotyped and phenotyped individuals.

The impact of epistasis in the heterosis and combining ability analyses.

The current theoretical knowledge concerning the influence of epistasis on heterosis is based on a simplified multiplicative model. The objective of this study was to assess how epistasis affects the heterosis and combining ability analyses, assuming additive model, hundreds of genes, linkage disequilibrium (LD), dominance, and seven types of digenic epistasis. We developed the quantitative genetics theory for supporting the simulation of the individual genotypic values in nine populations, the selfed populations, the 36 interpopulation crosses, 180 doubled haploids (DHs), and their 16,110 crosses, assuming 400 genes on 10 chromosomes of 200 cM. Epistasis only affects population heterosis if there is LD. Only additive × additive and dominance × dominance epistasis can affect the components of the heterosis and combining ability analyses of populations. Epistasis can have a negative impact on the heterosis and combining ability analysis of populations, leading to wrong inferences regarding the identification of superior and most divergent populations. However, this depends on the type of epistasis, percentage of epistatic genes, and magnitude of their effects. Except for duplicate genes with cumulative effects and non-epistatic genic interaction, there was a decrease in the average heterosis by increasing the percentage of epistatic genes and the magnitude of their effects. The same results are generally true for the combining ability analysis of DHs. The combining ability analyses of subsets of 20 DHs showed no significant average impact of epistasis on the identification of the most divergent ones, regardless of the number of epistatic genes and magnitude of their effects. However, a negative effect on the assessment of the superior DHs can occur assuming 100% of epistatic genes, but depending on the epistasis type and the epistatic effect magnitude.

Efficiency of mapping epistatic quantitative trait loci.

Most theoretical studies on epistatic QTL mapping have shown that this procedure is powerful, efficient to control the false positive rate (FPR), and precise to localize QTLs. The objective of this simulation-based study was to show that mapping epistatic QTLs is not an almost-perfect process. We simulated 50 samples of 400 F2 plants/recombinant inbred lines, genotyped for 975 SNPs distributed in 10 chromosomes of 100 cM. The plants were phenotyped for grain yield, assuming 10 epistatic QTLs and 90 minor genes. Adopting basic procedures of r/qtl package, we maximized the power of detection for QTLs (56-74%, on average) but associated with a very high FPR (65%) and a low detection power for the epistatic pairs (7%). Increasing the average detection power for epistatic pairs (14%) highly increased the related FPR. Adopting a procedure to find the best balance between power and FPR, there was a significant decrease in the power of QTL detection (17-31%, on average), associated with a low average detection power for epistatic pairs (8%) and an average FPR of 31% for QTLs and 16% for epistatic pairs. The main reasons for these negative results are a simplified specification of the coefficients of epistatic effects, as theoretically proved, and the effects of minor genes since 2/3 of the FPR for QTLs were due to them. We hope that this study, including the partial derivation of the coefficients of epistatic effects, motivates investigations on how to increase the power of detection for epistatic pairs, effectively controlling the FPR.

Tolerance mechanisms to aluminum in popcorn inbred lines involving aluminum compartmentalization and ascorbate-glutathione redox pathway.

