QU-GENE: a simulation platform for quantitative analysis of genetic models

A framework for simulating genotype-by-environment interaction using multiplicative models

KEY MESSAGE

The simulation of genotype-by-environment interaction using multiplicative models provides a general and scalable framework to generate realistic multi-environment datasets and model plant breeding programmes. Plant breeding has been historically shaped by genotype-by-environment interaction (GEI). Despite its importance, however, many current simulations do not adequately capture the complexity of GEI inherent to plant breeding. The framework developed in this paper simulates GEI with desirable structure using multiplicative models. The framework can be used to simulate a hypothetical target population of environments (TPE), from which many different multi-environment trial (MET) datasets can be sampled. Measures of variance explained and expected accuracy are developed to tune the simulation of non-crossover and crossover GEI and quantify the MET-TPE alignment. The framework has been implemented within the R package FieldSimR, and is demonstrated here using two working examples supported by R code. The first example embeds the framework into a linear mixed model to generate MET datasets with low, moderate and high GEI, which are used to compare several popular statistical models applied to plant breeding. The prediction accuracy generally increases as the level of GEI decreases or the number of environments sampled in the MET increases. The second example integrates the framework into a breeding programme simulation to compare genomic and phenotypic selection strategies over time. Genomic selection outperforms phenotypic selection by ∼ 50-70% in the TPE, depending on the level of GEI. These examples demonstrate how the new framework can be used to generate realistic MET datasets and model plant breeding programmes that better reflect the complexity of real-world settings, making it a valuable tool for optimising a wide range of breeding methodologies.

FieldSimR: an R package for simulating plot data in multi-environment field trials

This paper presents a general framework for simulating plot data in multi-environment field trials with one or more traits. The framework is embedded within the R package FieldSimR, whose core function generates plot errors that capture global field trend, local plot variation, and extraneous variation at a user-defined ratio. FieldSimR's capacity to simulate realistic plot data makes it a flexible and powerful tool for a wide range of improvement processes in plant breeding, such as the optimisation of experimental designs and statistical analyses of multi-environment field trials. FieldSimR provides crucial functionality that is currently missing in other software for simulating plant breeding programmes and is available on CRAN. The paper includes an example simulation of field trials that evaluate 100 maize hybrids for two traits in three environments. To demonstrate FieldSimR's value as an optimisation tool, the simulated data set is then used to compare several popular spatial models for their ability to accurately predict the hybrids' genetic values and reliably estimate the variance parameters of interest. FieldSimR has broader applications to simulating data in other agricultural trials, such as glasshouse experiments.

Two decades of harnessing standing genetic variation for physiological traits to improve drought tolerance in maize

We review approaches to maize breeding for improved drought tolerance during flowering and grain filling in the central and western US corn belt and place our findings in the context of results from public breeding. Here we show that after two decades of dedicated breeding efforts, the rate of crop improvement under drought increased from 6.2 g m-2 year-1 to 7.5 g m-2 year-1, closing the genetic gain gap with respect to the 8.6 g m-2 year-1 observed under water-sufficient conditions. The improvement relative to the long-term genetic gain was possible by harnessing favourable alleles for physiological traits available in the reference population of genotypes. Experimentation in managed stress environments that maximized the genetic correlation with target environments was key for breeders to identify and select for these alleles. We also show that the embedding of physiological understanding within genomic selection methods via crop growth models can hasten genetic gain under drought. We estimate a prediction accuracy differential (Δr) above current prediction approaches of ~30% (Δr=0.11, r=0.38), which increases with increasing complexity of the trait environment system as estimated by Shannon information theory. We propose this framework to inform breeding strategies for drought stress across geographies and crops.

Breeding crops for drought-affected environments and improved climate resilience

Breeding climate-resilient crops with improved levels of abiotic and biotic stress resistance as a response to climate change presents both opportunities and challenges. Applying the framework of the "breeder's equation," which is used to predict the response to selection for a breeding program cycle, we review methodologies and strategies that have been used to successfully breed crops with improved levels of drought resistance, where the target population of environments (TPEs) is a spatially and temporally heterogeneous mixture of drought-affected and favorable (water-sufficient) environments. Long-term improvement of temperate maize for the US corn belt is used as a case study and compared with progress for other crops and geographies. Integration of trait information across scales, from genomes to ecosystems, is needed to accurately predict yield outcomes for genotypes within the current and future TPEs. This will require transdisciplinary teams to explore, identify, and exploit novel opportunities to accelerate breeding program outcomes; both improved germplasm resources and improved products (cultivars, hybrids, clones, and populations) that outperform and replace the products in use by farmers, in combination with modified agronomic management strategies suited to their local environments.

Blib is a multi-module simulation platform for genetics studies and intelligent breeding

Simulation is an efficient approach for the investigation of theoretical and applied issues in population and quantitative genetics, and animal and plant breeding. In this study, we report a multi-module simulation platform called Blib, that is able to handle more complicated genetic effects and models than existing tools. Two derived data types are first defined in Blib, one to hold the required information on genetic models, and the other one to represent the genetics and breeding populations. A number of subroutines are then developed to perform specific tasks. Four case studies are present as examples to show the applications of Blib, i.e., genetic drift of multiple alleles in randomly mating populations, joint effects of neutral mutation and genetic drift, comparison of mass versus family selection, and choice of testers in hybrid breeding. Blib together with its application modules, has great potential to benefit theoretical genetic studies and intelligent breeding by simulating and predicting outcomes in a large number of scenarios, and identifying the best optimum selection and crossing schemes.

Improving drought tolerance in maize: Tools and techniques

Drought is an important constraint to agricultural productivity worldwide and is expected to worsen with climate change. To assist farmers, especially in sub-Saharan Africa (SSA), to adapt to climate change, continuous generation of stress-tolerant and farmer-preferred crop varieties, and their adoption by farmers, is critical to curb food insecurity. Maize is the most widely grown staple crop in SSA and plays a significant role in food security. The aim of this review is to present an overview of a broad range of tools and techniques used to improve drought tolerance in maize. We also present a summary of progress in breeding for maize drought tolerance, while incorporating research findings from disciplines such as physiology, molecular biology, and systems modeling. The review is expected to complement existing knowledge about breeding maize for climate resilience. Collaborative maize drought tolerance breeding projects in SSA emphasize the value of public-private partnerships in increasing access to genomic techniques and useful transgenes. To sustain the impact of maize drought tolerance projects in SSA, there must be complementary efforts to train the next generation of plant breeders and crop scientists.

genomicSimulation: fast R functions for stochastic simulation of breeding programs

Simulation tools are key to designing and optimizing breeding programs that are multiyear, high-effort endeavors. Tools that operate on real genotypes and integrate easily with other analysis software can guide users toward crossing decisions that best balance genetic gains and genetic diversity required to maintain gains in the future. Here, we present genomicSimulation, a fast and flexible tool for the stochastic simulation of crossing and selection based on real genotypes. It is fully written in C for high execution speeds, has minimal dependencies, and is available as an R package for the integration with R’s broad range of analysis and visualization tools. Comparisons of a simulated recreation of a breeding program to a real data set demonstrate the simulated offspring from the tool correctly show key population features, such as genomic relationships and approximate linkage disequilibrium patterns. Both versions of genomicSimulation are freely available on GitHub: The R package version at https://github.com/vllrs/genomicSimulation/ and the C library version at https://github.com/vllrs/genomicSimulationC/.

