Quantitative Genetics and Plant Breeding

John W. Dudley    Department of Crop Sciences, University of Illinois, Urbana, Illinois 61801

I INTRODUCTION

The objective of this chapter is to review the relationship between quantitative genetics and plant breeding from a plant breeding perspective. Plant breeding is the science and art of genetic improvement of crop plants. Quantitative genetics is the study of genetic control of traits that show a continuous distribution in segregating generations. Quantitative genetics is concerned with the inheritance of those differences between individuals that are of degree rather than kind, quantitative rather than qualitative (Falconer, 1989). Where do these disciplines intersect? At one extreme, Kempthome (1977) defined plant breeding as applied quantitative genetics. Simmonds (1984) on the other hand, considered biometrical genetics "to have helped to interpret what has already been done and to point questions, especially about the all important matter of response to selection, but to have had little impact on the actual practice of breeding." Baker (1984) provided an intermediate view when he suggested an understanding of quantitative genetic principles is critical to the design of efficient breeding programs. In this review, Baker's viewpoint will be followed. Because many of the most important traits with which breeders work are inherited quantitatively, quantitative genetics must be of concern to breeders.

II HISTORY

A PLANT BREEDING

Plant breeding started with primitive people saving seed to plant in succeeding years. In the process, most of our major crops, such as maize (Zea mays L.), wheat (Triticum aestivum L.), barley (Hordeum vulgare L.), and many others, were domesticated. Although there is a tendency to equate the beginnings of plant breeding with the rediscovery of Mendel's laws, major plant breeding discoveries were made prior to 1900. For example, mass selection for sucrose concentration in the beet root began in 1786 and was continued until 1830. The first beet sugar factory was erected in 1802 (Smith, 1987). Thus, planned, directed plant breeding efforts resulted in a cultivar that allowed development of a new industry 100 years before the rediscovery of Mendel's laws. The basic principles underlying maize breeding, i.e., that inbreeding reduces vigor, cross-breeding increases vigor, hybrids could be produced by detasseling one parent, and that hybridization needed to be done each generation if vigor was to be maintained, were known prior to 1900 (Zirkle, 1952)

With the rediscovery of Mendel's laws, genetic principles began to be applied to plant breeding. Smith (1966) traces the developments from 1901 to 1965, including developments in statistical theory that had important implications for plant breeders. The development of hybrid corn and the principles leading to it have been reviewed extensively (Crabb, 1947; Hayes, 1963; Wallace and Brown, 1956) and will not be reviewed in detail here.

Because most of the traits of economic importance are under quantitative genetic control, quantitative genetics became an important contributor to plant breeding theory.

B QUANTITATIVE GENETICS

Selection for quantitative traits began with the first person to select for productivity of the plants from which seeds were saved for the next generation. However, the origins of quantitative genetics can be traced to Darwin's concept of natural selection (Griffing, 1994). Early statistical concepts, such as regression (Galton, 1889) and use of correlation and multiple regression to describe relationships among relatives (Pearson, 1894), were developed prior to rediscovery of Mendel's laws. Griffing (1994) listed the demonstration of the environmental nature of variation among plants within lines and the genetic nature of variation among lines (Johannsen, 1903, 1909) along with the establishment of the multiple factor hypothesis for inheritance of quantitative traits by the experimental studies of Nilsson-Ehle (1909) and East (1910) as keys to demystification of inheritance of quantitative traits. On the theoretical side, the development of the Hardy-Weinberg equilibrium concept demonstrated a mechanism for maintenance of genetic variability in populations. The study that formed the basis for most of the theoretical quantitative genetics work to follow was that of Fisher (1918), which showed that biometric results (involving correlations among relatives) could be interpreted in terms of Mendelian inheritance. Griffing (1994) traces the history of quantitative genetics in detail. A few additional milestones that he identifies include the work of Cockerham (1954) and Kempthorne (1954) in partitioning epistatic variation and the contributions of Kempthorne (1957) in bringing together and interpreting in a common statistical genetic language the diverse concepts of prominent statistical geneticists.

As areas of plant breeding in which they were important are considered, other important steps in the history of quantitative genetics will be reviewed.

C USE OF QUANTITATIVE GENETICS IN PLANT BREEDING

Quantitative genetic principles apply to almost any area of plant breeding. Breeders recognize the need for more extensive testing for traits of low heritability than for traits of high heritability. They cross good × good, understanding the principle that lines with similar means are likely to differ at fewer loci than dissimilar lines and thus transgressive segregants are more likely to occur. However, the formal use of such quantitative genetic techniques as estimation of genetic variances and prediction of genetic gain is rare in most plant breeding programs. In this review, each of the steps in a plant breeding program will be examined and the utility of quantitative genetic techniques considered. However, before describing the use of these techniques in plant breeding, a brief description of the tools available from quantitative genetics is provided.

III TOOLS OF QUANTITATIVE GENETICS

Because quantitative traits are those for which the effects of genotype and environment cannot be readily distinguished, a major contribution of quantitative genetic theory was to provide methods for separating genetic effects from environmental effects. As a first step, genetic expectations of means and variances were obtained.

A DESCRIPTION OF GENETIC VARIATION

Based on the work of Fisher (1918) and the elaborations by Cockerham (1954) and Kempthorne (1954), procedures for describing genetic variation in a population were developed. These procedures are based on first describing within-locus variation in terms of average effect of substitution of an allele and deviations from that average effect. Variation associated with the average effect of substitution is called additive genetic variance and variance associated with deviations is called dominance genetic variance (see Falconer, 1989, for details). Variance associated with interaction among alleles at different loci is termed epistatic genetic variance and can be subdivided into additive × additive, additive × dominance, and dominance × dominance variance when two loci are involved. When additional loci are involved, higher-order interactions can be described. Genetic variance components can be estimated from covariances between relatives as described by Cockerham (1963).

The general procedure for estimating genetic components of variance is to devise a mating design that will estimate covariances between relatives (such as the covariance of full-sibs or half-sibs). The mating design is then grown in an environmental design. The environmental design includes the choice of environments (usually locations and years) and environmental stresses (such as plant population, irrigation or lack thereof, fertility levels, etc.) as well as the experimental design (such as a randomized complete block, incomplete block, or other type of design). From the appropriate analysis of variance, design components of variance are estimated and equated to covariances between relatives. Estimates of covariances between relatives are then equated to expected genetic variance components and genetic variances are estimated (Cockerham, 1963). Such estimates have limitations. Assumptions usually include linkage equilibrium in the population from which the parents of the mating design were obtained and negligible higher-order epistatic effects. The epistatic effects assumed negligible vary with the mating design, e.g., if only one covariance between relatives, such as half-sibs, is estimated, then all epistatic effects are assumed negligible if the covariance of half-sibs is assumed to be an estimate of a portion of the additive genetic variance.

As will be discussed later, estimates of genetic variance components can be used to predict gain from selection (thus allowing comparisons among breeding methods), determine degree of dominance for genes controlling quantitative traits, and compare heritability of different traits.

B DESCRIPTION OF ENVIRONMENTAL VARIATION

For any plant breeding program to be successful, the environments in which the cultivars being developed are to be grown must be defined. Selection is then concentrated on developing cultivars that can take maximum advantage of that environment. The one factor that dictates...