MAIN CONCLUSION: Inbred line 11-133 of popcorn showed the lowest apoplast Al and total Al concentrations and Al-lumogallion complex, associated with a more efficient antioxidant system, mainly due to glutathione metabolism. Popcorn (Zea mays L. var. everta) is largely intended for human consumption. About 40% of the world's arable soils are acidic. In soils acidic, aluminum (Al) ionizes producing the trivalent cation, which is highly toxic to plants. Hence, this work aimed to: (1) evaluate the Al toxicity sites and its effect on the structure of the root tips, (2) quantify Al concentrations in the apoplast and symplast of the roots, and (3) to elucidate the modulation on the activity of antioxidant enzymes and metabolites of the ascorbate-glutathione cycle in two popcorn inbred lines (ILs) 11-133 and 11-60, classified as tolerant and sensitive to this metal, respectively. Aluminum toxicity did not affect the shoot growth; however, there was a yellowing of the oldest leaf blade only in 11-60. The better performance of 11-133 is related to lower apoplastic and total Al concentrations and Al accumulation in the root associated with a lower fluorescence of Al-lumogallion complex at the root tip, indicating the presence of mechanisms of chelation with this metal. Consequently, this IL showed less change in root morphoanatomy and lower reactive oxygen species and malondialdehyde content, which are associated with a more efficient enzymatic and non-enzymatic system, mainly due to the higher content of the glutathione metabolite and the higher activities of superoxide dismutase, monodehydroascorbate reductase, dehydroascorbate reductase, γ-glutamylcysteine synthetase, and glutathione peroxidase enzymes. Thus, these findings illustrated above indicate how internal mechanisms of detoxification respond to Al in popcorn, which can be used as tolerance biomarkers.

Significance of linkage disequilibrium and epistasis on genetic variances in noninbred and inbred populations.

BACKGROUND: The influence of linkage disequilibrium (LD), epistasis, and inbreeding on genotypic variance continues to be an important area of investigation in genetics and evolution. Although the current knowledge about biological pathways and gene networks indicates that epistasis is important in determining quantitative traits, the empirical evidence for a range of species and traits is that the genotypic variance is most additive. This has been confirmed by some recent theoretical studies. However, because these investigations assumed linkage equilibrium, considered only additive effects, or used simplified assumptions for two- and higher-order epistatic effects, the objective of this investigation was to provide additional information about the impact of LD and epistasis on genetic variances in noninbred and inbred populations, using a simulated dataset. RESULTS: In general, the most important component of the genotypic variance was additive variance. Because of positive LD values, after 10 generations of random crosses there was generally a decrease in all genetic variances and covariances, especially the nonepistatic variances. Thus, the epistatic variance/genotypic variance ratio is inversely proportional to the LD level. Increasing inbreeding increased the magnitude of the additive, additive x additive, additive x dominance, and dominance x additive variances, and decreased the dominance and dominance x dominance variances. Except for duplicate epistasis with 100% interacting genes, the epistatic variance/genotypic variance ratio was proportional to the inbreeding level. In general, the additive x additive variance was the most important component of the epistatic variance. Concerning the genetic covariances, in general, they showed lower magnitudes relative to the genetic variances and positive and negative signs. The epistatic variance/genotypic variance ratio was maximized under duplicate and dominant epistasis and minimized assuming recessive and complementary epistasis. Increasing the percentage of epistatic genes from 30 to 100% increased the epistatic variance/genotypic variance ratio by a rate of 1.3 to 12.6, especially in inbred populations. The epistatic variance/genotypic variance ratio was maximized in the noninbred and inbred populations with intermediate LD and an average allelic frequency of the dominant genes of 0.3 and in the noninbred and inbred populations with low LD and an average allelic frequency of 0.5. CONCLUSIONS: Additive variance is in general the most important component of genotypic variance. LD and inbreeding have a significant effect on the magnitude of the genetic variances and covariances. In general, the additive x additive variance is the most important component of epistatic variance. The maximization of the epistatic variance/genotypic variance ratio depends on the LD level, degree of inbreeding, epistasis type, percentage of interacting genes, and average allelic frequency.

Deciphering the major metabolic pathways associated with aluminum tolerance in popcorn roots using label-free quantitative proteomics.