R. Patiranage D, Johansen K, Schmöckel SM, Bertero D, Oakey H, Colque-Little C, Afzal I, Raubach S, Miller N, Streich J, Amby DB, Emrani N, Warmington M, Mousa MAA, Wu D, Jacobson D, Andreasen C, Jung C, Murphy K, Bazile D, Tester M. Quinoa Phenotyping Methodologies: An International Consensus

Quinoa is a crop originating in the Andes but grown more widely and with the genetic potential for significant further expansion. Due to the phenotypic plasticity of quinoa, varieties need to be assessed across years and multiple locations. To improve comparability among field trials across the globe and to facilitate collaborations, components of the trials need to be kept consistent, including the type and methods of data collected. Here, an internationally open-access framework for phenotyping a wide range of quinoa features is proposed to facilitate the systematic agronomic, physiological and genetic characterization of quinoa for crop adaptation and improvement. Mature plant phenotyping is a central aspect of this paper, including detailed descriptions and the provision of phenotyping cards to facilitate consistency in data collection. High-throughput methods for multi-temporal phenotyping based on remote sensing technologies are described. Tools for higher-throughput post-harvest phenotyping of seeds are presented. A guideline for approaching quinoa field trials including the collection of environmental data and designing layouts with statistical robustness is suggested. To move towards developing resources for quinoa in line with major cereal crops, a database was created. The Quinoa Germinate Platform will serve as a central repository of data for quinoa researchers globally.

Deterministic and stochastic modelling of impacts from genomic selection and phenomics on genetic gain for perennial ryegrass dry matter yield

Increasing the efficiency of current forage breeding programs through adoption of new technologies, such as genomic selection (GS) and phenomics (Ph), is challenging without proof of concept demonstrating cost effective genetic gain (∆G). This paper uses decision support software DeltaGen (tactical tool) and QU-GENE (strategic tool), to model and assess relative efficiency of five breeding methods. The effect on ∆G and cost ($) of integrating GS and Ph into an among half-sib (HS) family phenotypic selection breeding strategy was investigated. Deterministic and stochastic modelling were conducted using mock data sets of 200 and 1000 perennial ryegrass HS families using year-by-season-by-location dry matter (DM) yield data and in silico generated data, respectively. Results demonstrated short (deterministic)- and long-term (stochastic) impacts of breeding strategy and integration of key technologies, GS and Ph, on ∆G. These technologies offer substantial improvements in the rate of ∆G, and in some cases improved cost-efficiency. Applying 1% within HS family GS, predicted a 6.35 and 8.10% ∆G per cycle for DM yield from the 200 HS and 1000 HS, respectively. The application of GS in both among and within HS selection provided a significant boost to total annual ∆G, even at low GS accuracy r_A of 0.12. Despite some reduction in ∆G, using Ph to assess seasonal DM yield clearly demonstrated its impact by reducing cost per percentage ∆G relative to standard DM cuts. Open-source software tools, DeltaGen and QuLinePlus/QU-GENE, offer ways to model the impact of breeding methodology and technology integration under a range of breeding scenarios.

Tackling G × E × M interactions to close on-farm yield-gaps: creating novel pathways for crop improvement by predicting contributions of genetics and management to crop productivity

KEY MESSAGE

Climate change and Genotype-by-Environment-by-Management interactions together challenge our strategies for crop improvement. Research to advance prediction methods for breeding and agronomy is opening new opportunities to tackle these challenges and overcome on-farm crop productivity yield-gaps through design of responsive crop improvement strategies. Genotype-by-Environment-by-Management (G × E × M) interactions underpin many aspects of crop productivity. An important question for crop improvement is "How can breeders and agronomists effectively explore the diverse opportunities within the high dimensionality of the complex G × E × M factorial to achieve sustainable improvements in crop productivity?" Whenever G × E × M interactions make important contributions to attainment of crop productivity, we should consider how to design crop improvement strategies that can explore the potential space of G × E × M possibilities, reveal the interesting Genotype-Management (G-M) technology opportunities for the Target Population of Environments (TPE), and enable the practical exploitation of the associated improved levels of crop productivity under on-farm conditions. Climate change adds additional layers of complexity and uncertainty to this challenge, by introducing directional changes in the environmental dimension of the G × E × M factorial. These directional changes have the potential to create further conditional changes in the contributions of the genetic and management dimensions to future crop productivity. Therefore, in the presence of G × E × M interactions and climate change, the challenge for both breeders and agronomists is to co-design new G-M technologies for a non-stationary TPE. Understanding these conditional changes in crop productivity through the relevant sciences for each dimension, Genotype, Environment, and Management, creates opportunities to predict novel G-M technology combinations suitable to achieve sustainable crop productivity and global food security targets for the likely climate change scenarios. Here we consider critical foundations required for any prediction framework that aims to move us from the current unprepared state of describing G × E × M outcomes to a future responsive state equipped to predict the crop productivity consequences of G-M technology combinations for the range of environmental conditions expected for a complex, non-stationary TPE under the influences of climate change.

Strategies and considerations for implementing genomic selection to improve traits with additive and non-additive genetic architectures in sugarcane breeding

Simulations highlight the potential of genomic selection to substantially increase genetic gain for complex traits in sugarcane. The success rate depends on the trait genetic architecture and the implementation strategy. Genomic selection (GS) has the potential to increase the rate of genetic gain in sugarcane beyond the levels achieved by conventional phenotypic selection (PS). To assess different implementation strategies, we simulated two different GS-based breeding strategies and compared genetic gain and genetic variance over five breeding cycles to standard PS. GS scheme 1 followed similar routines like conventional PS but included three rapid recurrent genomic selection (RRGS) steps. GS scheme 2 also included three RRGS steps but did not include a progeny assessment stage and therefore differed more fundamentally from PS. Under an additive trait model, both simulated GS schemes achieved annual genetic gains of 2.6-2.7% which were 1.9 times higher compared to standard phenotypic selection (1.4%). For a complex non-additive trait model, the expected annual rates of genetic gain were lower for all breeding schemes; however, the rates for the GS schemes (1.5-1.6%) were still greater than PS (1.1%). Investigating cost-benefit ratios with regard to numbers of genotyped clones showed that substantial benefits could be achieved when only 1500 clones were genotyped per 10-year breeding cycle for the additive genetic model. Our results show that under a complex non-additive genetic model, the success rate of GS depends on the implementation strategy, the number of genotyped clones and the stage of the breeding program, likely reflecting how changes in QTL allele frequencies change additive genetic variance and therefore the efficiency of selection. These results are encouraging and motivate further work to facilitate the adoption of GS in sugarcane breeding.

Reinventing quantitative genetics for plant breeding: something old, something new, something borrowed, something BLUE

The goals of quantitative genetics differ according to its field of application. In plant breeding, the main focus of quantitative genetics is on identifying candidates with the best genotypic value for a target population of environments. Keeping quantitative genetics current requires keeping old concepts that remain useful, letting go of what has become archaic, and introducing new concepts and methods that support contemporary breeding. The core concept of continuous variation being due to multiple Mendelian loci remains unchanged. Because the entirety of germplasm available in a breeding program is not in Hardy-Weinberg equilibrium, classical concepts that assume random mating, such as the average effect of an allele and additive variance, need to be retired in plant breeding. Doing so is feasible because with molecular markers, mixed-model approaches that require minimal genetic assumptions can be used for best linear unbiased estimation (BLUE) and prediction. Plant breeding would benefit from borrowing approaches found useful in other disciplines. Examples include reliability as a new measure of the influence of genetic versus nongenetic effects, and operations research and simulation approaches for designing breeding programs. The genetic entities in such simulations should not be generic but should be represented by the pedigrees, marker data, and phenotypic data for the actual germplasm in a breeding program. Over the years, quantitative genetics in plant breeding has become increasingly empirical and computational and less grounded in theory. This trend will continue as the amount and types of data available in a breeding program increase.

