Can we harness digital technologies and physiology to hasten genetic gain in US maize breeding?

Plant physiology can offer invaluable insights to accelerate genetic gain. However, translating physiological understanding into breeding decisions has been an ongoing and complex endeavor. Here we demonstrate an approach to leverage physiology and genomics to hasten crop improvement. A half-diallel maize (Zea mays) experiment resulting from crossing 9 elite inbreds was conducted at 17 locations in the USA corn belt and 6 locations at managed stress environments between 2017 and 2019 covering a range of water environments from 377 to 760 mm of evapotranspiration and family mean yields from 542 to 1,874 g m-2. Results from analyses of 35 families and 2,367 hybrids using crop growth models linked to whole-genome prediction (CGM-WGP) demonstrated that CGM-WGP offered a predictive accuracy advantage compared to BayesA for untested genotypes evaluated in untested environments (r = 0.43 versus r = 0.27). In contrast to WGP, CGMs can deal effectively with time-dependent interactions between a physiological process and the environment. To facilitate the selection/identification of traits for modeling yield, an algorithmic approach was introduced. The method was able to identify 4 out of 12 candidate traits known to explain yield variation in maize. The estimation of allelic and physiological values for each genotype using the CGM created in silico phenotypes (e.g. root elongation) and physiological hypotheses that could be tested within the breeding program in an iterative manner. Overall, the approach and results suggest a promising future to fully harness digital technologies, gap analysis, and physiological knowledge to hasten genetic gain by improving predictive skill and definition of breeding goals.

Back to the future: implications of genetic complexity for the structure of hybrid breeding programs.

Commercial hybrid breeding operations can be described as decentralized networks of smaller, more or less isolated breeding programs. There is further a tendency for the disproportionate use of successful inbred lines for generating the next generation of recombinants, which has led to a series of significant bottlenecks, particularly in the history of the North American and European maize germplasm. Both the decentralization and the disproportionate contribution of inbred lines reduce effective population size and constrain the accessible genetic space. Under these conditions, long-term response to selection is not expected to be optimal under the classical infinitesimal model of quantitative genetics. In this study, we therefore aim to propose a rationale for the success of large breeding operations in the context of genetic complexity arising from the structure and properties of interactive genetic networks. For this, we use simulations based on the NK model of genetic architecture. We indeed found that constraining genetic space through program decentralization and disproportionate contribution of parental inbred lines, is required to expose additive genetic variation and thus facilitate heritable genetic gains under high levels of genetic complexity. These results introduce new insights into why the historically grown structure of hybrid breeding programs was successful in improving the yield potential of hybrid crops over the last century. We also hope that a renewed appreciation for "why things worked" in the past can guide the adoption of novel technologies and the design of future breeding strategies for navigating biological complexity.

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.

Mixed model approaches for the identification of QTLs within a maize hybrid breeding program.

Two outlines for mixed model based approaches to quantitative trait locus (QTL) mapping in existing maize hybrid selection programs are presented: a restricted maximum likelihood (REML) and a Bayesian Markov Chain Monte Carlo (MCMC) approach. The methods use the in-silico-mapping procedure developed by Parisseaux and Bernardo (2004) as a starting point. The original single-point approach is extended to a multi-point approach that facilitates interval mapping procedures. For computational and conceptual reasons, we partition the full set of relationships from founders to parents of hybrids into two types of relations by defining so-called intermediate founders. QTL effects are defined in terms of those intermediate founders. Marker based identity by descent relationships between intermediate founders define structuring matrices for the QTL effects that change along the genome. The dimension of the vector of QTL effects is reduced by the fact that there are fewer intermediate founders than parents. Furthermore, additional reduction in the number of QTL effects follows from the identification of founder groups by various algorithms. As a result, we obtain a powerful mixed model based statistical framework to identify QTLs in genetic backgrounds relevant to the elite germplasm of a commercial breeding program. The identification of such QTLs will provide the foundation for effective marker assisted and genome wide selection strategies. Analyses of an example data set show that QTLs are primarily identified in different heterotic groups and point to complementation of additive QTL effects as an important factor in hybrid performance.

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.

A mixed-model quantitative trait loci (QTL) analysis for multiple-environment trial data using environmental covariables for QTL-by-environment interactions, with an example in maize.

