QUANTITATIVE GENETICSAND PLANT BREEDING

John W Dudley

Department of Crop SciencesUniversity of Illinois

Urbana, Illinois 61801

I. IntroductionII. History

A. Plant BreedingB. Quantitative GeneticsC. Use of Quantitative Genetics in Plant Breeding

III. Tools of Quantitative GeneticsA. Description of Genetic VariationB. Description of Environmental VariationC. Predicted Gain EquationD. Correlated Response EquationE. Multiple Trait Selection IndexF. Molecular Markers

G. Generation Mean AnalysisIV: Application of Quantitative Genetics to Plant Breeding

A. Choice of ParentsB. Selection during InbreedingC. Recurrent SelectionD. Marker-Assisted Selection

v: Future Role of Quantitative Genetics in Plant BreedingReferences

I. INTRODUCTION

The objective of this chapter is to review the relationship between quantitativegenetics and plant breeding from a plant breeding perspective. Plant breeding isthe science and art of genetic improvement of crop plants. Quantitative genetics isthe study of genetic control of traits that show a continuous distribution in segre­gating generations. Quantitative genetics is concerned with the inheritance ofthose differences between individuals that are of degree rather than kind, quanti-

Advances in Agronomy, Volume 59Copyright © 1997 by Academic Press, Inc. All rights of reproduction in any fann reserved.

2 JOHNWDUDLEY

tative rather than qualitative (Falconer, 1989). Where do these disciplines inter­sect? At one extreme, Kempthorne (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 pointquestions, especially about the all important matter of response to selection, but tohave had little impact on the actual practice of breeding." Baker (1984) providedan intermediate view when he suggested an understanding of quantitative geneticprinciples is critical to the design of efficient breeding programs. In this review,Baker's viewpoint will be followed. Because many of the most important traitswith which breeders work are inherited quantitatively, quantitative genetics mustbe of concern to breeders.

II. HISTORY

A. PLANT BREEDING

Plant breeding started with primitive people saving seed to plant in succeedingyears. 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 weremade prior to 1900. For example, mass selection for sucrose concentration in thebeet 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 yearsbefore the rediscovery of Mendel's laws. The basic principles underlying maizebreeding, i.e., that inbreeding reduces vigor, cross-breeding increases vigor, hy­brids could be produced by detasseling one parent, and that hybridization neededto 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 appliedto plant breeding. Smith (1966) traces the developments from 1901 to 1965, in­cluding developments in statistical theory that had important implications for plantbreeders. The development of hybrid com and the principles leading to it have beenreviewed extensively (Crabb, 1947; Hayes, 1963; Wallace and Brown, 1956) andwill 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.

2 JOHNWDUDLEY

tative 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 pointquestions, especially about the all important matter of response to selection, but tohave had little impact on the actual practice of breeding." Baker (1984) providedan intermediate view when he suggested an understanding of quantitative geneticprinciples is critical to the design of efficient breeding programs. In this review,Baker's viewpoint will be followed. Because many of the most important traitswith which breeders work are inherited quantitatively, quantitative genetics mustbe of concern to breeders.

II. HISTORY

A. PLANT BREEDING

Plant breeding started with primitive people saving seed to plant in succeedingyears. 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 weremade prior to 1900. For example, mass selection for sucrose concentration in thebeet 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 yearsbefore the rediscovery of Mendel's laws. The basic principles underlying maizebreeding, i.e., that inbreeding reduces vigor, cross-breeding increases vigor, hy­brids could be produced by detasseling one parent, and that hybridization neededto 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 appliedto plant breeding. Smith (1966) traces the developments from 1901 to 1965, in­cluding developments in statistical theory that had important implications for plantbreeders. The development of hybrid com and the principles leading to it have beenreviewed extensively (Crabb, 1947; Hayes, 1963; Wallace and Brown, 1956) andwill 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.

2 JOHN W DUDLEY

tative 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 pointquestions, especially about the all important matter of response to selection, but tohave had little impact on the actual practice of breeding." Baker (1984) providedan intermediate view when he suggested an understanding of quantitative geneticprinciples is critical to the design of efficient breeding programs. In this review,Baker's viewpoint will be followed. Because many of the most important traitswith which breeders work are inherited quantitatively, quantitative genetics mustbe of concern to breeders.

II. HISTORY

A. PLANT BREEDING

Plant breeding started with primitive people saving seed to plant in succeedingyears. 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 weremade prior to 1900. For example, mass selection for sucrose concentration in thebeet 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 yearsbefore the rediscovery of Mendel's laws. The basic principles underlying maizebreeding, i.e., that inbreeding reduces vigor, cross-breeding increases vigor, hy­brids could be produced by detasseling one parent, and that hybridization neededto 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 appliedto plant breeding. Smith (1966) traces the developments from 1901 to 1965, in­cluding developments in statistical theory that had important implications for plantbreeders. The development of hybrid com and the principles leading to it have beenreviewed extensively (Crabb, 1947; Hayes, 1963; Wallace and Brown, 1956) andwill 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.