Expectation and variance of the estimator of the maximized selection response of linear selection indices with normal distribution

The expectation and variance of the estimator of the maximized index selection response allow the breeders to construct confidence intervals and to complete the analysis of a selection process. The maximized selection response and the correlation of the linear selection index (LSI) with the net genetic merit are the main criterion to compare the efficiency of any LSI. The estimator of the maximized selection response is the square root of the variance of the estimated LSI values multiplied by the selection intensity. The expectation and variance of this estimator allow the breeder to construct confidence intervals and determine the appropriate sample size to complete the analysis of a selection process. Assuming that the estimated LSI values have normal distribution, we obtained those two parameters as follows. First, with the Fourier transform, we found the distribution of the variance of the estimated LSI values, which was a Gamma distribution; therefore, the expectation and variance of this distribution were the expectation and variance of the variance of the estimated LSI values. Second, with these results, we obtained the expectation and the variance of the estimator of the selection response using the Delta method. We validated the theoretical results in the phenotypic selection context using real and simulated dataset. With the simulated dataset, we compared the LSI efficiency when the genotypic covariance matrix is known versus when this matrix is estimated; the differences were not significant. We concluded that our results are valid for any LSI with normal distribution and that the method described in this work is useful for finding the expectation and variance of the estimator of any LSI response in the phenotypic or genomic selection context.

Combined Multistage Linear Genomic Selection Indices To Predict the Net Genetic Merit in Plant Breeding

A combined multistage linear genomic selection index (CMLGSI) is a linear combination of phenotypic and genomic estimated breeding values useful for predicting the individual net genetic merit, which in turn is a linear combination of the true unobservable breeding values of the traits weighted by their respective economic values. The CMLGSI is a cost-saving strategy for improving multiple traits because the breeder does not need to measure all traits at each stage. The optimum (OCMLGSI) and decorrelated (DCMLGSI) indices are the main CMLGSIs. Whereas the OCMLGSI takes into consideration the index correlation values among stages, the DCMLGSI imposes the restriction that the index correlation values among stages be zero. Using real and simulated datasets, we compared the efficiency of both indices in a two-stage context. The criteria we applied to compare the efficiency of both indices were that the total selection response of each index must be lower than or equal to the single-stage combined linear genomic selection index (CLGSI) response and that the correlation of each index with the net genetic merit should be maximum. Using four different total proportions for the real dataset, the estimated total OCMLGSI and DCMLGSI responses explained 97.5% and 90%, respectively, of the estimated single-stage CLGSI selection response. In addition, at stage two, the estimated correlations of the OCMLGSI and the DCMLGSI with the net genetic merit were 0.84 and 0.63, respectively. We found similar results for the simulated datasets. Thus, we recommend using the OCMLGSI when performing multistage selection.

Efficiency of a Constrained Linear Genomic Selection Index To Predict the Net Genetic Merit in Plants

The constrained linear genomic selection index (CLGSI) is a linear combination of genomic estimated breeding values useful for predicting the net genetic merit, which in turn is a linear combination of true unobservable breeding values of the traits weighted by their respective economic values. The CLGSI is the most general genomic index and allows imposing constraints on the expected genetic gain per trait to make some traits change their mean values based on a predetermined level, while the rest of them remain without restrictions. In addition, it includes the unconstrained linear genomic index as a particular case. Using two real datasets and simulated data for seven selection cycles, we compared the theoretical results of the CLGSI with the theoretical results of the constrained linear phenotypic selection index (CLPSI). The criteria used to compare CLGSI vs. CLPSI efficiency were the estimated expected genetic gain per trait values, the selection response, and the interval between selection cycles. The results indicated that because the interval between selection cycles is shorter for the CLGSI than for the CLPSI, CLGSI is more efficient than CLPSI per unit of time, but its efficiency could be lower per selection cycle. Thus, CLGSI is a good option for performing genomic selection when there are genotyped candidates for selection.

Combining Crop Growth Modeling and Statistical Genetic Modeling to Evaluate Phenotyping Strategies

Genomic prediction of complex traits, say yield, benefits from including information on correlated component traits. Statistical criteria to decide which yield components to consider in the prediction model include the heritability of the component traits and their genetic correlation with yield. Not all component traits are easy to measure. Therefore, it may be attractive to include proxies to yield components, where these proxies are measured in (high-throughput) phenotyping platforms during the growing season. Using the Agricultural Production Systems Simulator (APSIM)-wheat cropping systems model, we simulated phenotypes for a wheat diversity panel segregating for a set of physiological parameters regulating phenology, biomass partitioning, and the ability to capture environmental resources. The distribution of the additive quantitative trait locus effects regulating the APSIM physiological parameters approximated the same distribution of quantitative trait locus effects on real phenotypic data for yield and heading date. We use the crop growth model APSIM-wheat to simulate phenotypes in three Australian environments with contrasting water deficit patterns. The APSIM output contained the dynamics of biomass and canopy cover, plus yield at the end of the growing season. Each water deficit pattern triggered different adaptive mechanisms and the impact of component traits differed between drought scenarios. We evaluated multiple phenotyping schedules by adding plot and measurement error to the dynamics of biomass and canopy cover. We used these trait dynamics to fit parametric models and P-splines to extract parameters with a larger heritability than the phenotypes at individual time points. We used those parameters in multi-trait prediction models for final yield. The combined use of crop growth models and multi-trait genomic prediction models provides a procedure to assess the efficiency of phenotyping strategies and compare methods to model trait dynamics. It also allows us to quantify the impact of yield components on yield prediction accuracy even in different environment types. In scenarios with mild or no water stress, yield prediction accuracy benefitted from including biomass and green canopy cover parameters. The advantage of the multi-trait model was smaller for the early-drought scenario, due to the reduced correlation between the secondary and the target trait. Therefore, multi-trait genomic prediction models for yield require scenario-specific correlated traits.

Optimum and Decorrelated Constrained Multistage Linear Phenotypic Selection Indices Theory

Some authors have evaluated the unconstrained optimum and decorrelated multistage linear phenotypic selection indices (OMLPSI and DMLPSI, respectively) theory. We extended this index theory to the constrained multistage linear phenotypic selection index context, where we denoted OMLPSI and DMLPSI as OCMLPSI and DCMLPSI, respectively. The OCMLPSI (DCMLPSI) is the most general multistage index and includes the OMLPSI (DMLPSI) as a particular case. The OCMLPSI (DCMLPSI) predicts the individual net genetic merit at different individual ages and allows imposing constraints on the genetic gains to make some traits change their mean values based on a predetermined level, while the rest of them remain without restrictions. The OCMLPSI takes into consideration the index correlation values among stages, whereas the DCMLPSI imposes the restriction that the index correlation values among stages be null. The criteria to evaluate OCMLPSI efficiency vs. DCMLPSI efficiency were that the total response of each index must be lower than or equal to the single-stage constrained linear phenotypic selection index response and that the expected genetic gain per trait values should be similar to the constraints imposed by the breeder. We used one real and one simulated dataset to validate the efficiency of the indices. The results indicated that OCMLPSI accuracy when predicting the selection response and expected genetic gain per trait was higher than DCMLPSI accuracy when predicting them. Thus, breeders should use the OCMLPSI when making a phenotypic selection.

