Using visual scores for genomic prediction of complex traits in breeding programs

KEY MESSAGE

An approach for handling visual scores with potential errors and subjectivity in scores was evaluated in simulated and blueberry recurrent selection breeding schemes to assist breeders in their decision-making. Most genomic prediction methods are based on assumptions of normality due to their simplicity and ease of implementation. However, in plant and animal breeding, continuous traits are often visually scored as categorical traits and analyzed as a Gaussian variable, thus violating the normality assumption, which could affect the prediction of breeding values and the estimation of genetic parameters. In this study, we examined the main challenges of visual scores for genomic prediction and genetic parameter estimation using mixed models, Bayesian, and machine learning methods. We evaluated these approaches using simulated and real breeding data sets. Our contribution in this study is a five-fold demonstration: (i) collecting data using an intermediate number of categories (1-3 and 1-5) is the best strategy, even considering errors associated with visual scores; (ii) Linear Mixed Models and Bayesian Linear Regression are robust to the normality violation, but marginal gains can be achieved when using Bayesian Ordinal Regression Models (BORM) and Random Forest Classification; (iii) genetic parameters are better estimated using BORM; (iv) our conclusions using simulated data are also applicable to real data in autotetraploid blueberry; and (v) a comparison of continuous and categorical phenotypes found that investing in the evaluation of 600-1000 categorical data points with low error, when it is not feasible to collect continuous phenotypes, is a strategy for improving predictive abilities. Our findings suggest the best approaches for effectively using visual scores traits to explore genetic information in breeding programs and highlight the importance of investing in the training of evaluator teams and in high-quality phenotyping.

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.

Increasing cassava root yield: Additive-dominant genetic models for selection of parents and clones

Genomic selection has been promising in situations where phenotypic assessments are expensive, laborious, and/or inefficient. This work evaluated the efficiency of genomic prediction methods combined with genetic models in clone and parent selection with the goal of increasing fresh root yield, dry root yield, as well as dry matter content in cassava roots. The bias and predictive ability of the combinations of prediction methods Genomic Best Linear Unbiased Prediction (G-BLUP), Bayes B, Bayes Cπ, and Reproducing Kernel Hilbert Spaces with additive and additive-dominant genetic models were estimated. Fresh and dry root yield exhibited predominantly dominant heritability, while dry matter content exhibited predominantly additive heritability. The combination of prediction methods and genetic models did not show significant differences in the predictive ability for dry matter content. On the other hand, the prediction methods with additive-dominant genetic models had significantly higher predictive ability than the additive genetic models for fresh and dry root yield, allowing higher genetic gains in clone selection. However, higher predictive ability for genotypic values did not result in differences in breeding value predictions between additive and additive-dominant genetic models. G-BLUP with the classical additive-dominant genetic model had the best predictive ability and bias estimates for fresh and dry root yield. For dry matter content, the highest predictive ability was obtained by G-BLUP with the additive genetic model. Dry matter content exhibited the highest heritability, predictive ability, and bias estimates compared with other traits. The prediction methods showed similar selection gains with approximately 67% of the phenotypic selection gain. By shortening the breeding cycle time by 40%, genomic selection may overcome phenotypic selection by 10%, 13%, and 18% for fresh root yield, dry root yield, and dry matter content, respectively, with a selection proportion of 15%. The most suitable genetic model for each trait allows for genomic selection optimization in cassava with high selection gains, thereby accelerating the release of new varieties.

Multivariate analysis methods improve the selection of strawberry genotypes with low cold requirement

Methods of multivariate analysis is a powerful approach to assist the initial stages of crops genetic improvement, particularly, because it allows many traits to be evaluated simultaneously. In this study, heat-tolerant genotypes have been selected by analyzing phenotypic diversity, direct and indirect relationships among traits were identified, and four selection indices compared. Diversity was estimated using K-means clustering with the number of clusters determined by the Elbow method, and the relationship among traits was quantified by path analysis. Parametric and non-parametric indices were applied to selected genotypes using the magnitude of genotypic variance, heritability, genotypic coefficient of variance, and assigned economic weight as selection criteria. The variability among materials led to the formation of two non-overlapping clusters containing 40 and 154 genotypes. Strong to moderate correlations were found between traits with direct effect of the number of commercial fruit on the mass of commercial fruit. The Smith and Hazel index showed the greatest total gains for all criteria; however, concerning the biochemical traits, the Mulamba and Mock index showed the highest magnitudes of predicted gains. Overall, the K-means clustering, correlation analysis, and path analysis complement the use of selection indices, allowing for selection of genotypes with better balance among the assessed traits.