QUANTITATIVE GENETICS AND PLANT BREEDING 3

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 relationshipsamong relatives (Pearson, 1894), were developed prior to rediscovery of Mendel'slaws. 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-Weinbergequilibrium concept demonstrated a mechanism for maintenance of genetic vari­ability in populations. The study that formed the basis for most of the theoreticalquantitative genetics work to follow was that of Fisher (1918), which showed thatbiometric results (involving correlations among relatives) could be interpreted interms of Mendelian inheritance. Griffing (1994) traces the history of quantitativegenetics in detail. A few additional milestones that he identifies include the workof Cockerham (1954) and Kempthome (1954) in partitioning epistatic variationand the contributions of Kempthome (1957) in bringing together and interpretingin a common statistical genetic language the diverse concepts of prominent statis­tical geneticists.

As areas of plant breeding in which they were important are considered, otherimportant 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 X good, understanding theprinciple 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. Inthis review, each of the steps in a plant breeding program will be examined and theutility of quantitative genetic techniques considered. However, before describingthe use of these techniques in plant breeding, a brief description of the tools avail­able from quantitative genetics is provided.

4 JOHN W DUDLEY

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 wereobtained.

A. DESCRIPTION OF GENETIC VARIATION

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

The general procedure for estimating genetic components of variance is to de­vise a mating design that will estimate covariances between relatives (such as thecovariance 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 covariancesbetween relatives are then equated to expected genetic variance components and

ogenetic variances are estimated (Cockerham, 1963). Such estimates have limita­tions. Assumptions usually include linkage equilibrium in the population fromwhich the parents of the mating design were obtained and negligible higher-orderepistatic 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-sibsis assumed to be an estimate of a portion of the additive genetic variance.

QUANTITATIVE GENETICS AND PLANT BREEDING 5

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

B. DESCRIPTION OF ENVIRONMENTAL VARIATION

For any plant breeding program to be successful, the environments in which thecultivars 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 extensive, expensive testing of genotypes ina plant breeding program is the existence of genotype-environment interaction(GXE).

Four aspects of GXE need to be considered. First, does GXE exist? Comstockand Moll (1963) described in detail methods of estimating GXE components ofvariance and detecting the existence of GXE. Second, if GXE does exist, are geno­types ranked the same in different environments? If GXE effects are significantbecause of differences in magnitude of differences between genotypes in differentenvironments (non-crossover interaction) rather than differences in ranking ofgenotypes between environments (crossover interactions), then the GXE effectsare of little consequence to the breeder. An extensive discussion of methods ofmeasuring the importance of crossover and non-crossover interaction effects isgiven by Baker (1988). Third, which genotypes respond most favorably to changesin environment? Regression of performance of a genotype on the average perfor­mance of a set of genotypes in an environment (Finlay and Wilkinson, 1963; Eber­hart and Russell, 1966) has been used to identify genotypes that respond favorablyto environments or that do not respond to increased environmental inputs. Detaileddiscussion is found in Lin et al. (1986) and Romagosa and Fox (1993). Fourth,measures of GXE have been used to define geographic regions with similar envi­ronments in order to identify areas in which test sites should be located (Ouyanget aI., 1995). Clustering procedures described by Ouyang et aI., emphasize de­tecting crossover interaction and allow computation of distances between envi­ronments for unbalanced or missing data.

Although the procedures used for dealing with GXE are primarily statistical, thetraits being considered are quantitative and the genetic constitution of the entriesbeing evaluated affects the results. For example, Eberhart and Russell (1969) de­termined single crosses were, on average, less stable than double crosses. How­ever, they found individual single crosses that were as stable as most doublecrosses. The removal of GXE variance from estimates of genetic variance is an in­tegral part of any attempt to estimate genetic variances for prediction of gain fromselection. Choice of environments for such a study is also critical. A symposium

6 JOHN w: DUDLEY

volume edited by Kang (1990) provides a detailed look at the interrelationships ofGXE and plant breeding.

c. PREDICTED GAIN EQUATION

One of the major contributions of quantitative genetics to plant breeding wasthe development of an equation for predicting gain from selection. Griffing (1994)reviews the historical development of the prediction equation beginning with Fish­er's (1918) consideration of the ratios of a}!a~ and a6/a~ as measuring the rela­tive importance of additive genetic and dominance contributions to correlationanalysis. Wright (1921) originated the concept of broad-sense heritability andLush (1935), using Fisher's least squares gene model, partitioned the hereditarycontribution into additive and nonadditive portions. From this work came the con­cept of the ratio of uJ,fu~ as a measure of heritability in the narrow sense. A de­tailed discussion of the estimation of heritability is given by Nyquist (1991).

In its simplest form, the predicted gain equation has been expressed as R =iuJ,fup, which can be recast as R = ihiup, where R is response to selection, i is thestandardized selection differential, and hi is narrow-sense heritability. This ex­pression assumes selection based on phenotype of individuals and recombinationof selected individuals. However, there are a number of factors in plant breedingprograms that complicate this simple expression. Hallauer and Miranda (1988),Empig et al. (1972), and Nyquist (1991) explore these factors in detail. Becauseselection in plant breeding programs is based on progenies and these progeniesvary in the types and proportions of genetic variance expressed, the appropriatetypes of genetic variance to be included in the numerator of the selection equationvary. In addition, the estimate of phenotypic variance to be included in the de­nominator varies with the experimental and environmental designs used. The ba­sis for comparison of results from the prediction equation may also vary. For ex­ample, selection procedures may be compared on either a per year or a per cyclebasis. Finally, the choice of whether recombination is such that selection is basedon both the male and female parents of the next generation or only on one sex willplaya role in progress from selection.