MAIN CONCLUSION: Al responsive proteins are associated with starch, sucrose, and other carbohydrate metabolic pathways. Sucrose synthase is a candidate to Al tolerance. Al responses are regulated at transcriptional and post-transcriptional levels. Aluminum toxicity is one of the important abiotic stresses that affects worldwide crop production. The soluble form of aluminum (Al3+) inhibits root growth by altering water and nutrient uptake, a process that also reduces plant growth and development. Under long-term Al3+ exposure, plants can activate several tolerance mechanisms. To date, no reports of large-scale proteomic data concerning maize responses to this ion have been published. To investigate the post-transcriptional regulation in response to Al toxicity, we performed label-free quantitative proteomics for comparative analysis of two Al-contrasting popcorn inbred lines and an Al-tolerant commercial hybrid during 72 h under Al-stress conditions. A total of 489 differentially accumulated proteins (DAPs) were identified in the Al-sensitive inbred line, 491 in the Al-tolerant inbred line, and 277 in the commercial hybrid. Among them, 120 DAPs were co-expressed in both Al tolerant genotypes. Bioinformatics analysis indicated that starch, sucrose, and other components of carbohydrate metabolism and glycolysis/gluconeogenesis are the biochemical processes regulated in response to Al toxicity. Sucrose synthase accumulation and an increase in sucrose content and starch degradation suggest that these components may enhance popcorn tolerance to Al stress. The accumulation of citrate synthase suggests a key role for this enzyme in the detoxification process in the Al-tolerant inbred line. The integration of transcriptomic and proteomic data indicates that the Al tolerance response presents a complex regulatory network into the transcription and translation dynamics of popcorn root development.

Uncovering the transcriptional response of popcorn (Zea mays L. var. everta) under long-term aluminum toxicity.

To date, the investigation of genes involved in Al resistance has focused mainly on microarrays and short periods of Al exposure. We investigated genes involved in the global response under Al stress by tracking the expression profile of two inbred popcorn lines with different Al sensitivity during 72 h of Al stress. A total of 1003 differentially expressed genes were identified in the Al-sensitive line, and 1751 were identified in the Al-resistant line, of which 273 were shared in both lines. Genes in the category of "response to abiotic stress" were present in both lines, but there was a higher number in the Al-resistant line. Transcription factors, genes involved in fatty acid biosynthesis, and genes involved in cell wall modifications were also detected. In the Al-resistant line, GST6 was identified as one of the key hub genes by co-expression network analysis, and ABC6 may play a role in the downstream regulation of CASP-like 5. In addition, we suggest a class of SWEET transporters that might be involved in the regulation of vacuolar sugar storage and may serve as mechanisms for Al resistance. The results and conclusions expand our understanding of the complex mechanisms involved in Al toxicity and provide a platform for future functional analyses and genomic studies of Al stress in popcorn.

Linkage disequilibrium and haplotype block patterns in popcorn populations.

Linkage disequilibrium (LD) analysis provides information on the evolutionary aspects of populations. Recently, haplotype blocks have been used to increase the power of quantitative trait loci detection in genome-wide association studies and the prediction accuracy of genomic selection. Our objectives were as follows: to compare the degree of LD, LD decay, and LD decay extent in popcorn populations; to characterize the number and length of haplotype blocks in the populations; and to determine whether maize chromosomes also have a pattern of interspaced regions of high and low rates of recombination. We used a biparental population, a synthetic, and a breeding population, genotyped for approximately 75,000 single nucleotide polymorphisms (SNPs). The sample size ranged from 190 to 192 plants. For the whole-genome LD and haplotype block analyses, we assumed a window of 500 kb. To characterize the block and step patterns of LD in the populations, we constructed LD maps by chromosome, defining a cold spot as a chromosome segment including SNPs with the same LDU position. The LD and haplotype block analyses were also performed at the intragenic level, selecting 12 genes related to zein, starch, cellulose, and fatty acid biosynthesis. The populations with the higher and lower frequencies of |D'| values greater than 0.75 were the biparental (65-74%) and the breeding population (26-58%), respectively. There were slight differences between the populations regarding the average distance for SNPs with |D'| values greater than 0.75 (in the range of approximately 207 to 229 kb). The level of LD expressed by the r2 values was low in the populations (0.02, 0.04, and 0.04, on average) but comparable to some non-isolated human populations. The frequency of r2 values greater than 0.75 was lower in the biparental population (0.2-0.5%) and higher in the other populations (0.2-1.6%). The average distance for SNPs with r2 values greater than 0.75 was much higher in the biparental population (approximately 80 to 126 kb). In the other populations, the ranges were approximately 6 to 19 and 6 to 35 kb. The heatmaps for the regions covered by the first 100 SNPs in each chromosome, in each population (1 to 3.3 Mb, approximately), provided evidence that the comparatively few high r2 values (close to 1.0) occurred only for SNPs in close proximity, especially in the synthetic and breeding populations. Due to the reduced number of SNPs in the haplotype blocks (2 to 3) in the populations, it is not expected advantage of a haplotype-based association study as well as genomic selection along generations. The results concerning LD decay (rapid decay after 5-10 kb) and LD decay extent (along up to 300 kb) are in the range observed with maize inbred line panels. The LD maps indicate that maize chromosomes had a pattern of regions of extensive LD interspaced with regions of low LD. However, our simulated LD map provides evidence that this pattern can reflect regions with differences in allele frequencies and LD levels (expressed by |D'|) and not regions with high and low rates of recombination.

