An R package for ensemble learning stacking.

Summary: Supervised learning is widely used in biology for prediction, and ensemble learning, including stacking, is a promising technique for increasing and stabilizing the prediction accuracy. In this study, we developed an R package for stacking. This package depends on the R package caret and can handle models supported by caret. Stacking involves cross-validation of training data with multiple base learners, and the predicted values are used as explanatory variables for the meta-learner. In the prediction, the testing data were fed into the base models, and the returned values were averaged for each base learner. The averaged values were then fed into the meta-model, and the final predictions were returned. Using this package, the training and prediction procedures for stacking can be conducted using one-row scripts. Availability and implementation: The R package stacking is available at the Comprehensive R Archive Network (CRAN) (https://cran.r-project.org/) and GitHub (https://github.com/Onogi/stacking). R scripts to reproduce the presented results are also reposited at GitHub.

An R package VIGoR for joint estimation of multiple linear learners with variational Bayesian inference.

SUMMARY: An R package that can implement multiple linear learners, including penalized regression and regression with spike and slab priors, in a single model has been developed. Solutions are obtained with fast minorize-maximization algorithms in the framework of variational Bayesian inference. This package helps to incorporate multimodal and high-dimensional explanatory variables in a single regression model. AVAILABILITY AND IMPLEMENTATION: The R package VIGoR (Variational Bayesian Inference for Genome-wide Regression) is available at the Comprehensive R Archive Network (CRAN) (https://cran.r-project.org/) and at GitHub (https://github.com/Onogi/VIGoR). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Integration of Crop Growth Models and Genomic Prediction.

Crop growth models (CGMs) consist of multiple equations that represent physiological processes of plants and simulate crop growth dynamically given environmental inputs. Because parameters of CGMs are often genotype-specific, gene effects can be related to environmental inputs through CGMs. Thus, CGMs are attractive tools for predicting genotype by environment (G×E) interactions. This chapter reviews CGMs, genetic analyses using these models, and the status of studies that integrate genomic prediction with CGMs. Examples of CGM analyses are also provided.

Genomic prediction with non-additive effects in beef cattle: stability of variance component and genetic effect estimates against population size.

BACKGROUND: Genomic prediction is now an essential technology for genetic improvement in animal and plant breeding. Whereas emphasis has been placed on predicting the breeding values, the prediction of non-additive genetic effects has also been of interest. In this study, we assessed the potential of genomic prediction using non-additive effects for phenotypic prediction in Japanese Black, a beef cattle breed. In addition, we examined the stability of variance component and genetic effect estimates against population size by subsampling with different sample sizes. RESULTS: Records of six carcass traits, namely, carcass weight, rib eye area, rib thickness, subcutaneous fat thickness, yield rate and beef marbling score, for 9850 animals were used for analyses. As the non-additive genetic effects, dominance, additive-by-additive, additive-by-dominance and dominance-by-dominance effects were considered. The covariance structures of these genetic effects were defined using genome-wide SNPs. Using single-trait animal models with different combinations of genetic effects, it was found that 12.6-19.5 % of phenotypic variance were occupied by the additive-by-additive variance, whereas little dominance variance was observed. In cross-validation, adding the additive-by-additive effects had little influence on predictive accuracy and bias. Subsampling analyses showed that estimation of the additive-by-additive effects was highly variable when phenotypes were not available. On the other hand, the estimates of the additive-by-additive variance components were less affected by reduction of the population size. CONCLUSIONS: The six carcass traits of Japanese Black cattle showed moderate or relatively high levels of additive-by-additive variance components, although incorporating the additive-by-additive effects did not improve the predictive accuracy. Subsampling analysis suggested that estimation of the additive-by-additive effects was highly reliant on the phenotypic values of the animals to be estimated, as supported by low off-diagonal values of the relationship matrix. On the other hand, estimates of the additive-by-additive variance components were relatively stable against reduction of the population size compared with the estimates of the corresponding genetic effects.

OryzaGenome2.1: Database of Diverse Genotypes in Wild Oryza Species.