Given the factors mentioned in the preceding paragraph, a generalized predic­tion equation for gain per year can be written as follows (Empig et al., 1972):

R = cis~/yap, (1)

where c is a pollen control factor (t if selection is after pollination, 1 if selectionis prior to pollination, and 2 if selfed progenies are recombined), y is the numberof years per cycle, i is the selection differential expressed as number of a p' s~ isthe appropriate genetic variance for the type of selection being practiced, and up

is the appropriate phenotypic standard deviation for the progenies being evaluat-

QUANTITATIVE GENETICS AND PLANT BREEDING 7

ed in the selection program. If comparisons on a per cycle basis are desired, theny can be set as 1 for all types of selection being compared. This equation is criti­cal for comparing selection procedures. Examples of its use are given by Hallauerand Miranda (1988) and Fehr (1987).

D. CORRELATED RESPONSE EQUATION

When selection is applied by plant breeders, changes are likely to occur, not onlyin the trait for which selection is being practiced but in other traits as well (corre­lated response). The extent of correlated response is a function of the heritabilitiesof the primary and correlated traits, as well as the genetic correlation between thetraits. Falconer (1989) presents the correlated response equation as

CRy = ihJ1IA (Jpy' (2)

where CRy is the correlated response in trait Y when selection is based on trait X,i is the standardized selection differential for X, hx and hy are the square roots ofheritability of traits X and Y, respectively, rA is the additive genetic correlation be­tween X and Yand (Jpy is the appropriate phenotypic standard deviation for Y. Mul­tiplying CRy by ely generalizes the equation to a form corresponding to Eq. (1).Hallauer and Miranda (1988) describe calculation of genetic correlations. Equa­tion (2) becomes important not only in determining the type of correlated responsethat may occur under selection but also in determining effectiveness of indirect se­lection. If rAhX> hy then indirect selection for X will be more effective than di­rect selection for Y, all other factors being equal. If, in addition, selection for X al­lows progress in an environment where Y cannot be measured, as may be true formarker-assisted selection, then additional benefits accrue from indirect selection.

E. MULTIPLE TRAIT SELECTION INDEX

The cultivars arising from plant breeding programs must satisfy a number of cri­teria to be useful. For example, a high yielding cultivar susceptible to a prevalentdisease would be of little use to a grower. Thus, plant breeders must select for anumber of traits. Three general procedures-tandem selection, independentculling levels, and index selection-have been used to approach the question ofsimultaneous improvement of a population for multiple traits (Falconer, 1989). Anumber of forms of the equation for gain from index selection for multiple traitsare available. Smith (1936) was the first to present the concept of index selection.Smith presented an index of the form:

1= b1X1 + b2X2 + ... bmXm,

8 JOHN W DUDLEY

where I is an index of merit of an individual and b I ... bm are weights assigned tophenotypic trait measurements represented as XI ... Xm . The b values are the prod­uct of the inverse of the phenotypic variance-covariance matrix, the genotypicvariance-covariance matrix, and a vector of economic weights. A number of vari­ations of this index, most changing the manner of computing the b values, havebeen developed. These include the base index of Williams (1962), the desired gainindex of Pesek and Baker (1969), and retrospective indexes proposed by Johnsonet al. (1988) and Bernardo (1991). The emphasis in the retrospective index devel­opments is on quantifying the knowledge experienced breeders have obtained. Al­though breeders may not use a formal selection index in making selections, everybreeder either consciously or unconsciously assigns weights to different traitswhen making selections.

F. MOLECULAR MARKERS

Although molecular markers are not a direct product of quantitative genetics,the explosion of interest in their use in plants is in large part because of the impli­cations they have for helping solve problems that are common to quantitative ge­netics and plant breeding. The use of markers as a potential aid in selection datesback to Sax (1923) who found seed color related to seed size in beans. Stuber andEdwards (1986) pioneered the use of molecular markers in plant breeding withwork based on isozymes. Stuber (1992) reviewed this work. The use of markersfor selection in plant breeding programs is the application of a form of indirect se­lection. The use of markers to manipulate genes was reviewed in detail by Dudley(1993). Lee (1995) gave a comprehensive review of use of molecular markers inplant breeding. The availability of molecular markers provides an additional di­mension to the use of quantitative genetics in plant breeding. Potential applica­tions of molecular markers include marker-assisted selection, identification of thenumber of genes controlling quantitative traits, grouping germ plasm into relatedgroups, selection of parents, and marker-assisted backcrossing.