Designing the best breeding strategy for Coffea canephora: Genetic evaluation of pure and hybrid individuals aiming to select for productivity and disease resistance traits

Breeding programs of the species Coffea canephora rely heavily on the significant genetic variability between and within its two varietal groups (conilon and robusta). The use of hybrid families and individuals has been less common. The objectives of this study were to evaluate parents and families from the populations of conilon, robusta, and its hybrids and to define the best breeding and selection strategies for productivity and disease resistance traits. As such, 71 conilon clones, 56 robusta clones, and 20 hybrid families were evaluated over several years for the following traits: vegetative vigor, incidence of rust and cercosporiosis, fruit ripening time, fruit size, plant height, canopy diameter, and yield per plant. Components of variance and genetic parameters were estimated via residual maximum likelihood (REML) and genotypic values were predicted via best linear unbiased prediction (BLUP). Genetic variability among parents (clones) and hybrid families was detected for most of the evaluated traits. The Mulamba-Rank index suggests potential gains up to 17% for the genotypic aggregate of traits in the hybrid population. An intrapopulation recurrent selection within the hybrid population would be the best breeding strategy because the genetic variability, narrow and broad senses heritabilities and selective accuracies for important traits were maximized in the crossed population. Besides, such strategy is simple, low cost and quicker than the concurrent reciprocal recurrent selection in the two parental populations, and this maximizes the genetic gain for unit of time.

Can Cross-Country Genomic Predictions Be a Reasonable Strategy to Support Germplasm Exchange? - A Case Study With Hydrogen Cyanide in Cassava

Genomic prediction (GP) offers great opportunities for accelerated genetic gains by optimizing the breeding pipeline. One of the key factors to be considered is how the training populations (TP) are composed in terms of genetic improvement, kinship/origin, and their impacts on GP. Hydrogen cyanide content (HCN) is a determinant trait to guide cassava's products usage and processing. This work aimed to achieve the following objectives: (i) evaluate the feasibility of using cross-country (CC) GP between germplasm's of Embrapa Mandioca e Fruticultura (Embrapa, Brazil) and The International Institute of Tropical Agriculture (IITA, Nigeria) for HCN; (ii) provide an assessment of population structure for the joint dataset; (iii) estimate the genetic parameters based on single nucleotide polymorphisms (SNPs) and a haplotype-approach. Datasets of HCN from Embrapa and IITA breeding programs were analyzed, separately and jointly, with 1,230, 590, and 1,820 clones, respectively. After quality control, ∼14K SNPs were used for GP. The genomic estimated breeding values (GEBVs) were predicted based on SNP effects from analyses with TP composed of the following: (i) Embrapa genotypic and phenotypic data, (ii) IITA genotypic and phenotypic data, and (iii) the joint datasets. Comparisons on GEBVs' estimation were made considering the hypothetical situation of not having the phenotypic characterization for a set of clones for a certain research institute/country and might need to use the markers' effects that were trained with data from other research institutes/country's germplasm to estimate their clones' GEBV. Fixation index (F_ST) among the genetic groups identified within the joint dataset ranged from 0.002 to 0.091. The joint dataset provided an improved accuracy (0.8-0.85) compared to the prediction accuracy of either germplasm's sources individually (0.51-0.67). CC GP proved to have potential use under the present study's scenario, the correlation between GEBVs predicted with TP from Embrapa and IITA was 0.55 for Embrapa's germplasm, whereas for IITA's it was 0.1. This seems to be among the first attempts to evaluate the CC GP in plants. As such, a lot of useful new information was provided on the subject, which can guide new research on this very important and emerging field.