Complex quantitative traits of plants as measured on collections of genotypes across multiple environments are the outcome of processes that depend in intricate ways on genotype and environment simultaneously. For a better understanding of the genetic architecture of such traits as observed across environments, genotype-by-environment interaction should be modeled with statistical models that use explicit information on genotypes and environments. The modeling approach we propose explains genotype-by-environment interaction by differential quantitative trait locus (QTL) expression in relation to environmental variables. We analyzed grain yield and grain moisture for an experimental data set composed of 976 F(5) maize testcross progenies evaluated across 12 environments in the U.S. corn belt during 1994 and 1995. The strategy we used was based on mixed models and started with a phenotypic analysis of multi-environment data, modeling genotype-by-environment interactions and associated genetic correlations between environments, while taking into account intraenvironmental error structures. The phenotypic mixed models were then extended to QTL models via the incorporation of marker information as genotypic covariables. A majority of the detected QTL showed significant QTL-by-environment interactions (QEI). The QEI were further analyzed by including environmental covariates into the mixed model. Most QEI could be understood as differential QTL expression conditional on longitude or year, both consequences of temperature differences during critical stages of the growth.

Models for navigating biological complexity in breeding improved crop plants.

Progress in breeding higher-yielding crop plants would be greatly accelerated if the phenotypic consequences of making changes to the genetic makeup of an organism could be reliably predicted. Developing a predictive capacity that scales from genotype to phenotype is impeded by biological complexities associated with genetic controls, environmental effects and interactions among plant growth and development processes. Plant modelling can help navigate a path through this complexity. Here we profile modelling approaches for complex traits at gene network, organ and whole plant levels. Each provides a means to link phenotypic consequence to changes in genomic regions via stable associations with model coefficients. A unifying feature of the models is the relatively coarse level of granularity they use to capture system dynamics. Much of the fine detail is not directly required. Robust coarse-grained models might be the tool needed to integrate phenotypic and molecular approaches to plant breeding.

The selective values of alleles in a molecular network model are context dependent.

Classical quantitative genetics has applied linear modeling to the problem of mapping genotypic to phenotypic variation. Much of this theory was developed prior to the availability of molecular biology. The current understanding of the mechanisms of gene expression indicates the importance of nonlinear effects resulting from gene interactions. We provide a bridge between genetics and gene network theories by relating key concepts from quantitative genetics to the parameters, variables, and performance functions of genetic networks. We illustrate this methodology by simulating the genetic switch controlling galactose metabolism in yeast and its response to selection for a population of individuals. Results indicate that genes have heterogeneous contributions to phenotypes and that additive and nonadditive effects are context dependent. Early cycles of selection suggest strong additive effects attributed to some genes. Later cycles suggest the presence of strong context-dependent nonadditive effects that are conditional on the outcomes of earlier selection cycles. A single favorable allele cannot be consistently identified for most loci. These results highlight the complications that can arise with the presence of nonlinear effects associated with genes acting in networks when selection is conducted on a population of individuals segregating for the genes contributing to the network.

On the determination of recombination rates in intermated recombinant inbred populations.

The recurrent intermating of F(2) individuals for some number of generations followed by several generations of inbreeding produces an intermated recombinant inbred (IRI) population. Such populations are currently being developed in the plant-breeding community because linkage associations present in an F(2) population are broken down and a population of fixed inbred lines is also created. The increased levels of recombination enable higher-resolution mapping in IRI populations relative to F(2) populations. Herein we derive relationships, under several limiting assumptions, for determining the expected recombination fraction in IRI populations from the crossover rate per meiosis. These relationships are applicable to situations where the inbreeding component of IRI population development is by either self-fertilization or full-sib mating. Additionally, we show that the derived equations can be solved for the crossover rate per meiosis if the recombination fraction is known for the IRI population. Thus, the observed recombination fraction in any IRI population can be expressed on an F(2) basis. The implications of this work on the expansion of genetic maps in IRI populations and limits for detecting linkage between markers are also considered.

The GP problem: quantifying gene-to-phenotype relationships.

In this paper we refer to the gene-to-phenotype modeling challenge as the GP problem. Integrating information across levels of organization within a genotype-environment system is a major challenge in computational biology. However, resolving the GP problem is a fundamental requirement if we are to understand and predict phenotypes given knowledge of the genome and model dynamic properties of biological systems. Organisms are consequences of this integration, and it is a major property of biological systems that underlies the responses we observe. We discuss the E(NK) model as a framework for investigation of the GP problem and the prediction of system properties at different levels of organization. We apply this quantitative framework to an investigation of the processes involved in genetic improvement of plants for agriculture. In our analysis, N genes determine the genetic variation for a set of traits that are responsible for plant adaptation to E environment-types within a target population of environments. The N genes can interact in epistatic NK gene-networks through the way that they influence plant growth and development processes within a dynamic crop growth model. We use a sorghum crop growth model, available within the APSIM agricultural production systems simulation model, to integrate the gene-environment interactions that occur during growth and development and to predict genotype-to-phenotype relationships for a given E(NK) model. Directional selection is then applied to the population of genotypes, based on their predicted phenotypes, to simulate the dynamic aspects of genetic improvement by a plant-breeding program. The outcomes of the simulated breeding are evaluated across cycles of selection in terms of the changes in allele frequencies for the N genes and the genotypic and phenotypic values of the populations of genotypes.