G. GENERATION MEAN ANALYSIS

The broad area of generation mean analysis is summarized by Mather and Jinks(1982). In essence, the procedure expresses the means of generations derived fromthe cross between homozygous lines in genetic terms. The generation means arethen analyzed to estimate additive, dominance, and epistatic effects. The referencepopulation is either the F2 mean or the mean of homozygous lines resulting fromselfing the F2 • Procedures for estimating the number of effective factors affectinga particular trait in the cross being studied are provided. One of the major limita-

QUANTITATIVE GENETICS AND PLANT BREEDING 9

tions of the procedure is the assumption that, for the trait being studied, one par­ent contains all the favorable alleles and the other all the unfavorable alleles at seg­regating loci. The procedure has found a great deal of use in studying genetics ofdisease resistance (Campbell and White, 1995; Carson and Hooker, 1981; Moll etai., 1963). An advantage cited by those using it is that the progenies used to de­termine segregation for single genes can also be used for generation mean analy­sis. In addition, means are less variable than variances.

IV. APPLICATION OF QUANTITATIVE GENETICSTO PLANT BREEDING

Plant breeding consists of selection of parents, crossing those parents to creategenetic variability, selection of elite types, and synthesis of a stable cultivar fromthe elite selections. Quantitative genetic principles playa role at each of thesestages. In this section, the role of quantitative genetics in each of these stages ofthe plant breeding process is considered.

A. CHOICE OF PARENTS

The choice of parental germ plasm with which to begin a breeding program isthe most important decision a breeder makes. However, it is only relatively re­cently that quantitative genetic theory has been applied to this question.

1. Self-Pollinated Crops

Discussion of choice of parents in self-pollinated crops will be in the context ofselecting parents from which selfed lines will be derived using a pedigree system,single-seed descent, or some other method of deriving inbreds. In self-pollinatedspecies, these lines usually are evaluated for their per se performance. In cross­pollinated species, in which hybrids are the end product, similar breeding proce­dures are used with the exception that the end product will be a hybrid. Thus, thecriterion for selection is combining ability of some form rather than line per se per­formance.

The objective when choosing parents is to maximize the probability of gener­ating new lines that will perform better than the best pure line currently in use. Theparents chosen should generate a population for selection that will meet the crite­rion of usefulness described by Schnell (1983) as discussed in Lamkey .et ai.(1995). Usefulness of a segregating population was described by Schnell as themean of the upper a% of the distribution expected from the population. Mathe-

QUANTITATIVE GENETICS AND PLANT BREEDING 9

tions of the procedure is the assumption that, for the trait being studied, one par­ent contains all the favorable alleles and the other all the unfavorable alleles at seg­regating loci. The procedure has found a great deal of use in studying genetics ofdisease resistance (Campbell and White, 1995; Carson and Hooker, 1981; Moll etaI., 1963). An advantage cited by those using it is that the progenies used to de­termine segregation for single genes can also be used for generation mean analy­sis. In addition, means are less variable than variances.

IV. APPLICATION OF QUANTITATIVE GENETICSTO PLANT BREEDING

Plant breeding consists of selection of parents, crossing those parents to creategenetic variability, selection of elite types, and synthesis of a stable cultivar fromthe elite selections. Quantitative genetic principles play a role at each of thesestages. In this section, the role of quantitative genetics in each of these stages ofthe plant breeding process is considered.

A. CHOICE OF PARENTS

The choice of parental germ plasm with which to begin a breeding program isthe most important decision a breeder makes. However, it is only relatively re­cently that quantitative genetic theory has been applied to this question.

1. Self-Pollinated Crops

Discussion of choice of parents in self-pollinated crops will be in the context ofselecting parents from which selfed lines will be derived using a pedigree system,single-seed descent, or some other method of deriving inbreds. In self-pollinatedspecies, these lines usually are evaluated for their per se performance. In cross­pollinated species, in which hybrids are the end product, similar breeding proce­dures are used with the exception that the end product will be a hybrid. Thus, thecriterion for selection is combining ability of some form rather than line per se per­formance.

The objective when choosing parents is to maximize the probability of gener­ating new lines that will perform better than the best pure line currently in use. Theparents chosen should generate a population for selection that will meet the crite­rion of usefulness described by Schnell (1983) as discussed in Lamkey et aI.(1995). Usefulness of a segregating population was described by Schnell as themean of the upper a% of the distribution expected from the population. Mathe-

10 JOHN w: DUDLEY

matically, U(a) = Y ± LlG(a), where U(a) is usefulness, Yis the mean of the un­selected population, and LlG(a) is gain from selection. This statistic takes into ac­count both the mean and the genetic variability, thus emphasizing a basic axiomin plant breeding: Both a high mean and adequate genetic variability are neededto produce a superior cultivar.

Another basic principle ofplant breeding is to cross good x good to obtain some­thing better. The quantitative genetic basis for this axiom was demonstrated byBailey and Comstock (1976). Theirresults demonstrated, based on probability the­ory and computer simulation results, the importance of each parent contributingfavorable alleles from nearly equal numbers of loci that are segregating in thecross. Their results can be illustrated by considering 60 loci segregating in an F2 .

With no selection, the probability of a line having >39 loci fixed at homozygositywould be 0.0067, whereas the probability of a line having greater than 30 loci fixedwould be 0.4487. Thus, if each parent line contributed favorable alleles at 30 loci,the probability of obtaining a line with a higher number of loci fixed with favor­able alleles than the better parent would be relatively large. However, if one par­ent contributed favorable alleles at 40 loci and the other at only 20, the probabili­ty of obtaining a new line better than the better parent would be small.