Efficiency of genomic prediction of non-assessed single crosses.

An important application of genomic selection in plant breeding is predicting untested single crosses (SCs). Most investigations on the prediction efficiency were based on tested SCs using cross-validation. The main objective was to assess the prediction efficiency by correlating the predicted and true genotypic values of untested SCs (accuracy) and measuring the efficacy of identification of the best 300 untested SCs (coincidence) using simulated data. We assumed 10,000 SNPs, 400 QTLs, two groups of 70 selected DH lines, and 4900 SCs. The heritabilities for the assessed SCs were 30, 60, and 100%. The scenarios included three sampling processes of DH lines, two sampling processes of SCs for testing, two SNP densities, DH lines from distinct and the same populations, DH lines from populations with lower LD, two genetic models, three statistical models, and three statistical approaches. We derived a model for genomic prediction based on SNP average effects of substitution and dominance deviations. The prediction accuracy is not affected by the linkage phase. The prediction of untested SCs is very efficient. The accuracies and coincidences ranged from ~0.8 and 0.5 at low heritability to 0.9 and 0.7 at high heritability, respectively. We also highlight the relevance of the overall LD and demonstrate that efficient prediction of untested SCs can be achieved for crops that show no heterotic pattern, for reduced training set size (10%), for SNP density of 1 cM, and for distinct sampling processes of DH lines based on random choice of the SCs for testing.

Linkage disequilibrium, SNP frequency change due to selection, and association mapping in popcorn chromosome regions containing QTLs for quality traits.

The objectives of this study were to assess linkage disequilibrium (LD) and selection-induced changes in single nucleotide polymorphism (SNP) frequency, and to perform association mapping in popcorn chromosome regions containing quantitative trait loci (QTLs) for quality traits. Seven tropical and two temperate popcorn populations were genotyped for 96 SNPs chosen in chromosome regions containing QTLs for quality traits. The populations were phenotyped for expansion volume, 100-kernel weight, kernel sphericity, and kernel density. The LD statistics were the difference between the observed and expected haplotype frequencies (D), the proportion of D relative to the expected maximum value in the population, and the square of the correlation between the values of alleles at two loci. Association mapping was based on least squares and Bayesian approaches. In the tropical populations, D-values greater than 0.10 were observed for SNPs separated by 100-150 Mb, while most of the D-values in the temperate populations were less than 0.05. Selection for expansion volume indirectly led to increase in LD values, population differentiation, and significant changes in SNP frequency. Some associations were observed for expansion volume and the other quality traits. The candidate genes are involved with starch, storage protein, lipid, and cell wall polysaccharides synthesis.

Ridge, Lasso and Bayesian additive-dominance genomic models.