BACKGROUND: OryzaGenome ( http://viewer.shigen.info/oryzagenome21detail/index.xhtml ), a feature within Oryzabase ( https://shigen.nig.ac.jp/rice/oryzabase/ ), is a genomic database for wild Oryza species that provides comparative and evolutionary genomics approaches for the rice research community. RESULTS: Here we release OryzaGenome2.1, the first major update of OryzaGenome. The main feature in this version is the inclusion of newly sequenced genotypes and their meta-information, giving a total of 217 accessions of 19 wild Oryza species (O. rufipogon, O. barthii, O. longistaminata, O. meridionalis, O. glumaepatula, O. punctata, O. minuta, O. officinalis, O. rhizomatis, O. eichingeri, O. latifolia, O. alta, O. grandiglumis, O. australiensis, O. brachyantha, O. granulata, O. meyeriana, O. ridleyi, and O. longiglumis). These 19 wild species belong to 9 genome types (AA, BB, CC, BBCC, CCDD, EE, FF, GG, and HHJJ), representing wide genomic diversity in the genus. Using the genotype information, we analyzed the genome diversity of Oryza species. Other features of OryzaGenome facilitate the use of information on single nucleotide polymorphisms (SNPs) between O. sativa and its wild progenitor O. rufipogon in rice research, including breeding as well as basic science. For example, we provide Variant Call Format (VCF) files for genome-wide SNPs of 33 O. rufipogon accessions against the O. sativa reference genome, IRGSP1.0. In addition, we provide a new SNP Effect Table function, allowing users to identify SNPs or small insertion/deletion polymorphisms in the 33 O. rufipogon accessions and to search for the effect of these polymorphisms on protein function if they reside in the coding region (e.g., are missense or nonsense mutations). Furthermore, the SNP Viewer for 446 O. rufipogon accessions was updated by implementing new tracks for possible selective sweep regions and highly mutated regions that were potentially exposed to selective pressures during the process of domestication. CONCLUSION: OryzaGenome2.1 focuses on comparative genomic analysis of diverse wild Oryza accessions collected around the world and on the development of resources to speed up the identification of critical trait-related genes, especially from O. rufipogon. It aims to promote the use of genotype information from wild accessions in rice breeding and potential future crop improvements. Diverse genotypes will be a key resource for evolutionary studies in Oryza, including polyploid biology.

A Method for Identifying Environmental Stimuli and Genes Responsible for Genotype-by-Environment Interactions From a Large-Scale Multi-Environment Data Set.

It has not been fully understood in real fields what environment stimuli cause the genotype-by-environment (G × E) interactions, when they occur, and what genes react to them. Large-scale multi-environment data sets are attractive data sources for these purposes because they potentially experienced various environmental conditions. Here we developed a data-driven approach termed Environmental Covariate Search Affecting Genetic Correlations (ECGC) to identify environmental stimuli and genes responsible for the G × E interactions from large-scale multi-environment data sets. ECGC was applied to a soybean (Glycine max) data set that consisted of 25,158 records collected at 52 environments. ECGC illustrated what meteorological factors shaped the G × E interactions in six traits including yield, flowering time, and protein content and when these factors were involved in the interactions. For example, it illustrated the relevance of precipitation around sowing dates and hours of sunshine just before maturity to the interactions observed for yield. Moreover, genome-wide association mapping on the sensitivities to the identified stimuli discovered candidate and known genes responsible for the G × E interactions. Our results demonstrate the capability of data-driven approaches to bring novel insights on the G × E interactions observed in fields.

Dynamic effects of interacting genes underlying rice flowering-time phenotypic plasticity and global adaptation.

The phenotypic variation of living organisms is shaped by genetics, environment, and their interaction. Understanding phenotypic plasticity under natural conditions is hindered by the apparently complex environment and the interacting genes and pathways. Herein, we report findings from the dissection of rice flowering-time plasticity in a genetic mapping population grown in natural long-day field environments. Genetic loci harboring four genes originally discovered for their photoperiodic effects (Hd1, Hd2, Hd5, and Hd6) were found to differentially respond to temperature at the early growth stage to jointly determine flowering time. The effects of these plasticity genes were revealed with multiple reaction norms along the temperature gradient. By coupling genomic selection and the environmental index, accurate performance predictions were obtained. Next, we examined the allelic variation in the four flowering-time genes across the diverse accessions from the 3000 Rice Genomes Project and constructed haplotypes at both individual-gene and multigene levels. The geographic distribution of haplotypes revealed their preferential adaptation to different temperature zones. Regions with lower temperatures were dominated by haplotypes sensitive to temperature changes, whereas the equatorial region had a majority of haplotypes that are less responsive to temperature. By integrating knowledge from genomics, gene cloning and functional characterization, and environment quantification, we propose a conceptual model with multiple levels of reaction norms to help bridge the gaps among individual gene discovery, field-level phenotypic plasticity, and genomic diversity and adaptation.