Dudley (1982) suggested backcrossing one or more times to the superior parentif one parent was much superior to the other. The number of backcrosses needed de­pended on the relative number of favorable alleles coming from each parent-thegreater the divergence between parents, the more backcrossing would be needed.

Given the criteria of a high mean and relatively high genetic variance, what toolsare available to a breeder to identify parents that will provide segregating genera­tions with these characteristics? Baker (1984) reviewed this question in light of apaper by Busch et al. (1974) who evaluated F4 and Fs bulk populations, randomF2-derived Fs and F6 lines, and midparent values as predictors of cross perfor­mance. Baker suggests any of these methods should be useful predictors of themean performance of lines from an F2 with the caution that midparent values mightbe the weakest of the methods. Toledo (1992) found use of the midparent valueand the inverse of Malecot's coefficient of parentage to be effective in selectingcrosses that would produce superior lines in soybeans (Glycine max L., Merrill).Panter and Allen (1995) suggested using best linear unbiased prediction (BLUP)methods to predict the midparent value of soybean crosses. BLUP methods takeinto consideration the performance of lines related to the line for which perfor­mance is being predicted. They concluded BLUP had advantages over leastsquares estimates of midparent values. They found a correlation of - 0.47 betweencoefficient of parentage and genetic variance in progeny. Based on these results,they suggested that an effective method of choosing parents would be to identifypairs of lines with high midparent values estimated from BLUP and to selectamong such pairs those which were the most genetically diverse based on the ge-

QUANTITATIVE GENETICS AND PLANT BREEDING 11

netic relationship matrix. Their suggestion is supported by the results of Toledo(1992). With the availability of genetic markers, degree of relationship betweenlines can be established from molecular marker data (Lee, 1995). This provides analternative method of determining relatedness when pedigree information is un­available or of uncertain accuracy.

2. Cross-Pollinated Crops (Hybrid Cultivars)

For development of hybrid cultivars, there are two aspects to the choice ofparents: (i) choice of parents to cross to form base populations for selfing, and(ii) choice of parents to form a cultivar for use by farmers. These two aspects willbe addressed separately.

a. Choice of Parents to Form Base PopulationsConceptually, the problem of developing improved inbreds for use in hybrids is

one of adding favorable alleles from a donor source to an elite inbred without ma­terially reducing the frequency of favorable alleles already present in the elite in­bred (Dudley, 1982). The basic question in choosing parents is identification ofthose lines or populations that contain favorable alleles not present in a hybrid be­ing improved. Dudley (1984a) framed the following questions relative to choiceof parents for a hybrid com breeding program: Which hybrid should be improved?Which lines should be chosen as donors to improve the target hybrid? Which par­ent of the target hybrid should be improved? Should selfing begin in the F2 orshould backcrossing be used prior to selfing?

Procedures for answering these questions were developed based on the conceptof classes ofloci. This concept was first explored in Dudley (1982). The basic con­cept assumes that for any pair of lines the loci at which the lines differ for a giventrait can be divided into two classes: those loci for which PI contains favorable al­leles and P2 does not and those for which P2 contains favorable alleles and PI doesnot. When a donor inbred is considered, eight classes of loci exist as illustrated inTable 1. Of critical interest is the class of loci for which the donor contains favor­able alleles and both parents of the target hybrid have unfavorable alleles. Usingthis concept, methods of identifying donors with the greatest numbers of such lociwere devised for cases in which the donor was an inbred or a population (Dudley,1984b,c, 1987a,b). Modifications of these methods were proposed by Gerloff andSmith (1988), Bernardo (1990a,b), and Metz (1994). Evidence for their effective­ness in selecting superior parents and identifying heterotic relationships was pre­sented by Dudley (1988), Misevic (1989), Zanoni and Dudley (1989), Pfarr andLamkey (1992), and Hogan and Dudley (1991). These methods are beginning tobe used in commercial breeding programs in com and sorghum [Sorghum bicolor(L.) Moench].

QUANTITATIVE GENETICS AND PLANT BREEDING 11

netic relationship matrix. Their suggestion is supported by the results of Toledo(1992). With the availability of genetic markers, degree of relationship betweenlines can be established from molecular marker data (Lee, 1995). This provides analternative method of determining relatedness when pedigree information is un­available or of uncertain accuracy.

2. Cross-Pollinated Crops (Hybrid Cultivars)

For development of hybrid cultivars, there are two aspects to the choice ofparents: (i) choice of parents to cross to form base populations for selfing, and(ii) choice of parents to form a cultivar for use by farmers. These two aspects willbe addressed separately.

a. Choice of Parents to Form Base PopulationsConceptually, the problem of developing improved inbreds for use in hybrids is

one of adding favorable alleles from a donor source to an elite inbred without ma­terially reducing the frequency of favorable alleles already present in the elite in­bred (Dudley, 1982). The basic question in choosing parents is identification ofthose lines or populations that contain favorable alleles not present in a hybrid be­ing improved. Dudley (1984a) framed the following questions relative to choiceof parents for a hybrid com breeding program: Which hybrid should be improved?Which lines should be chosen as donors to improve the target hybrid? Which par­ent of the target hybrid should be improved? Should selfing begin in the F2 orshould backcrossing be used prior to selfing?