Technological advances in maize breeding: past, present and future

Maize has for many decades been both one of the most important crops worldwide and one of the primary genetic model organisms. More recently, maize breeding has been impacted by rapid technological advances in sequencing and genotyping technology, transformation including genome editing, doubled haploid technology, parallelled by progress in data sciences and the development of novel breeding approaches utilizing genomic information. Herein, we report on past, current and future developments relevant for maize breeding with regard to (1) genome analysis, (2) germplasm diversity characterization and utilization, (3) manipulation of genetic diversity by transformation and genome editing, (4) inbred line development and hybrid seed production, (5) understanding and prediction of hybrid performance, (6) breeding methodology and (7) synthesis of opportunities and challenges for future maize breeding.

QuLinePlus: extending plant breeding strategy and genetic model simulation to cross-pollinated populations-case studies in forage breeding

Plant breeders are supported by a range of tools that assist them to make decisions about the conduct or design of plant breeding programs. Simulations are a strategic tool that enables the breeder to integrate the multiple components of a breeding program into a number of proposed scenarios that are compared by a range of statistics measuring the efficiency of the proposed systems. A simulation study for the trait growth score compared two major strategies for breeding forage species, among half-sib family selection and among and within half-sib family selection. These scenarios highlighted new features of the QuLine program, now called QuLinePlus, incorporated to enable the software platform to be used to simulate breeding programs for cross-pollinated species. Each strategy was compared across three levels of half-sib family mean heritability (0.1, 0.5, and 0.9), across three sizes of the initial parental population (10, 50, and 100), and across three genetic effects models (fully additive model, a mixture of additive, partial and over dominance model, and a mixture of partial dominance and over dominance model). Among and within half-sib selection performed better than among half-sib selection for all scenarios. The new tools introduced into QuLinePlus should serve to accurately compare among methods and provide direction on how to achieve specific goals in the improvement of plant breeding programs for cross breeding species.

Increased genomic prediction accuracy in wheat breeding using a large Australian panel

KEY MESSAGE

Genomic prediction accuracy within a large panel was found to be substantially higher than that previously observed in smaller populations, and also higher than QTL-based prediction. In recent years, genomic selection for wheat breeding has been widely studied, but this has typically been restricted to population sizes under 1000 individuals. To assess its efficacy in germplasm representative of commercial breeding programmes, we used a panel of 10,375 Australian wheat breeding lines to investigate the accuracy of genomic prediction for grain yield, physical grain quality and other physiological traits. To achieve this, the complete panel was phenotyped in a dedicated field trial and genotyped using a custom AxiomTM Affymetrix SNP array. A high-quality consensus map was also constructed, allowing the linkage disequilibrium present in the germplasm to be investigated. Using the complete SNP array, genomic prediction accuracies were found to be substantially higher than those previously observed in smaller populations and also more accurate compared to prediction approaches using a finite number of selected quantitative trait loci. Multi-trait genetic correlations were also assessed at an additive and residual genetic level, identifying a negative genetic correlation between grain yield and protein as well as a positive genetic correlation between grain size and test weight.

Optimization of Allelic Combinations Controlling Parameters of a Peach Quality Model

Process-based models are effective tools to predict the phenotype of an individual in different growing conditions. Combined with a quantitative trait locus (QTL) mapping approach, it is then possible to predict the behavior of individuals with any combinations of alleles. However the number of simulations to explore the realm of possibilities may become infinite. Therefore, the use of an efficient optimization algorithm to intelligently explore the search space becomes imperative. The optimization algorithm has to solve a multi-objective problem, since the phenotypes of interest are usually a complex of traits, to identify the individuals with best tradeoffs between those traits. In this study we proposed to unroll such a combined approach in the case of peach fruit quality described through three targeted traits, using a process-based model with seven parameters controlled by QTL. We compared a current approach based on the optimization of the values of the parameters with a more evolved way to proceed which consists in the direct optimization of the alleles controlling the parameters. The optimization algorithm has been adapted to deal with both continuous and combinatorial problems. We compared the spaces of parameters obtained with different tactics and the phenotype of the individuals resulting from random simulations and optimization in these spaces. The use of a genetic model enabled the restriction of the dimension of the parameter space toward more feasible combinations of parameter values, reproducing relationships between parameters as observed in a real progeny. The results of this study demonstrated the potential of such an approach to refine the solutions toward more realistic ideotypes. Perspectives of improvement are discussed.

A Genomic Selection Index Applied to Simulated and Real Data

A genomic selection index (GSI) is a linear combination of genomic estimated breeding values that uses genomic markers to predict the net genetic merit and select parents from a nonphenotyped testing population. Some authors have proposed a GSI; however, they have not used simulated or real data to validate the GSI theory and have not explained how to estimate the GSI selection response and the GSI expected genetic gain per selection cycle for the unobserved traits after the first selection cycle to obtain information about the genetic gains in each subsequent selection cycle. In this paper, we develop the theory of a GSI and apply it to two simulated and four real data sets with four traits. Also, we numerically compare its efficiency with that of the phenotypic selection index (PSI) by using the ratio of the GSI response over the PSI response, and the PSI and GSI expected genetic gain per selection cycle for observed and unobserved traits, respectively. In addition, we used the Technow inequality to compare GSI vs. PSI efficiency. Results from the simulated data were confirmed by the real data, indicating that GSI was more efficient than PSI per unit of time.

Using the UK reference population Avalon × Cadenza as a platform to compare breeding strategies in elite Western European bread wheat

Wheat breeders select for qualitative and quantitative traits, the latter often detected as quantitative trait loci (QTL). It is, however, a long procedure from QTL discovery to the successful introduction of favourable alleles into new elite varieties and finally into farmers' crops. As a proof of principle for this process, QTL for grain yield (GY), yield components, plant height (PH), ear emergence (EM), solid stem (SS) and yellow rust resistance (Yr) were identified in segregating UK bread wheat reference population, Avalon × Cadenza. Among the 163 detected QTL were several not reported before: 17 for GY, the major GY QTL on 2D; a major SS QTL on 3B; and Yr6 on 7B. Common QTL were identified on ten chromosomes, most interestingly, grain number (GN) was found to be associated with Rht-D1b; and GY and GN with a potential new allele of Rht8. The interaction of other QTL with GY and yield components was discussed in the context of designing a UK breeding target genotype. Desirable characteristics would be: similar PH and EM to Avalon; Rht-D1b and Vrn-A1b alleles; high TGW and GN; long and wide grains; a large root system, resistance to diseases; and maximum GY. The potential of the identified QTL maximising transgressive segregation to produce a high-yielding and resilient genotype was demonstrated by simulation. Moreover, simulating breeding strategies with F₂ enrichment revealed that the F₂-DH procedure was superior to the RIL and the modified SSD procedure to achieve that genotype. The proposed strategies of parent selection and breeding methodology can be used as guidance for marker-assisted wheat breeding.

