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.

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.