Procedures for answering these questions were developed based on the conceptof classes ofloci. This concept was first explored in Dudley (1982). The basic con­cept assumes that for any pair of lines the loci at which the lines differ for a giventrait can be divided into two classes: those loci for which PI contains favorable al­leles and P2 does not and those for which P2 contains favorable alleles and PI doesnot. When a donor inbred is considered, eight classes of loci exist as illustrated inTable 1. Of critical interest is the class of loci for which the donor contains favor­able alleles and both parents of the target hybrid have unfavorable alleles. Usingthis concept, methods of identifying donors with the greatest numbers of such lociwere devised for cases in which the donor was an inbred or a population (Dudley,1984b,c, 1987a,b). Modifications of these methods were proposed by Gerloff andSmith (1988), Bernardo (1990a,b), and Metz (1994). Evidence for their effective­ness in selecting superior parents and identifying heterotic relationships was pre­sented by Dudley (1988), Misevic (1989), Zanoni and Dudley (1989), Pfarr andLamkey (1992), and Hogan and Dudley (1991). These methods are beginning tobe used in commercial breeding programs in com and sorghum [Sorghum bicolor(L.) Moench].

12 JOHN W DUDLEY

Table I

Genotypes for the Classes of Loci Possible forthe Parents of a Hybrid to Improve (PI and P2)

and a Donor Inbred (Py).

Genotypesa for

Class of loci PI Pz Py

A ++ ++ ++B ++ ++C ++ ++D ++E ++ ++F ++G ++H

a + +, The line is homozygous for the dominant fa­vorable allele; - -, homozygous for the recessive unfa­vorable allele.

b. Choice of Parents of a Hybrid CultivarChoice of parents to produce a cultivar directly is usually the result of extensive

testing of a number of combinations of potential parents. One of the major prob­lems facing breeders is reducing the number of possible hybrids to be tested to areasonable number. In general, breeders work with heterotic groups and crosseslikely to be successful as cultivars are usually between inbreds from different het­erotic groups (Hallauer et ai., 1988). However, even if breeding is restricted to twoheterotic groups, thousands of potential hybrids are possible.

Bernardo (1994) proposed applying BLUP to this problem. In this procedure,information on hybrid performance of a subset of lines is combined with infor­mation on genetic relationship between the lines tested and an untested set of linesto predict the performance of untested hybrids. This procedure has been widelyused in dairy cattle breeding (Henderson, 1988). Bernardo (1994), using a limitednumber of hybrids, found correlations between observed and predicted perfor­mance ranging from 0.65 to 0.80. He compared RFLP-based estimates of rela­tionship with pedigree-based estimates and found higher correlations for theRFLP-based estimates. In a study (Bernardo, 1996) involving 600 inbreds and4099 tested single crosses, correlations between predicted and observed yieldsranged from 0.426 to 0.762. Bernardo concluded BLUP was useful for routineidentification of single crosses prior to testing.

--QUANTITATIVE GENETICS AND PLANT BREEDING 13

3. Cross-Pollinated Crops (Synthetic Cultivars)

The mean of a synthetic is a function of the mean of all possible crosses amongparents and inbreeding depression (Hallauer and Miranda, 1988). Predicted meanof a synthetic is given by Wright's equation Y2 = y\ - (Y\ - Yo)/n, where Y2 isthe predicted mean of the synthetic, Y\ is the average performance of all possiblesingle crosses among the parents, and Yo is the mean of the parental inbreds usedto produce the synthetic. A general formula for predicting yield of synthetics thatconsidered the frequency of selfing, the number of parents, the coefficient ofparentage of the parents, and ploidy level was given by Busbice (1970).

4. Role ofMolecular Marker Technology

Use of molecular markers to determine relationships among potential parentshas been proposed in a number of species (see Lee, 1995, for a review). Such in­formation is useful for assigning inbreds to heterotic groups in hybrid breedingprograms (Mumm and Dudley, 1994). Marker-based relationships could also besubstituted for pedigree-based relationships using the methods proposed by Pan­ter and Allen (1995) and Toledo (1992) for predicting genetic variability in cross­es between homozygous lines. Bernardo (1994) suggested using genetic relation­ships based on molecular marker information and BLUP methodology to predictperformance of untested hybrids.

B. SELECTION DURING INBREEDING

Comstock (1978) suggested that development of a theoretical basis for com­paring breeding methods was one of the most significant contributions of quanti­tative genetics to maize breeding. Baker (1984) suggested this statement could beextended to all economically important crops. Because breeding procedures aresimilar for both self- and cross-pollinated crops, discussion of application of quan­titative genetics to selection procedures will be divided into selection during in­breeding and recurrent selection procedures. As Hallauer et ai. (1988) point out,the methods used to select during inbreeding and recurrent selection proceduresare complementary parts of a breeding program. In fact, becauseone result of se­lection during inbreeding is the development of improved lines that are thencrossed and another round of selection carried out, selection during inbreeding isone form of recurrent selection.

Two major questions exist relative to selection during inbreeding. First, howshould resources be divided between number of crosses to be evaluated and num­ber of plants or lines to sample per cross? Second, at what stage in the inbreeding

14 JOHN W DUDLEY

process should replicated testing for yield and other traits of low heritabilitybegin?