BACKGROUND: A complete approach for genome-wide selection (GWS) involves reliable statistical genetics models and methods. Reports on this topic are common for additive genetic models but not for additive-dominance models. The objective of this paper was (i) to compare the performance of 10 additive-dominance predictive models (including current models and proposed modifications), fitted using Bayesian, Lasso and Ridge regression approaches; and (ii) to decompose genomic heritability and accuracy in terms of three quantitative genetic information sources, namely, linkage disequilibrium (LD), co-segregation (CS) and pedigree relationships or family structure (PR). The simulation study considered two broad sense heritability levels (0.30 and 0.50, associated with narrow sense heritabilities of 0.20 and 0.35, respectively) and two genetic architectures for traits (the first consisting of small gene effects and the second consisting of a mixed inheritance model with five major genes). RESULTS: G-REML/G-BLUP and a modified Bayesian/Lasso (called BayesA*B* or t-BLASSO) method performed best in the prediction of genomic breeding as well as the total genotypic values of individuals in all four scenarios (two heritabilities x two genetic architectures). The BayesA*B*-type method showed a better ability to recover the dominance variance/additive variance ratio. Decomposition of genomic heritability and accuracy revealed the following descending importance order of information: LD, CS and PR not captured by markers, the last two being very close. CONCLUSIONS: Amongst the 10 models/methods evaluated, the G-BLUP, BAYESA*B* (-2,8) and BAYESA*B* (4,6) methods presented the best results and were found to be adequate for accurately predicting genomic breeding and total genotypic values as well as for estimating additive and dominance in additive-dominance genomic models.

Efficacy of population structure analysis with breeding populations and inbred lines.

The objective was to assess by simulation the efficacy of population structure analysis in plant breeding. Twelve populations and 300 inbred lines were simulated and genotyped using 100 microsatellite loci. The experimental material included populations with and without admixture, ancestry relationship and linkage disequilibrium, and with distinct levels of genetic differentiation and effective sizes. The analyses were performed using Structure software and employed all available models. For all the group number (K) tested, for both populations and inbred lines, the admixture model with correlated allelic frequencies provided the highest value for the logarithm of the marginal likelihood. Fitting appropriate model and using adequate sample size for individuals and markers, Structure was effective in identifying the correct population structure, migrants and individuals with genome from distinct populations. The linkage model did not result in an improvement in clustering relative to the admixture model with correlated allelic frequencies. The inclusion of prior information did not change the results; for some K values the analyses showed slight higher values of the marginal likelihood. The reduction in the number of individuals and markers negatively affected the results. There was a high variation in the most probable K value between the evaluated methods.

Bayesian inference of mixed models in quantitative genetics of crop species.

The objectives of this study were to implement a Bayesian framework for mixed models analysis in crop species breeding and to exploit alternatives for informative prior elicitation. Bayesian inference for genetic evaluation in annual crop breeding was illustrated with the first two half-sib selection cycles in a popcorn population. The Bayesian framework was based on the Just Another Gibbs Sampler software and the R2jags package. For the first cycle, a non-informative prior for the inverse of the variance components and an informative prior based on meta-analysis were used. For the second cycle, a non-informative prior and an informative prior defined as the posterior from the non-informative and informative analyses of the first cycle were used. Regarding the first cycle, the use of an informative prior from the meta-analysis provided clearly distinct results relative to the analysis with a non-informative prior only for the grain yield. Regarding the second cycle, the results for the expansion volume and grain yield showed differences among the three analyses. The differences between the non-informative and informative prior analyses were restricted to variance components and heritability. The correlations between the predicted breeding values from these analyses were almost perfect.

Relative efficiency of the genotypic value and combining ability effects on reciprocal recurrent selection.