Multiple-trait model through Bayesian inference applied to Jatropha curcas breeding for bioenergy

Multiple-trait model tends to be the best alternative for the analysis of repeated measures, since they consider the genetic and residual correlations between measures and improve the selective accuracy. Thus, the objective of this study was to propose a multiple-trait Bayesian model for repeated measures analysis in Jatropha curcas breeding for bioenergy. To this end, the grain yield trait of 730 individuals of 73 half-sib families was evaluated over six harvests. The Markov Chain Monte Carlo algorithm was used to estimate genetic parameters and genetic values. Genetic correlation between pairs of measures were estimated and four selective intensities (27.4%, 20.5%, 13.7%, and 6.9%) were used to compute the selection gains. The full model was selected based on deviance information criterion. Genetic correlations of low (ρ_g ≤ 0.33), moderate (0.34 ≤ ρ_g ≤ 0.66), and high magnitude (ρ_g ≥ 0.67) were observed between pairs of harvests. Bayesian analyses provide robust inference of genetic parameters and genetic values, with high selective accuracies. In summary, the multiple-trait Bayesian model allowed the reliable selection of superior Jatropha curcas progenies. Therefore, we recommend this model to genetic evaluation of Jatropha curcas genotypes, and its generalization, in other perennials.

Random regression for modeling yield genetic trajectories in Jatropha curcas breeding

Random regression models (RRM) are a powerful tool to evaluate genotypic plasticity over time. However, to date, RRM remains unexplored for the analysis of repeated measures in Jatropha curcas breeding. Thus, the present work aimed to apply the random regression technique and study its possibilities for the analysis of repeated measures in Jatropha curcas breeding. To this end, the grain yield (GY) trait of 730 individuals of 73 half-sib families was evaluated over six years. Variance components were estimated by restricted maximum likelihood, genetic values were predicted by best linear unbiased prediction and RRM were fitted through Legendre polynomials. The best RRM was selected by Bayesian information criterion. According to the likelihood ratio test, there was genetic variability among the Jatropha curcas progenies; also, the plot and permanent environmental effects were statistically significant. The variance components and heritability estimates increased over time. Non-uniform trajectories were estimated for each progeny throughout the measures, and the area under the trajectories distinguished the progenies with higher performance. High accuracies were found for GY in all harvests, which indicates the high reliability of the results. Moderate to strong genetic correlation was observed across pairs of harvests. The genetic trajectories indicated the existence of genotype × measurement interaction, once the trajectories crossed, which implies a different ranking in each year. Our results suggest that RRM can be efficiently applied for genetic selection in Jatropha curcas breeding programs.

Multiple-trait, random regression, and compound symmetry models for analyzing multi-environment trials in maize breeding

An efficient and informative statistical method to analyze genotype-by-environment interaction (GxE) is needed in maize breeding programs. Thus, the objective of this study was to compare the effectiveness of multiple-trait models (MTM), random regression models (RRM), and compound symmetry models (CSM) in the analysis of multi-environment trials (MET) in maize breeding. For this, a data set with 84 maize hybrids evaluated across four environments for the trait grain yield (GY) was used. Variance components were estimated by restricted maximum likelihood (REML), and genetic values were predicted by best linear unbiased prediction (BLUP). The best fit MTM, RRM, and CSM were identified by the Akaike information criterion (AIC), and the significance of the genetic effects were tested using the likelihood ratio test (LRT). Genetic gains were predicted considering four selection intensities (5, 10, 15, and 20 hybrids). The selected MTM, RRM, and CSM models fit heterogeneous residuals. Moreover, for RRM the genetic effects were modeled by Legendre polynomials of order two. Genetic variability between maize hybrids were assessed for GY. In general, estimates of broad-sense heritability, selective accuracy, and predicted selection gains were slightly higher when obtained using MTM and RRM. Thus, considering the criterion of parsimony and the possibility of predicting genetic values of hybrids for untested environments, RRM is a preferential approach for analyzing MET in maize breeding.

Overcoming collinearity in path analysis of soybean [Glycine max (L.) Merr.] grain oil content

Path analysis allows understanding the direct and indirect effects among traits. Multicollinearity in correlation matrices may cause a bias in path analysis estimates. This study aimed to: a) understand the correlation among soybean traits and estimate their direct and indirect effects on gain oil content; b) verify the efficiency of ridge path analysis and trait culling to overcome colinearity. Three different matrices with different levels of collinearity were obtained by trait culling. Ridge path analysis was performed on matrices with strong collinearity; otherwise, a traditional path analysis was performed. The same analyses were run on a simulated dataset. Trait culling was applied to matrix R originating the matrices R1 and R2. Path analysis for matrices R1 and R2 presented a high determination coefficient (0.856 and 0.832, respectively) and low effect of the residual variable (0.379 and 0.410 respectively). Ridge path analysis presented low determination coefficient (0.657) and no direct effects greater than the effects of the residual variable (0.585). Trait culling was more effective to overcome collinearity. Mass of grains, number of nodes, and number of pods are promising for indirect selection for oil content.