Baker (1984) considered application of quantitative genetics to the question ofthe optimum allocation of resources to selection among crosses versus selectionwithin crosses. Optimum allocation of resources was a function of among andwithin cross heritabilities and additive genetic variances. With a fixed number ofplots, the optimum proportion of lines/cross to crosses varied with heritability. Al­though the equations presented by Baker provided insights into the problem of al­location of resources, he concluded there was a lack of objective criteria for de­termining the appropriate number of crosses to evaluate.

The appropriate selfing generation in which to begin testing for yield is a majorquestion in any breeding program from which inbreds are to be produced. Inspecies in which cultivars are inbreds, testing is for line per se performance. Inspecies in which hybrids are to be produced, testing is for combining ability. Thetwo cases will be considered separately.

1. Line per se Performance

As inbreeding progresses, variability among lines increases and variabilitywithin lines decreases (Hallauer and Miranda, 1988). This is a basic principle ofquantitative genetics. An application of this principle to breeding of self-pollinat­ed crops that had major impact was development of the modified pedigree (single­seed descent) method. This procedure was proposed by Goulden (1941) and its ad­vantages in quantitative genetic terms were detailed by Brim (1966). Brim notedmost genetic variance in soybeans was additive. Thus, means did not change dur­ing selfing generations. Furthermore, variance among lines increased with in­breeding and an advantage in terms of gain from selection almost always occurredwhen selection was delayed to at least the F3 and often to the F4 . The advantagewas particularly apparent when selfing generations could be advanced rapidly inthe off-season. The extent of use of single-seed descent or a modification thereofvaries with the species. In soybean [Glycine max (L.) Merrill], single-seed descentprocedures are used extensively (Fehr, 1987), but less extensive use has been madein winter wheat (Allan, 1987).

A breeding method related to the single-seed descent method is the use of dou­bled haploids. In this procedure, homozygous lines are produced by doubling hap­loid plants arising from gametes, thus reducing the time required to obtain homozy­gous lines. Choo et al. (1985) cite empirical results indicating similar efficiencies forthe two methods. The most extensive use of this procedure has been in barley. Workon doubled haploids in maize was discussed by Chase (1974). Both single-seed de­scent and doubled haploid procedures assume that gains from early generation test­ing are offset by the increased gain from selection among homozygous lines and thereduced time necessary to obtain homozygous lines using these procedures.

14 JOHN W DUDLEY

process should replicated testing for yield and other traits of low heritabilitybegin?

Baker (1984) considered application of quantitative genetics to the question ofthe optimum allocation of resources to selection among crosses versus selectionwithin crosses. Optimum allocation of resources was a function of among andwithin cross heritabilities and additive genetic variances. With a fixed number ofplots, the optimum proportion of lines/cross to crosses varied with heritability. Al­though the equations presented by Baker provided insights into the problem of al­location of resources, he concluded there was a lack of objective criteria for de­tennining the appropriate number of crosses to evaluate.

The appropriate selfing generation in which to begin testing for yield is a majorquestion in any breeding program from which inbreds are to be produced. Inspecies in which cultivars are inbreds, testing is for line per se perfonnance. Inspecies in which hybrids are to be produced, testing is for combining ability. Thetwo cases will be considered separately.

1. Line per se Perfonnance

As inbreeding progresses, variability among lines increases and variabilitywithin lines decreases (Hallauer and Miranda, 1988). This is a basic principle ofquantitative genetics. An application of this principle to breeding of self-pollinat­ed crops that had major impact was development of the modified pedigree (single­seed descent) method. This procedure was proposed by Goulden (1941) and its ad­vantages in quantitative genetic terms were detailed by Brim (1966). Brim notedmost genetic variance in soybeans was additive. Thus, means did not change dur­ing selfing generations. Furthermore, variance among lines increased with in­breeding and an advantage in tenns of gain from selection almost always occurredwhen selection was delayed to at least the F3 and often to the F4 . The advantagewas particularly apparent when selfing generations could be advanced rapidly inthe off-season. The extent of use of single-seed descent or a modification thereofvaries with the species. In soybean [Glycine max (L.) Merrill], single-seed descentprocedures are used extensively (Fehr, 1987), but less extensive use has been madein winter wheat (Allan, 1987).

A breeding method related to the single-seed descent method is the use of dou­bled haploids. In this procedure, homozygous lines are produced by doubling hap­loid plants arising from gametes, thus reducing the time required to obtain homozy­gous lines. Choo et al. (1985) cite empirical results indicating similar efficiencies forthe two methods. The most extensive use of this procedure has been in barley. Workon doubled haploids in maize was discussed by Chase (1974). Both single-seed de­scent and doubled haploid procedures assume that gains from early generation test­ing are offset by the increased gain from selection among homozygous lines and thereduced time necessary to obtain homozygous lines using these procedures.

QUANTITATIVE GENETICS AND PLANT BREEDING 15

2. Combining Ability

Early in the development of hybrid com, the importance of testing for combin­ing ability was recognized. The correlations between inbred traits and hybrid per­formance were generally low and not predictive of hybrid performance (Hallaueret ai., 1988). Thus, some method of measuring the value of lines in hybrid com­bination was needed. Smith (1986) presented the theoretical basis for the correla­tion between testcross and per se performance. His computer simulation resultssuggested that for traits conditioned by a large number of genes showing completedominance, correlations between line per se performance and testcross perfor­mance are expected to be less than 0.5.