Characterizing drought stress and trait influence on maize yield under current and future conditions

Global climate change is predicted to increase temperatures, alter geographical patterns of rainfall and increase the frequency of extreme climatic events. Such changes are likely to alter the timing and magnitude of drought stresses experienced by crops. This study used new developments in the classification of crop water stress to first characterize the typology and frequency of drought-stress patterns experienced by European maize crops and their associated distributions of grain yield, and second determine the influence of the breeding traits anthesis-silking synchrony, maturity and kernel number on yield in different drought-stress scenarios, under current and future climates. Under historical conditions, a low-stress scenario occurred most frequently (ca. 40%), and three other stress types exposing crops to late-season stresses each occurred in ca. 20% of cases. A key revelation shown was that the four patterns will also be the most dominant stress patterns under 2050 conditions. Future frequencies of low drought stress were reduced by ca. 15%, and those of severe water deficit during grain filling increased from 18% to 25%. Despite this, effects of elevated CO2 on crop growth moderated detrimental effects of climate change on yield. Increasing anthesis-silking synchrony had the greatest effect on yield in low drought-stress seasonal patterns, whereas earlier maturity had the greatest effect in crops exposed to severe early-terminal drought stress. Segregating drought-stress patterns into key groups allowed greater insight into the effects of trait perturbation on crop yield under different weather conditions. We demonstrate that for crops exposed to the same drought-stress pattern, trait perturbation under current climates will have a similar impact on yield as that expected in future, even though the frequencies of severe drought stress will increase in future. These results have important ramifications for breeding of maize and have implications for studies examining genetic and physiological crop responses to environmental stresses.

Inheritance of evolved resistance to a novel herbicide (pyroxasulfone)

Agricultural weeds have rapidly adapted to intensive herbicide selection and resistance to herbicides has evolved within ecological timescales. Yet, the genetic basis of broad-spectrum generalist herbicide resistance is largely unknown. This study aims to determine the genetic control of non-target-site herbicide resistance trait(s) that rapidly evolved under recurrent selection of the novel lipid biosynthesis inhibitor pyroxasulfone in Lolium rigidum. The phenotypic segregation of pyroxasulfone resistance in parental, F1 and back-cross (BC) families was assessed in plants exposed to a gradient of pyroxasulfone doses. The inheritance of resistance to chemically dissimilar herbicides (cross-resistance) was also evaluated. Evolved resistance to the novel selective agent (pyroxasulfone) is explained by Mendelian segregation of one semi-dominant allele incrementally herbicide-selected at higher frequency in the progeny. In BC families, cross-resistance is conferred by an incompletely dominant single major locus. This study confirms that herbicide resistance can rapidly evolve to any novel selective herbicide agents by continuous and repeated herbicide use. The results imply that the combination of herbicide options (rotation, mixtures or combinations) to exploit incomplete dominance can provide acceptable control of broad-spectrum generalist resistance-endowing monogenic traits. Herbicide diversity within a set of integrated management tactics can be one important component to reduce the herbicide selection intensity.

Simulated breeding with QU-GENE graphical user interface

Comparing the efficiencies of breeding methods with field experiments is a costly, long-term process. QU-GENE is a highly flexible genetic and breeding simulation platform capable of simulating the performance of a range of different breeding strategies and for a continuum of genetic models ranging from simple to complex. In this chapter we describe some of the basic mechanics behind the QU-GENE user interface and give a simplified example of how it works.

Genotype to phenotype maps: multiple input abiotic signals combine to produce growth effects via attenuating signaling interactions in maize

The complexity of allele interactions constrains crop improvement and the prediction of disease susceptibility. Additive allele effects are the foundation for selection in animal and plant breeding, and complex genetic and environmental interactions contribute to inefficient detection of desirable loci. Manipulation and modeling of other sources of variation, such as environmental variables, have the potential to improve our prediction of phenotype from genotype. As an example of our approach to analysis of the network linking environmental input to alleles, we mapped the genetic architecture of single and combined abiotic stress responses in two maize mapping populations and compared the observed genetic architecture patterns to simple theoretical predictions. Comparisons of single and combined stress effects on growth and biomass traits exhibit patterns of allele effects that suggest attenuating interactions among physiological signaling steps in drought and ultraviolet radiation stress responses. The presence of attenuating interactions implies that shared QTL found in sets of environments could be used to group environment types and identify underlying environmental similarities, and that patterns of stress-dependent genetic architecture should be studied as a way to prioritize prebreeding populations. A better understanding of whole-plant interactor pathways and genetic architecture of multiple-input environmental signaling has the potential to improve the prediction of genomic value in plant breeding and crop modeling.

Post-GWAS: where next? More samples, more SNPs or more biology?

The power of genome-wide association studies (GWAS) rests on several foundations: (i) there is a significant amount of additive genetic variation, (ii) individual causal polymorphisms often have sizable effects and (iii) they segregate at moderate-to-intermediate frequencies, or will be effectively 'tagged' by polymorphisms that do. Each of these assumptions has recently been questioned. (i) Why should genetic variation appear additive given that the underlying molecular networks are highly nonlinear? (ii) A new generation of relatedness-based analyses directs us back to the nearly infinitesimal model for effect sizes that quantitative genetics was long based upon. (iii) Larger effect causal polymorphisms are often low frequency, as selection might lead us to expect. Here, we review these issues and other findings that appear to question many of the foundations of the optimism GWAS prompted. We then present a roadmap emerging as one possible future for quantitative genetics. We argue that in future GWAS should move beyond purely statistical grounds. One promising approach is to build upon the combination of population genetic models and molecular biological knowledge. This combined treatment, however, requires fitting experimental data to models that are very complex, as well as accurate capturing of the uncertainty of resulting inference. This problem can be resolved through Bayesian analysis and tools such as approximate Bayesian computation-a method growing in popularity in population genetic analysis. We show a case example of anterior-posterior segmentation in Drosophila, and argue that similar approaches will be helpful as a GWAS augmentation, in human and agricultural research.

Evolved polygenic herbicide resistance in Lolium rigidum by low-dose herbicide selection within standing genetic variation

The interaction between environment and genetic traits under selection is the basis of evolution. In this study, we have investigated the genetic basis of herbicide resistance in a highly characterized initially herbicide-susceptible Lolium rigidum population recurrently selected with low (below recommended label) doses of the herbicide diclofop-methyl. We report the variability in herbicide resistance levels observed in F₁ families and the segregation of resistance observed in F₂ and back-cross (BC) families. The selected herbicide resistance phenotypic trait(s) appear to be under complex polygenic control. The estimation of the effective minimum number of genes (N_E), depending on the herbicide dose used, reveals at least three resistance genes had been enriched. A joint scaling test indicates that an additive-dominance model best explains gene interactions in parental, F₁, F₂ and BC families. The Mendelian study of six F₂ and two BC segregating families confirmed involvement of more than one resistance gene. Cross-pollinated L. rigidum under selection at low herbicide dose can rapidly evolve polygenic broad-spectrum herbicide resistance by quantitative accumulation of additive genes of small effect. This can be minimized by using herbicides at the recommended dose which causes high mortality acting outside the normal range of phenotypic variation for herbicide susceptibility.

Probability of success of breeding strategies for improving pro-vitamin A content in maize

Biofortification for pro-vitamin A content (pVAC) of modern maize inbreds and hybrids is a feasible way to deal with vitamin A deficiency in rural areas in developing countries. The objective of this study was to evaluate the probability of success of breeding strategies when transferring the high pVAC present in donors to elite modern-adapted lines. For this purpose, a genetic model was built based on previous genetic studies, and different selection schemes including phenotypic selection (PS) and marker-assisted selection (MAS) were simulated and compared. MAS for simultaneously selecting all pVAC genes and a combined scheme for selecting two major pVAC genes by MAS followed by ultra performance liquid chromatography screening for the remaining genetic variation on pVAC were identified as being most effective and cost-efficient. The two schemes have 83.7 and 84.8% probabilities of achieving a predefined breeding target on pVAC and adaptation in one breeding cycle under the current breeding scale. When the breeding scale is increased by making 50% more crosses, the probability values could reach 94.8 and 95.1% for the two schemes. Under fixed resources, larger early generation populations with fewer crosses had similar breeding efficiency to smaller early generation populations with more crosses. Breeding on a larger scale was more efficient both genetically and economically. The approach presented in this study could be used as a general way in quantifying probability of success and comparing different breeding schemes in other breeding programs.