Reciprocal recurrent selection (RRS) has been successfully applied to maize breeding for more than 60 years. Our objective was to assess the relative efficiency of the genotypic value and the effects of general and specific combining abilities (GCA and SCA) on selection. The GCA effect reflects the number of favorable genes in the parent. The SCA effect primarily reflects the differences in the gene frequencies between the parents. We simulated three traits, three classes of populations, and 10 cycles of half- and full-sib RRS. The RRS is a highly efficient process for intra- and interpopulation breeding, regardless of the trait or the level of divergence among the populations. The RRS increases the heterosis of the interpopulation cross when there is dominance, and it decreases the inbreeding depression in the populations and the genetic variability in the populations and in the hybrid. When there is not dominance and the populations are not divergent, the RRS also determines population differentiation. The half-sib RRS, which is equivalent to selection based on the GCA effect, is more efficient than the full-sib RRS based on the genotypic value, regardless of the trait or the level of improvement of the populations. The full-sib RRS based on the SCA effect is not efficient for intra- and interpopulation breeding.

Bias in the prediction of genetic gain due to mass and half-sib selection in random mating populations.

The prediction of gains from selection allows the comparison of breeding methods and selection strategies, although these estimates may be biased. The objective of this study was to investigate the extent of such bias in predicting genetic gain. For this, we simulated 10 cycles of a hypothetical breeding program that involved seven traits, three population classes, three experimental conditions and two breeding methods (mass and half-sib selection). Each combination of trait, population, heritability, method and cycle was repeated 10 times. The predicted gains were biased, even when the genetic parameters were estimated without error. Gain from selection in both genders is twice the gain from selection in a single gender only in the absence of dominance. The use of genotypic variance or broad sense heritability in the predictions represented an additional source of bias. Predictions based on additive variance and narrow sense heritability were equivalent, as were predictions based on genotypic variance and broad sense heritability. The predictions based on mass and family selection were suitable for comparing selection strategies, whereas those based on selection within progenies showed the largest bias and lower association with the realized gain.

Bias in the prediction of genetic gain due to mass and half-sib selection in random mating populations

The prediction of gains from selection allows the comparison of breeding methods and selection strategies, although these estimates may be biased. The objective of this study was to investigate the extent of such bias in predicting genetic gain. For this, we simulated 10 cycles of a hypothetical breeding program that involved seven traits, three population classes, three experimental conditions and two breeding methods (mass and half-sib selection). Each combination of trait, population, heritability, method and cycle was repeated 10 times. The predicted gains were biased, even when the genetic parameters were estimated without error. Gain from selection in both genders is twice the gain from selection in a single gender only in the absence of dominance. The use of genotypic variance or broad sense heritability in the predictions represented an additional source of bias. Predictions based on additive variance and narrow sense heritability were equivalent, as were predictions based on genotypic variance and broad sense heritability. The predictions based on mass and family selection were suitable for comparing selection strategies, whereas those based on selection within progenies showed the largest bias and lower association with the realized gain.

Dominance, epistasis, heritabilities and expected genetic gains

Although epistasis is common in gene systems that determine quantitative traits, it is usually not possible to estimate the epistatic components of genotypic variance because experiments in breeding programs include only one type of progeny. As the study of this phenomenon is complex, there is a lack of theoretical knowledge on the contribution of the epistatic variances when predicting gains from selection and on the bias in estimating genetic parameters when fitting the additive-dominant model. The objective of this paper is to discuss these aspects. Regarding a non-inbred population, the genetic value due to dominance and the epistatic components of the genotypic value are not indicators of the number of favorable genes present in an individual. Thus, the efficiency of a selection process should be based on the narrow-sense heritability, a function only of additive variance. If there is no epistasis, generally it is satisfactory to assess the selection efficiency and to predict gain based on the broad-sense heritability. Regardless of the selection unit or type of epistasis, the bias in the estimate of the additive variance when assuming the additive-dominant model is considerable. This implies overestimation of the heritabilities at half sib family mean, plant within family and plant levels, and underestimation if the selection units are full sib progenies. The predicted gains will have a bias proportional to that of the heritability.