Unraveling candidate genes underlying biomass digestibility in elephant grass (Cenchrus purpureus)

BACKGROUND

Elephant grass [Cenchrus purpureus (Schumach.) Morrone] is used for bioenergy and animal feed. In order to identify candidate genes that could be exploited for marker-assisted selection in elephant grass, this study aimed to investigate changes in predictive accuracy using genomic relationship information and simple sequence repeats for eight traits (height, green biomass, dry biomass, acid and neutral detergent fiber, lignin content, biomass digestibility, and dry matter concentration) linked to bioenergetics and animal feeding.

RESULTS

We used single-step, genome-based best linear unbiased prediction and genome association methods to investigate changes in predictive accuracy and find candidate genes using genomic relationship information. Genetic variability (p < 0.05) was detected for most of the traits evaluated. In general, the overall means for the traits varied widely over the cuttings, which was corroborated by a significant genotype by cutting interaction. Knowing the genomic relationships increased the predictive accuracy of the biomass quality traits. We found that one marker (M28_161) was significantly associated with high values of biomass digestibility. The marker had moderate linkage disequilibrium with another marker (M35_202) that, in general, was detected in genotypes with low values of biomass digestibility. In silico analysis revealed that both markers have orthologous regions in other C4 grasses such as Setaria viridis, Panicum hallii, and Panicum virgatum, and these regions are located close to candidate genes involved in the biosynthesis of cell wall molecules (xyloglucan and lignin), which support their association with biomass digestibility.

CONCLUSIONS

The markers and candidate genes identified here are useful for breeding programs aimed at changing biomass digestibility in elephant grass. These markers can be used in marker-assisted selection to grow elephant grass cultivars for different uses, e.g., bioenergy production, bio-based products, co-products, bioactive compounds, and animal feed.

Cassava yield traits predicted by genomic selection methods

Genomic selection (GS) has been used to optimize genetic gains when phenotypic selection is considered costly and difficult to measure. The objective of this work was to evaluate the efficiency and consistency of GS prediction for cassava yield traits (Manihot esculenta Crantz) using different methods, taking into account the effect of population structure. BLUPs and deregressed BLUPs were obtained for 888 cassava accessions and evaluated for fresh root yield, dry root yield and dry matter content in roots in 21 trials conducted from 2011 to 2016. The deregressed BLUPs obtained for the accessions from a 48K single nucleotide polymorphism dataset were used for genomic predictions based on the BayesB, BLASSO, RR-BLUP, G-BLUP and RKHS methods. The accessions’ BLUPs were used in the validation step using four cross-validation strategies, taking into account population structure and different GS methods. Similar estimates of predictive ability and bias were identified for the different genomic selection methods in the first cross-validation strategy. Lower predictive ability was observed for fresh root yield (0.4569 –RR-BLUP to 0.4756—RKHS) and dry root yield (0.4689 –G-BLUP to 0.4818—RKHS) in comparison with dry matter content (0.5655 –BLASSO to 0.5670 –RKHS). However, the RKHS method exhibited higher efficiency and consistency in most of the validation scenarios in terms of prediction ability for fresh root yield and dry root yield. The correlations of the genomic estimated breeding values between the genomic selection methods were quite high (0.99–1.00), resulting in high coincidence of clone selection regardless of the genomic selection method. The deviance analyses within and between the validation clusters formed by the discriminant analysis of principal components were significant for all traits. Therefore, this study indicated that i) the prediction of dry matter content was more accurate compared to that of yield traits, possibly as a result of the smaller influence of non-additive genetic effects; ii) the RKHS method resulted in high and stable prediction ability in most of the validation scenarios; and iii) some kinship between the validation and training populations is desirable in order for genomic selection to succeed due to the significant effect of population structure on genomic selection predictions.