Connecting mathematical models to genomes: joint estimation of model parameters and genome-wide marker effects on these parameters.

MOTIVATION: Parameters of mathematical models used in biology may be genotype-specific and regarded as new traits. Therefore, an accurate estimation of these parameters and the association mapping on the estimated parameters can lead to important findings regarding the genetic architecture of biological processes. In this study, a statistical framework for a joint analysis (JA) of model parameters and genome-wide marker effects on these parameters was proposed and evaluated. RESULTS: In the simulation analyses based on different types of mathematical models, the JA inferred the model parameters and identified the responsible genomic regions more accurately than the independent analysis (IA). The JA of real plant data provided interesting insights into photosensitivity, which were uncovered by the IA. AVAILABILITY AND IMPLEMENTATION: The statistical framework is provided by the R package GenomeBasedModel available at https://github.com/Onogi/GenomeBasedModel. All R and C++ scripts used in this study are also available at the site. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Changes of sires in a breeding farm enables maintenance of DNA-level genetic variation in a produced herd of Hokkaido Native Horses.

We investigated whether regular changes of the sire in a breeding farm of Hokkaido Native Horses (HKDs) enables the DNA-level genetic variation of the produced animals to be maintained. The genotypes of 31 microsatellite markers were identified and analyzed in 207 animals produced in a breeding farm in which the sire was replaced every 3 to 5 years. The mean allele number indicating the degree of genetic variation was 5.97 and was similar to those reported previously. The mean observed heterozygosity was 0.74 and was higher than the expected heterozygosity, 0.69; FIS was -0.07, indicating that the analyzed animals reflected frequent outbreeding and had maintained genetic variation. Based on genetic structural analysis, the number of genetic subpopulations of the animals was estimated to be as 6, and the majority (more than 50%) of each subpopulation corresponded to the progeny of one of the sires used in the breeding farm; these observations suggested that genetic variation in the analyzed animals reflected the genetic differences among sires. Pedigree records indicated that the average co-ancestry coefficient between sires used in the breeding farm was 0.015 corresponding to second cousin. This level of kinship among sires is acceptable for producing HKDs that maintain genetic variation.

Development of a structural growth curve model that considers the causal effect of initial phenotypes.

BACKGROUND: Growth curves have been widely used in genetic analyses to gain insights into the growth characteristics of both animals and plants. However, several questions remain unanswered, including how the initial phenotypes affect growth and what is the duration of any such impact. For beef cattle production in Japan, calves are procured from farms that specialize in reproduction and then moved to other farms where they are fattened to achieve their market/purchase value. However, the causal effect of growth, while calves are on the reproductive farms, on their growth during fattening remains unclear. To investigate this, we developed a model that combines a structural equation with a growth curve model. The causal effect was modeled with B-splines, which allows inference of the effect as a curve. We fitted the proposed structural growth curve model to repeated measures of body weight from a Japanese beef cattle population (n = 3831) to estimate the curve of the causal effect of the calves' initial weight on their trajectory of growth when they are on fattening farms. RESULTS: Maternal and reproduction farm effects explained 26% of the phenotypic variance of initial weight at fattening farms. The structural growth curve model was fitted to remove the effects of these factors in growth curve analysis at fattening farms. The estimated curve of causal effects remained at approximately 0.8 for 200 d after the calves entered the fattening farms, which means that 64% of the phenotypic variance was explained by the initial weight. Then, the effect decreased linearly and disappeared approximately 620 d after entering the fattening farms, which corresponded to an average age of 871.5 d. CONCLUSIONS: The proposed model is expected to provide more accurate estimates of genetic values for growth patterns because the confounding causal factors such as maternal and reproduction farm effects are removed. Moreover, examination of the inferred curve of the causal effect enabled us to estimate the effect of a calf's initial weight at arbitrary times during growth, which could provide suitable information for decision-making when shifting the time of slaughter, building models for genetic evaluation, and selecting calves for market.

Comparison of F-tests for Univariate and Multivariate Mixed-Effect Models in Genome-Wide Association Mapping.