Optimal Design for Marker-assisted Gene Pyramiding in Cross Population

Marker-assisted gene pyramiding aims to produce individuals with superior economic traits according to the optimal breeding scheme which involves selecting a series of favorite target alleles after cross of base populations and pyramiding them into a single genotype. Inspired by the science of evolutionary computation, we used the metaphor of hill-climbing to model the dynamic behavior of gene pyramiding. In consideration of the traditional cross program of animals along with the features of animal segregating populations, four types of cross programs and two types of selection strategies for gene pyramiding are performed from a practical perspective. Two population cross for pyramiding two genes (denoted II), three population cascading cross for pyramiding three genes(denoted III), four population symmetry (denoted IIII-S) and cascading cross for pyramiding four genes (denoted IIII-C), and various schemes (denoted cross program-A–E) are designed for each cross program given different levels of initial favorite allele frequencies, base population sizes and trait heritabilities. The process of gene pyramiding breeding for various schemes are simulated and compared based on the population hamming distance, average superior genotype frequencies and average phenotypic values. By simulation, the results show that the larger base population size and the higher the initial favorite allele frequency the higher the efficiency of gene pyramiding. Parents cross order is shown to be the most important factor in a cascading cross, but has no significant influence on the symmetric cross. The results also show that genotypic selection strategy is superior to phenotypic selection in accelerating gene pyramiding. Moreover, the method and corresponding software was used to compare different cross schemes and selection strategies.

Prediction of flowering time in Brassica oleracea using a quantitative trait loci-based phenology model

Uniformly developing plants with a predictable time to harvest or flowering under unfavourable climate conditions are a major breeding goal in crop species. The main flowering regulators and their response to environmental signals have been identified in Arabidopsis thaliana and homologues of flowering genes have been mapped in many crop species. However, it remains unclear which genes determine within and across genotype flowering time variability in Brassica oleracea and how genetic flowering time regulation is influenced by environmental factors. The goal of this study is model-based prediction of flowering time in a B. oleracea DH-line population using genotype-specific and quantitative trait loci (QTL) model input parameters. A QTL-based phenology model accounting for genotypic differences in temperature responses during vernalisation and non-temperature-sensitive durations from floral transition to flowering was evaluated in two field trials. The model was parameterised using original genotype-specific model input parameters and QTL effects. The genotype-specific model parameterisation showed accurate predictability of flowering time if floral induction was promoted by low temperature (R(2) = 0.81); unfavourably high temperatures reduced predictability (R(2) = 0.65). Replacing original model input parameters by QTL effects reduced the capability of the model to describe across-genotype variability (R(2) = 0.59 and 0.50). Flowering time was highly correlated with a model parameter accounting for vernalisation effects. Within-genotype variability was significantly correlated with the same parameter if temperature during the inductive phase was high. We conclude that flowering time variability across genotypes was largely due to differences in vernalisation response, although it has been shown elsewhere that the candidate FLOWERING LOCUS C (FLC) did not co-segregate with flowering time in the same population. FLC independent vernalisation pathways have been described for several species, but not yet for B. oleracea.

Environment characterization as an aid to wheat improvement: interpreting genotype-environment interactions by modelling water-deficit patterns in North-Eastern Australia

Genotype-environment interactions (GEI) limit genetic gain for complex traits such as tolerance to drought. Characterization of the crop environment is an important step in understanding GEI. A modelling approach is proposed here to characterize broadly (large geographic area, long-term period) and locally (field experiment) drought-related environmental stresses, which enables breeders to analyse their experimental trials with regard to the broad population of environments that they target. Water-deficit patterns experienced by wheat crops were determined for drought-prone north-eastern Australia, using the APSIM crop model to account for the interactions of crops with their environment (e.g. feedback of plant growth on water depletion). Simulations based on more than 100 years of historical climate data were conducted for representative locations, soils, and management systems, for a check cultivar, Hartog. The three main environment types identified differed in their patterns of simulated water stress around flowering and during grain-filling. Over the entire region, the terminal drought-stress pattern was most common (50% of production environments) followed by a flowering stress (24%), although the frequencies of occurrence of the three types varied greatly across regions, years, and management. This environment classification was applied to 16 trials relevant to late stages testing of a breeding programme. The incorporation of the independently-determined environment types in a statistical analysis assisted interpretation of the GEI for yield among the 18 representative genotypes by reducing the relative effect of GEI compared with genotypic variance, and helped to identify opportunities to improve breeding and germplasm-testing strategies for this region.

Dissecting genetic networks underlying complex phenotypes: the theoretical framework

Great progress has been made in genetic dissection of quantitative trait variation during the past two decades, but many studies still reveal only a small fraction of quantitative trait loci (QTLs), and epistasis remains elusive. We integrate contemporary knowledge of signal transduction pathways with principles of quantitative and population genetics to characterize genetic networks underlying complex traits, using a model founded upon one-way functional dependency of downstream genes on upstream regulators (the principle of hierarchy) and mutual functional dependency among related genes (functional genetic units, FGU). Both simulated and real data suggest that complementary epistasis contributes greatly to quantitative trait variation, and obscures the phenotypic effects of many 'downstream' loci in pathways. The mathematical relationships between the main effects and epistatic effects of genes acting at different levels of signaling pathways were established using the quantitative and population genetic parameters. Both loss of function and "co-adapted" gene complexes formed by multiple alleles with differentiated functions (effects) are predicted to be frequent types of allelic diversity at loci that contribute to the genetic variation of complex traits in populations. Downstream FGUs appear to be more vulnerable to loss of function than their upstream regulators, but this vulnerability is apparently compensated by different FGUs of similar functions. Other predictions from the model may account for puzzling results regarding responses to selection, genotype by environment interaction, and the genetic basis of heterosis.

Yield-trait performance landscapes: from theory to application in breeding maize for drought tolerance

The effectiveness of breeding strategies to increase drought resistance in crops could be increased further if some of the complexities in gene-to-phenotype (G → P) relations associated with epistasis, pleiotropy, and genotype-by-environment interactions could be captured in realistic G → P models, and represented in a quantitative manner useful for selection. This paper outlines a promising methodology. First, the concept of landscapes was extended from the study of fitness landscapes used in evolutionary genetics to the characterization of yield-trait-performance landscapes for agricultural environments and applications in plant breeding. Second, the E(NK) model of trait genetic architecture was extended to incorporate biophysical, physiological, and statistical components. Third, a graphical representation is proposed to visualize the yield-trait performance landscape concept for use in selection decisions. The methodology was demonstrated at a particular stage of a maize breeding programme with the objective of improving the drought tolerance of maize hybrids for the US Western Corn-Belt. The application of the framework to the genetic improvement of drought tolerance in maize supported selection of Doubled Haploid (DH) lines with improved levels of drought tolerance based on physiological genetic knowledge, prediction of test-cross yield within the target population of environments, and their predicted potential to sustain further genetic progress with additional cycles of selection. The existence of rugged yield-performance landscapes with multiple peaks and intervening valleys of lower performance, as shown in this study, supports the proposition that phenotyping strategies, and the directions emphasized in genomic selection can be improved by creating knowledge of the topology of yield-trait performance landscapes.