Multi-trait multi-environment models in the genetic selection of segregating soybean progeny

At present, single-trait best linear unbiased prediction (BLUP) is the standard method for genetic selection in soybean. However, when genetic selection is performed based on two or more genetically correlated traits and these are analyzed individually, selection bias may arise. Under these conditions, considering the correlation structure between the evaluated traits may provide more-accurate genetic estimates for the evaluated parameters, even under environmental influences. The present study was thus developed to examine the efficiency and applicability of multi-trait multi-environment (MTME) models by the residual maximum likelihood (REML/BLUP) and Bayesian approaches in the genetic selection of segregating soybean progeny. The study involved data pertaining to 203 soybean F2:4 progeny assessed in two environments for the following traits: number of days to maturity (DM), 100-seed weight (SW), and average seed yield per plot (SY). Variance components and genetic and non-genetic parameters were estimated via the REML/BLUP and Bayesian methods. The variance components estimated and the breeding values and genetic gains predicted with selection through the Bayesian procedure were similar to those obtained by REML/BLUP. The frequentist and Bayesian MTME models provided higher estimates of broad-sense heritability per plot (or heritability of total effects of progeny; [Formula: see text]) and mean accuracy of progeny than their respective single-trait versions. Bayesian analysis provided the credibility intervals for the estimates of [Formula: see text]. Therefore, MTME led to greater predicted gains from selection. On this basis, this procedure can be efficiently applied in the genetic selection of segregating soybean progeny.

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.

Identification of Fungus Resistant Wild Accessions and Interspecific Hybrids of the Genus Arachis

Peanut, Arachis hypogaea L., is a protein-rich species consumed worldwide. A key improvement to peanut culture involves the development of cultivars that resist fungal diseases such as rust, leaf spot and scab. Over three years, we evaluated fungal resistance under field conditions of 43 wild accessions and three interspecific hybrids of the genus Arachis, as well as six A. hypogaea genotypes. In the first year, we evaluated resistance to early and late leaf spot, rust and scab. In the second and third years, we evaluated the 18 wild species with the best resistance scores and control cultivar IAC Caiapó for resistance to leaf spot and rust. All wild accessions displayed greater resistance than A. hypogaea but differed in their degree of resistance, even within the same species. We found accessions with as good as or better resistance than A. cardenasii, including: A. stenosperma (V15076 and Sv 3712), A. kuhlmannii (V 6413), A. kempff-mercadoi (V 13250), A. hoehnei (KG 30006), and A. helodes (V 6325). Amphidiploids and hybrids of A. hypogaea behaved similarly to wild species. An additional four accessions deserve further evaluation: A. magna (V 13751 and KG 30097) and A. gregoryi (V 14767 and V 14957). Although they did not display as strong resistance as the accessions cited above, they belong to the B genome type that is crucial to resistance gene introgression and pyramidization in A. hypogaea.

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.

The influence of animals from embryo transfer on the genetic evaluation of growth in Simmental beef cattle by using multi-trait models

The weight records from Simmental beef cattle were used in a genetic evaluation of growth with or without the inclusion of animals obtained by embryo transfer. A multi-trait model in which embryo transfer individuals were excluded (MTM1) contained 29,510 records from 10,659 animals, while another model without exclusion of these animals (MTM2) contained 62,895 weight records from 23,160 animals. The weight records were adjusted for ages of 100, 205, 365, 450, 550 and 730 days. The (co)variance components and genetic parameters were estimated by the restricted maximum likelihood method. The (co)variance components were similar in both models, except for maternal permanent environment variance. Direct heritabilities (h(2) d) in MTM1 were 0.04, 0.11, 0.20, 0.27, 0.31 and 0.42, while in MTM2 they were 0.11, 0.11, 0.17, 0.21, 0.22 and 0.26 for 100, 205, 365, 450, 550 and 730 days of age, respectively. Estimates of h(2) d in MTM1 were higher than in MTM2 for the weight at 365 days of age. Genetic correlations between weights in both models ranged from moderate to high, suggesting that these traits may be determined mainly by the same genes. Animals from embryo transfer may be included in the genetic evaluation of Simmental beef cattle in Brazil; this inclusion may provide potential gains in accuracy and genetic gains by reducing the interval between generations.