Genome-wide association mapping (GWA) has been widely applied to a variety of species to identify genomic regions responsible for quantitative traits. The use of multivariate information could enhance the detection power of GWA. Although mixed-effect models are frequently used for GWA, the utility of F-tests for multivariate mixed-effect models is not well-recognized. Thus, we compared the F-tests for univariate and multivariate mixed-effect models with simulations. The superiority of the multivariate F-test over the univariate test varied depending on three parameters: phenotypic correlation between variates (r), relative size of quantitative trait locus effects between variates (a d), and missing proportion of phenotypic records (m prop). Simulation results showed that, when m prop was low, the multivariate F-test outperformed the univariate test as r and a d differ, and as m prop increased, the multivariate F-test outperformed as a d increased. These observations were consistent with results of the analytical evaluation of the F-value. When m prop was at the maximum, i.e., when no individual had phenotypic values for multiple variates, as in the case of meta-analysis, the multivariate F-test gained more detection power as a d increased. Although using multivariate information in mixed-effect model contexts did not always ensure more detection power than with univariate tests, the multivariate F-test will be a method applied when multivariate data are available because it does not show inflation of signals and could lead to new findings.

Genome-wide association study and genomic prediction using parental and breeding populations of Japanese pear (Pyrus pyrifolia Nakai).

Breeding of fruit trees is hindered by their large size and long juvenile period. Genome-wide association study (GWAS) and genomic selection (GS) are promising methods for circumventing this hindrance, but preparing new large datasets for these methods may not always be practical. Here, we evaluated the potential of breeding populations evaluated routinely in breeding programs for GWAS and GS. We used a pear parental population of 86 varieties and breeding populations of 765 trees from 16 full-sib families, which were phenotyped for 18 traits and genotyped for 1,506 single nucleotide polymorphisms (SNPs). The power of GWAS and accuracy of genomic prediction were improved when we combined data from the breeding populations and the parental population. The accuracy of genomic prediction was improved further when full-sib data of the target family were available. The results suggest that phenotype data collected in breeding programs can be beneficial for GWAS and GS when they are combined with genome-wide marker data. The potential of GWAS and GS will be further extended if we can build a system for routine collection of the phenotype and marker genotype data for breeding populations.

Identification of QTLs for rice grain size using a novel set of chromosomal segment substitution lines derived from Yamadanishiki in the genetic background of Koshihikari.

Grain size is important for brewing-rice cultivars, but the genetic basis for this trait is still unclear. This paper aims to identify QTLs for grain size using novel chromosomal segment substitution lines (CSSLs) harboring chromosomal segments from Yamadanishiki, an excellent sake-brewing rice, in the genetic background of Koshihikari, a cooking cultivar. We developed a set of 49 CSSLs. Grain length (GL), grain width (GWh), grain thickness (GT), 100-grain weight (GWt) and days to heading (DTH) were evaluated, and a CSSL-QTL analysis was conducted. Eighteen QTLs for grain size and DTH were identified. Seven (qGL11, qGWh5, qGWh10, qGWt6-2, qGWt10-2, qDTH3, and qDTH6) that were detected in F2 and recombinant inbred lines (RILs) from Koshihikari/Yamadanishiki were validated, suggesting that they are important for large grain size and heading date in Yamadanishiki. Additionally, QTL reanalysis for GWt showed that qGWt10-2 was only detected in early-flowering RILs, while qGWt5 (in the same region as qGWh5) was only detected in late-flowering RILs, suggesting that these QTLs show different responses to the environment. Our study revealed that grain size in the Yamadanishiki cultivar is determined by a complex genetic mechanism. These findings could be useful for the breeding of both cooking and brewing rice.

Effects of selection index coefficients that ignore reliability on economic weights and selection responses during practical selection.