Location of major effect genes in sorghum (Sorghum bicolor (L.) Moench)

Major effect genes are often used for germplasm identification, for diversity analyses and as selection targets in breeding. To date, only a few morphological characters have been mapped as major effect genes across a range of genetic linkage maps based on different types of molecular markers in sorghum (Sorghum bicolor (L.) Moench). This study aims to integrate all available previously mapped major effect genes onto a complete genome map, linked to the whole genome sequence, allowing sorghum breeders and researchers to link this information to QTL studies and to be aware of the consequences of selection for major genes. This provides new opportunities for breeders to take advantage of readily scorable morphological traits and to develop more effective breeding strategies. We also provide examples of the impact of selection for major effect genes on quantitative traits in sorghum. The concepts described in this paper have particular application to breeding programmes in developing countries where molecular markers are expensive or impossible to access.

Flapjack--graphical genotype visualization

Summary: New software tools for graphical genotyping are required that can routinely handle the large data volumes generated by the high-throughput single-nucleotide polymorphism (SNP) platforms, genotyping-by-sequencing and other comparable genotyping technologies. Flapjack has been developed to facilitate analysis of these data, providing real time rendering with rapid navigation and comparisons between lines, markers and chromosomes, with visualization, sorting and querying based on associated data, such as phenotypes, quantitative trait loci or other mappable features.

Availability: Flapjack is freely available for Microsoft Windows, Mac OS X, Linux and Solaris, and can be downloaded from http://bioinf.scri.ac.uk/flapjack

Contact:flapjack@scri.ac.uk

Root growth models: towards a new generation of continuous approaches

Models of root system growth emerged in the early 1970s, and were based on mathematical representations of root length distribution in soil. The last decade has seen the development of more complex architectural models and the use of computer-intensive approaches to study developmental and environmental processes in greater detail. There is a pressing need for predictive technologies that can integrate root system knowledge, scaling from molecular to ensembles of plants. This paper makes the case for more widespread use of simpler models of root systems based on continuous descriptions of their structure. A new theoretical framework is presented that describes the dynamics of root density distributions as a function of individual root developmental parameters such as rates of lateral root initiation, elongation, mortality, and gravitropsm. The simulations resulting from such equations can be performed most efficiently in discretized domains that deform as a result of growth, and that can be used to model the growth of many interacting root systems. The modelling principles described help to bridge the gap between continuum and architectural approaches, and enhance our understanding of the spatial development of root systems. Our simulations suggest that root systems develop in travelling wave patterns of meristems, revealing order in otherwise spatially complex and heterogeneous systems. Such knowledge should assist physiologists and geneticists to appreciate how meristem dynamics contribute to the pattern of growth and functioning of root systems in the field.

Adapting APSIM to model the physiology and genetics of complex adaptive traits in field crops

Progress in molecular plant breeding is limited by the ability to predict plant phenotype based on its genotype, especially for complex adaptive traits. Suitably constructed crop growth and development models have the potential to bridge this predictability gap. A generic cereal crop growth and development model is outlined here. It is designed to exhibit reliable predictive skill at the crop level while also introducing sufficient physiological rigour for complex phenotypic responses to become emergent properties of the model dynamics. The approach quantifies capture and use of radiation, water, and nitrogen within a framework that predicts the realized growth of major organs based on their potential and whether the supply of carbohydrate and nitrogen can satisfy that potential. The model builds on existing approaches within the APSIM software platform. Experiments on diverse genotypes of sorghum that underpin the development and testing of the adapted crop model are detailed. Genotypes differing in height were found to differ in biomass partitioning among organs and a tall hybrid had significantly increased radiation use efficiency: a novel finding in sorghum. Introducing these genetic effects associated with plant height into the model generated emergent simulated phenotypic differences in green leaf area retention during grain filling via effects associated with nitrogen dynamics. The relevance to plant breeding of this capability in complex trait dissection and simulation is discussed.

Simulating the yield impacts of organ-level quantitative trait loci associated with drought response in maize: a "gene-to-phenotype" modeling approach

Under drought, substantial genotype-environment (G x E) interactions impede breeding progress for yield. Identifying genetic controls associated with yield response is confounded by poor genetic correlations across testing environments. Part of this problem is related to our inability to account for the interplay of genetic controls, physiological traits, and environmental conditions throughout the crop cycle. We propose a modeling approach to bridge this "gene-to-phenotype" gap. For maize under drought, we simulated the impact of quantitative trait loci (QTL) controlling two key processes (leaf and silk elongation) that influence crop growth, water use, and grain yield. Substantial G x E interaction for yield was simulated for hypothetical recombinant inbred lines (RILs) across different seasonal patterns of drought. QTL that accelerated leaf elongation caused an increase in crop leaf area and yield in well-watered or preflowering water deficit conditions, but a reduction in yield under terminal stresses (as such "leafy" genotypes prematurely exhausted the water supply). The QTL impact on yield was substantially enhanced by including pleiotropic effects of these QTL on silk elongation and on consequent grain set. The simulations obtained illustrated the difficulty of interpreting the genetic control of yield for genotypes influenced only by the additive effects of QTL associated with leaf and silk growth. The results highlight the potential of integrative simulation modeling for gene-to-phenotype prediction and for exploiting G x E interactions for complex traits such as drought tolerance.

Evolution of glyphosate resistance in a Lolium rigidum population by glyphosate selection at sublethal doses

The majority of the documented cases of field-evolved herbicide-resistant weed biotypes established that single major genes confer glyphosate resistance. However, the contribution of minor genes endowing substantial plant survival at sublethal herbicide doses may be a potential complementary path to herbicide resistance evolution in weed populations under selection. Here, we subjected a number of susceptible individuals of Lolium rigidum to recurrent glyphosate selection to test the potential for sublethal glyphosate doses to additively select for glyphosate resistance. After 3-4 cycles of glyphosate selection in two distinct environments, the progenies of the initially susceptible population were shifted toward glyphosate resistance. The results indicate progressive enrichment of minor gene trait(s) contributing toward plant survival in the glyphosate-selected progenies. After three generations of selection, the estimated LD(50) values were doubled compared with the original population and up to 33% plant survival was obtained in the glyphosate-selected progeny at the recommended glyphosate label rate. This level of resistance probably was the maximum shift achievable with sublethal glyphosate dose selection in this small population. Cross-pollination was a crucial factor enabling the rapid rate of accumulation of minor glyphosate resistance gene trait(s) that are likely to be present at a relatively high frequency in a small susceptible population. The mechanistic basis of the moderate glyphosate resistance level selected by sublethal glyphosate doses remains unknown and warrants future research. Studying the main factors influencing the evolution of resistant weed populations is crucial for understanding, predicting and managing herbicide resistance.

Simultaneous selection of major and minor genes: use of QTL to increase selection efficiency of coleoptile length of wheat (Triticum aestivum L.)