Genetic control of Eucalyptus urophylla and E. grandis resistance to canker caused by Chrysoporthe cubensis

Chrysophorte cubensis induced canker occurs in nearly all tropical and subtropical regions where eucalypts are planted, causing losses in both wood quality and volume productivity, especially so in the warmer and more humid regions of Brazil. The wide inter and intra-specific genetic variability of resistance to canker among Eucalyptus species facilitates the selection of resistant plants. In this study, we evaluated resistance to this pathogen in five Eucalyptus grandis (G) and 15 E. urophylla (U) trees, as well as in 495 individuals from 27 progenies derived from crosses between the trees. In the field, six-months-old test seedlings were inoculated with C. cubensis. Lesion length in the xylem and bark was measured eight months later. The results demonstrated that xylem lesions could preferentially be used for the selection of resistant clones. Eight trees (7 U and 1 G) were susceptible, and the remainder (8 U and 4 G) resistant. Individual narrow and broad sense heritability estimates were 17 and 81%, respectively, thereby suggesting that canker resistance is quantitative and highly dependent on dominance and epistasis.

Selection and genetic gain in rubber tree (Hevea) populations using a mixed mating system

The components of genetic variation and genetic gain obtained with three selection methods - individual, combined and multi-effect index selection - were compared in rubber tree [Hevea brasiliensis (Willd. ex Adr. de Juss.) Muell. Arg.] progenies. The rubber tree is a cross pollinating species with a mixed reproductive system in which the self pollination rate is 22%. Twenty-two half sib progenies were planted at experimental stations at Pindorama, Votuporanga and Jaú, in São Paulo State, using a randomized and complete block design, with five replications and ten plants per plot. Dry rubber production was assessed when the plants were three years old. Based on the genetic variability of the populations, Pindorama was the best environment for the expression of variability. At the individual level, heritability was seriously affected when random progenies from an open pollinating population were considered as half sib progenies. Considerable overestimation of genetic gains occurred during individual, combined and multi-effect index selection when the rubber tree reproductive system was not considered as mixed. Selection based on the multi-effect index maximizes genetic progress and should be used more in rubber tree breeding programs.

Maximization of genetic gain in rubber tree (Hevea) breeding with effective size restriction

The heritability coefficients and the genetic gains associated with individual, combined and among and within progeny selection, and with multi-effect index selection in long-term rubber tree [Hevea brasiliensis (Willd. ex Adr. de Juss.) Muell.-Arg.] breeding were determined using effective population size (Ne) restriction. Twenty-two half sib progenies were planted at the Jaú Experimental Station, São Paulo State, Brazil, in a complete randomized block design, with five replications and 10 plants per plot. The following traits were assessed when the plants were three years old: number of laticiferous vessel rings (NR), dry rubber production (RP), bark thickness (BT) and stem girth (SG). Significant variability was found among progeny with good chances of obtaining genetic gain for RP, BT and SG. Effective population size restriction caused a greater reduction in genetic gain for RP with combined selection and with the multi-effect index than for individual or among and within progeny selection. The simultaneous use of accuracy values and genetic gain from the lower limits of the confidence intervals for gain indicated that individual selection is to be preferred in Hevea breeding programs.

Genotype-environment interaction and the number of test sites for the genetic improvement of rubber trees (Hevea) in São Paulo State, Brazil

The present study quantifies the possible genotype-environment interactions and determines the ideal number of test sites for rubber trees [Hevea brasiliensis (Willd ex Adr. de Juss.) Muell Arg] in the plateau region of São Paulo State. The study was based on the genetic correlation among progenies at three different sites and on estimates of genetic gains with indirect selection of rubber trees. Twenty-two half-sib progenies were planted at the Jaú, Pindorama and Votuporanga experimental stations using random blocks with five replications and 10 plants per plot. At three years of age, the plants were evaluated for their total number of latex ring vessels (NR), rubber production (RP), bark thickness (BT) and girth (SG). There was significant genetic variability in the characters RP, SG and BT, mainly among progenies from Pindorama and Votuporanga. The effects of genotype-site interactions were significant for RP and SG. The finding of significant interactions was not a complicating factor because of the large genetic correlation detected. These results indicate that the use of two sites is more profitable when the gains in efficiency of selection are greater than 10%. Thus, Pindorama and Votuporanga will satisfactorily attend the studied region.