OBJECTIVE: In practical breeding, selection is often performed by ignoring the accuracy of evaluations and applying economic weights directly to the selection index coefficients of genetically standardized traits. The denominator of the standardized component trait of estimated genetic evaluations in practical selection varies with its reliability. Whereas theoretical methods for calculating the selection index coefficients of genetically standardized traits account for this variation, practical selection ignores reliability and assumes that it is equal to unity for each trait. The purpose of this study was to clarify the effects of ignoring the accuracy of the standardized component trait in selection criteria on selection responses and economic weights in retrospect. METHODS: Theoretical methods were presented accounting for reliability of estimated genetic evaluations for the selection index composed of genetically standardized traits. RESULTS: Selection responses and economic weights in retrospect resulting from practical selection were greater than those resulting from theoretical selection accounting for reliability when the accuracy of the estimated breeding value (EBV) or genomically enhanced breeding value (GEBV) was lower than those of the other traits in the index, but the opposite occurred when the accuracy of the EBV or GEBV was greater than those of the other traits. This trend was more conspicuous for traits with low economic weights than for those with high weights. CONCLUSION: Failure of the practical index to account for reliability yielded economic weights in retrospect that differed from those obtained with the theoretical index. Our results indicated that practical indices that ignore reliability delay genetic improvement. Therefore, selection practices need to account for reliability, especially when the reliabilities of the traits included in the index vary widely.

Genetic dissection of grain traits in Yamadanishiki, an excellent sake-brewing rice cultivar.

KEY MESSAGE: The grain traits of Yamadanishiki, an excellent sake-brewing rice cultivar in Japan, are governed by multiple QTLs, namely, a total of 42 QTLs including six major QTLs. Japanese rice wine (sake) is produced using brewing rice (Oryza sativa L.) that carries traits desirable for sake-brewing, such as a larger grain size and higher white-core expression rate (WCE) compared to cooking rice cultivars. However, the genetic basis for these traits in brewing rice cultivars is still unclear. We performed analyses of quantitative trait locus (QTL) of grain and days to heading over 3 years on populations derived from crosses between Koshihikari, a cooking rice, and Yamadanishiki, an excellent sake-brewing rice. A total of 42 QTLs were detected for the grain traits, and the Yamadanishiki alleles at 16 QTLs contributed to larger grain size. Two major QTLs essential for regulating both 100-grain weight (GWt) and grain width (GWh) were harbored in the same regions on chromosomes 5 and 10. An interaction was noted between the environment and the QTL associated with WCE on chromosome 6, which was detected in two of 3 years. In addition, two QTLs for WCE on chromosomes 3 and 10 overlapped with the QTLs for GWt and GWh, suggesting that QTLs associated with grain size also play an important role in the formation of white-core. Despite differences in the rate of grain growth in both Koshihikari and Yamadanishiki across 2 years, the WCE in Yamadanishiki remained consistent, thus demonstrating that the formation of white-core does not depend on grain filling speed. These data can be informative for programs involved in breeding better cooking and brewing rice cultivars.

Investigation of genetic diversity and inbreeding in a Japanese native horse breed for suggestions on its conservation.

Because native breeds can serve as genetic resources for adapting to environment changes, their conservation is important for future agroecosystems. Using pedigree analysis, we investigated genetic diversity and inbreeding in Japanese Hokkaido native horses, which have adapted to a cold climate and roughage diet. Genetic diversity was measured as the number of founders and the effective number of founders, ancestors and genomes. All metrics imply a decrease in genetic diversity. A comparison of these metrics suggested that pedigree bottlenecks contributed more than did random gene losses to the reduction of genetic diversity. Estimates of marginal contributions of ancestors suggest that the bottlenecks arose mainly because related stallions had been used for breeding. A tendency for an increase in inbreeding coefficients was observed. F-statistics revealed that a small effective population size majorly contributed to this increase, although non-random mating in particular regions also contributed. Because the bottlenecks are thought to have reduced the effective population size, our results imply that mitigation of bottlenecks is important for conservation. To this end, breeding should involve genetically diverse stallions. In addition, to prevent non-random mating observed in particular regions, efforts should be made to plan mating with consideration of kinships.

Genome-wide association study and genomic prediction in citrus: Potential of genomics-assisted breeding for fruit quality traits.

Novel genomics-based approaches such as genome-wide association studies (GWAS) and genomic selection (GS) are expected to be useful in fruit tree breeding, which requires much time from the cross to the release of a cultivar because of the long generation time. In this study, a citrus parental population (111 varieties) and a breeding population (676 individuals from 35 full-sib families) were genotyped for 1,841 single nucleotide polymorphisms (SNPs) and phenotyped for 17 fruit quality traits. GWAS power and prediction accuracy were increased by combining the parental and breeding populations. A multi-kernel model considering both additive and dominance effects improved prediction accuracy for acidity and juiciness, implying that the effects of both types are important for these traits. Genomic best linear unbiased prediction (GBLUP) with linear ridge kernel regression (RR) was more robust and accurate than GBLUP with non-linear Gaussian kernel regression (GAUSS) in the tails of the phenotypic distribution. The results of this study suggest that both GWAS and GS are effective for genetic improvement of citrus fruit traits. Furthermore, the data collected from breeding populations are beneficial for increasing the detection power of GWAS and the prediction accuracy of GS.