Plant breeders simultaneously select for qualitative traits controlled by one or a small number of major genes, as well as for polygenic traits controlled by multiple genes that may be detected as quantitative trait loci (QTL). In this study, we applied computer simulation to investigate simultaneous selection for alleles at both major and minor gene (as QTL) loci in breeding populations of two wheat parental lines, HM14BS and Sunstate. Loci targeted for selection included six major genes affecting plant height, disease resistance, and grain quality, plus 6 known and 11 "unidentified" QTL affecting coleoptile length (CL). Parental line HM14BS contributed the target alleles at two of the major gene loci, while parental line Sunstate contributed target alleles at four loci. The parents have similar plant height, but HM14BS has a longer coleoptile, a desirable attribute for deep sowing in rainfed environments. Including the wild-type allele at the major reduced-height locus Rht-D1, HM14BS was assumed to have 13 QTL for increased CL, and Sunstate four; these assumptions being derived from mapping studies and empirical data from an actual HM14BS/Sunstate population. Simulation indicated that compared to backcross populations, a single biparental F(1) cross produced the highest frequency of target genotypes (six desired alleles at major genes plus desired QTL alleles for long CL). From 1,000 simulation runs, an average of 2.4 individuals with the target genotype were present in unselected F(1)-derived doubled haploid (DH) or recombinant inbred line (RIL) populations of size 200. A selection scheme for the six major genes increased the number of target individuals to 19.1, and additional marker-assisted selection (MAS) for CL increased the number to 23.0. Phenotypic selection (PS) of CL outperformed MAS in this study due to the high heritability of CL, incompletely linked markers for known QTL, and the existence of unidentified QTL. However, a selection scheme combining MAS and PS was equally as efficient as PS and would result in net savings in production and time to delivery of long coleoptile wheats containing the six favorable alleles.

Modeling QTL for complex traits: detection and context for plant breeding

The genetic architecture of a trait is defined by the set of genes contributing to genetic variation within a reference population of genotypes together with information on their location in the genome and the effects of their alleles on traits, including intra-locus and inter-locus interactions, environmental dependencies, and pleiotropy. Accumulated evidence from trait mapping studies emphasizes that plant breeders work within a trait genetic complexity continuum. Some traits show a relatively simple genetic architecture while others, such as grain yield, have a complex architecture. An important advance is that we now have empirical genetic models of trait genetic architecture obtained from mapping studies (multi-QTL models including various genetic effects that may vary in relation to environmental factors) to ground theoretical investigations on the merits of alternative breeding strategies. Such theoretical studies indicate that as the genetic complexity of traits increases the opportunities for realizing benefits from molecular enhanced breeding strategies increase. To realize these potential benefits and enable the plant breeder to increase rate of genetic gain for complex traits it is anticipated that the empirical genetic models of trait genetic architecture used for predicting trait variation will need to incorporate the effects of genetic interactions and be interpreted within a genotype-environment-management framework for the target agricultural production system.

Investigating the efficiency of the single backcrossing breeding strategy through computer simulation

A strategy combining single backcrossing with selected bulk breeding has been successfully used in wheat improvement at CIMMYT to introgress rust resistant genes from donor parents to elite adapted cultivars. In this research, the efficiency of this breeding strategy was compared to other crossing and selection strategies through computer simulation. Results indicated this breeding strategy has advantages in retaining or improving the adaptation of the recurrent parents, and at the same time transferring most of the desired donor genes in a wide range of scenarios. Two rounds of backcrossing have advantages when the adaptation of donor parents is much poorer than that of the adapted parents, but the advantage of three rounds of backcrossing over two rounds is minimal. We recommend using the single backcrossing breeding strategy (SBBS) when three conditions are met: (1) multiple genes govern the phenotypic traits to be transferred from donor parents to adapted parents, (2) the donor parents have some favorable genes that may contribute to the improvement of adaptation in the recipient parents, and (3) conventional phenotypic selection is being applied, or individual genotypes cannot be precisely identified. We envisage that all three conditions commonly exist in modern breeding programs, and therefore believe that SBBS could be applied widely. However, we do not exclude the use of repeated backcrossing if the transferred genes can be precisely identified by closely linked molecular markers, and the donor parents have extremely poor adaptation.

Identifying target traits and molecular mechanisms for wheat breeding under a changing climate

Global warming is causing changes in temperature at a rate unmatched by any temperature change over the last 50 million years. Crop cultivars have been selected for optimal performance under the current climatic conditions. With global warming, characterized by shifts in weather patterns and increases in frequency and magnitude of extreme weather events, new ideotypes will be required with a different set of physiological traits. Severe pressure has been placed on breeders to produce new crop cultivars for a future, rapidly-changing environment that can only be predicted with a great degree of uncertainty and is not available in the present day for direct experiments or field trials. Mathematical modelling, therefore, in conjunction with crop genetics, represents a powerful tool to assist in the breeding process. In this review, drought and high temperature are considered as key stress factors with a high potential impact on crop yield that are associated with global warming, focusing on their effects on wheat. Modelling techniques are described which can help to quantify future threats to wheat growth under climate change and simple component traits that are amenable to genetic analysis are identified. This approach could be used to support breeding programmes for new wheat cultivars suitable for future environments brought about by the changing climate.

Genomic approaches for designing durum wheat ready for climate change with a focus on drought

Climate change is projected to have a significant impact on temperature and precipitation profiles in the Mediterranean basin. The incidence and severity of drought will become commonplace and this will reduce the productivity of rain-fed crops such as durum wheat. Genetic diversity is the material basis for crop improvement and plant breeding has exploited naturally occurring variation to deliver cultivars with improved resistance to abiotic stresses. The coupling of new genomic tools, technologies, and resources with genetic approaches is essential to underpin wheat breeding through marker-assisted selection and hence mitigate climate change. Improvements in crop performance under abiotic stresses have primarily targeted yield-related traits and it is anticipated that the application of genomic technologies will introduce new target traits for consideration in wheat breeding for resistance to drought. Many traits relating to the plant's response and adaptation to drought are complex and multigenic, and quantitative genetics coupled with genomic technologies have the potential to dissect complex genetic traits and to identify regulatory loci, genes and networks. Full realization of our abilities to manipulate metabolism, transduction pathways, and transcription factors for crop improvement ultimately relies on our basic understanding of the regulation of plant networks at all levels of function.

Application of identified QTL-marker associations in rice quality improvement through a design-breeding approach

A permanent mapping population of rice consisting of 65 non-idealized chromosome segment substitution lines (denoted as CSSL1 to CSSL65) and 82 donor parent chromosome segments (denoted as M1 to M82) was used to identify QTL with additive effects for two rice quality traits, area of chalky endosperm (ACE) and amylose content (AC), by a likelihood ratio test based on stepwise regression. Subsequently, the genetics and breeding simulation tool QuLine was employed to demonstrate the application of the identified QTL in rice quality improvement. When a LOD threshold of 2.0 was used, a total of 16 chromosome segments were associated with QTL for ACE, and a total of 15 segments with QTL for AC in at least one environment. Four target genotypes denoted as DG1 to DG4 were designed based on the identified QTL, and according to low ACE and high AC breeding objectives. Target genotypes DG1 and DG2 can be achieved via a topcross (TC) among the three lines CSSL4, CSSL28, and CSSL49. Results revealed that TC2: (CSSL4 x CSSL49) x CSSL28 and TC3: (CSSL28 x CSSL49) x CSSL4 resulted in higher DG1 frequency in their doubled haploid populations, whereas TC1: (CSSL4 x CSSL28) x CSSL49 resulted in the highest DG2 frequency. Target genotypes DG3 and DG4 can be developed by a double cross among the four lines CSSL4, CSSL28, CSSL49, and CSSL52. In a double cross, the order of parents affects the frequency of target genotype to be selected. Results suggested that the double cross between the two single crosses (CSSL4 x CSSL28) and (CSSL49 x CSSL52) resulted in the highest frequency for DG3 and DG4 genotypes in its derived doubled haploid derivatives. Using an enhancement selection methodology, alternative ways were investigated to increase the target genotype frequency without significantly increasing the total cost of breeding operations.