Genetic Nature of Elemental Contents in Wheat Grains and Its Genomic Prediction: Toward the Effective Use of Wheat Landraces from Afghanistan.

Profiling elemental contents in wheat grains and clarifying the underlying genetic systems are important for the breeding of biofortified crops. Our objective was to evaluate the genetic potential of 269 Afghan wheat landraces for increasing elemental contents in wheat cultivars. The contents of three major (Mg, K, and P) and three minor (Mn, Fe, and Zn) elements in wheat grains were measured by energy dispersive X-ray fluorescence spectrometry. Large variations in elemental contents were observed among landraces. Marker-based heritability estimates were low to moderate, suggesting that the elemental contents are complex quantitative traits. Genetic correlations between two locations (Japan and Afghanistan) and among the six elements were estimated using a multi-response Bayesian linear mixed model. Low-to-moderate genetic correlations were observed among major elements and among minor elements respectively, but not between major and minor elements. A single-response genome-wide association study detected only one significant marker, which was associated with Zn, suggesting it will be difficult to increase the elemental contents of wheat by conventional marker-assisted selection. Genomic predictions for major elemental contents were moderately or highly accurate, whereas those for minor elements were mostly low or moderate. Our results indicate genomic selection may be useful for the genetic improvement of elemental contents in wheat.

Uncovering a Nuisance Influence of a Phenological Trait of Plants Using a Nonlinear Structural Equation: Application to Days to Heading and Culm Length in Asian Cultivated Rice (Oryza Sativa L.).

Phenological traits of plants, such as flowering time, are linked to growth phase transition. Thus, phenological traits often influence other traits through the modification of the duration of growth period. This influence is a nuisance in plant breeding because it hampers genetic evaluation of the influenced traits. Genetic effects on the influenced traits have two components, one that directly affects the traits and one that indirectly affects the traits via the phenological trait. These cannot be distinguished by phenotypic evaluation and ordinary linear regression models. Consequently, if a phenological trait is modified by introgression or editing of the responsible genes, the phenotypes of the influenced traits can change unexpectedly. To uncover the influence of the phenological trait and evaluate the direct genetic effects on the influenced traits, we developed a nonlinear structural equation (NSE) incorporating a nonlinear influence of the phenological trait. We applied the NSE to real data for cultivated rice (Oryza sativa L.): days to heading (DH) as a phenological trait and culm length (CL) as the influenced trait. This showed that CL of the cultivars that showed extremely early heading was shortened by the strong influence of DH. In a simulation study, it was shown that the NSE was able to infer the nonlinear influence and direct genetic effects with reasonable accuracy. However, the NSE failed to infer the linear influence in this study. When no influence was simulated, an ordinary bi-trait linear model (OLM) tended to infer the genetic effects more accurately. In such cases, however, by comparing the NSE and OLM using an information criterion, we could assess whether the nonlinear assumption of the NSE was appropriate for the data analyzed. This study demonstrates the usefulness of the NSE in revealing the phenotypic influence of phenological traits.

A simulation-based breeding design that uses whole-genome prediction in tomato.

Efficient plant breeding methods must be developed in order to increase yields and feed a growing world population, as well as to meet the demands of consumers with diverse preferences who require high-quality foods. We propose a strategy that integrates breeding simulations and phenotype prediction models using genomic information. The validity of this strategy was evaluated by the simultaneous genetic improvement of the yield and flavour of the tomato (Solanum lycopersicum), as an example. Reliable phenotype prediction models for the simulation were constructed from actual genotype and phenotype data. Our simulation predicted that selection for both yield and flavour would eventually result in morphological changes that would increase the total plant biomass and decrease the light extinction coefficient, an essential requirement for these improvements. This simulation-based genome-assisted approach to breeding will help to optimise plant breeding, not only in the tomato but also in other important agricultural crops.