Two major decisions, which can be approached from a quantitative genetics per­spective, exist. First, what tester should be used? Second, when should testing be­gin? The principles related to the second question are the same as those for earlygeneration testing when the objective is a pure line. That is, as inbreeding advancestestcross variation increases among lines and decreases within lines.

a. Choice of TesterA major step in evaluating the type of tester to be used was the development of

the concept of general and specific combining ability (Sprague and Tatum, 1942).This work supported use of a broadbase tester for preliminary screening for gen­eral combining ability, followed by testing in specific combinations. One methodof evaluating for specific combining ability was use of a diallel cross. Griffing(1994) reviews the development of the analysis of the diallel cross. Griffing (1956)provided clear statements of methods of analysis of diallel crosses in terms of gen­eral and specific combining ability and the circumstances in which each methodof analysis should be used. Hallauer and Miranda (1988) review the use of dial­leIs in com breeding.

The choice of a tester to use in a hybrid breeding program is dictated by the ob­jectives of the program and the type of gene action controlling the traits of inter­est. If the objective is to improve population per se performance, then the testershould be one that has a low frequency of favorable alleles at the loci for whichthe population needs improvement. If additive gene action is of primary impor­tance, then any tester will be effective. However, if dominance, partial dominance,or overdominance are important the tester should be one that has a high frequen­cy of recessive alleles at loci for which improvement is needed. Mathematically,this can be seen from the expression for genetic variance among testcross meansfor a single locus presented by Homer et ai. (1969):

(J"T~ = O.5pq(1 + F)[a + d(Q - p)F (3)

where p and q are frequencies of favorable and unfavorable alleles, respectively,in the population of lines being tested, F is the inbreeding coefficient of the lines

QUA...1\JTITATIVE GENETICS AND PLANT BREEDING 15

2. Combining Ability

Early in the development of hybrid com, the importance of testing for combin­ing ability was recognized. The correlations between inbred traits and hybrid per­formance were generally low and not predictive of hybrid performance (Hallaueret ai., 1988). Thus, some method of measuring the value of lines in hybrid com­bination was needed. Smith (1986) presented the theoretical basis for the correla­tion between testcross and per se performance. His computer simulation resultssuggested that for traits conditioned by a large number ofgenes showing completedominance, correlations between line per se performance and testcross perfor­mance are expected to be less than 0.5.

Two major decisions, which can be approached from a quantitative genetics per­spective, exist. First, what tester should be used? Second, when should testing be­gin? The principles related to the second question are the same as those for earlygeneration testing when the objective is a pure line. That is, as inbreeding advancestestcross variation increases among lines and decreases within lines.

a. Choice of TesterA major step in evaluating the type of tester to be used was the development of

the concept of general and specific combining ability (Sprague and Tatum, 1942).This work supported use of a broadbase tester for preliminary screening for gen­eral combining ability, followed by testing in specific combinations. One methodof evaluating for specific combining ability was use of a diallel cross. Griffing(1994) reviews the development of the analysis of the diallel cross. Griffing (1956)provided clear statements of methods of analysis of diallel crosses in terms of gen­eral and specific combining ability and the circumstances in which each methodof analysis should be used. Hallauer and Miranda (1988) review the use of dial­leis in com breeding.

The choice of a tester to use in a hybrid breeding program is dictated by the ob­jectives of the program and the type of gene action controlling the traits of inter­est. If the objective is to improve population per se performance, then the testershould be one that has a low frequency of favorable alleles at the loci for whichthe population needs improvement. If additive gene action is of primary impor­tance, then any tester will be effective. However, if dominance, partial dominance,or overdominance are important the tester should be one that has a high frequen­cy of recessive alleles at loci for which improvement is needed. Mathematically,this can be seen from the expression for genetic variance among testcross meansfor a single locus presented by Homer et ai. (1969):

(jT~ = O.5pq(l + F)[a + d(Q - p)F (3)

where p and q are frequencies of favorable and unfavorable alleles, respectively,in the population of lines being tested, F is the inbreeding coefficient of the lines

16 JOHN W DUDLEY

being tested, a is half the difference between homozygotes, d is the deviation ofthe heterozygote value from the midparent, and P and Q are frequencies of favor­able and unfavorable alIeles, respectively, in the tester. If the tester is homozygous,then either P or Q = 1. Several points are apparent from this equation. If d = 0,i.e., there is no dominance, gene frequency in the tester does not affect aT~ andany tester will be satisfactory. If dominance exists, then the higher the frequencyof the recessive allele in the tester, the higher the testcross variance. Likewise, thegreater the inbreeding of the lines being tested, the greater the testcross variance.Thus, with complete dominance maximum aT~ will occur when the tester ishomozygous recessive and the lines being tested are homozygous.

Because interest is in increasing frequencies of favorable alleles at loci wherethe line to be used in combination with the line being developed has recessive al­leles, the tester should be closely related to the line to be used in the ultimate hy­brid. This minimizes genetic variability in testcross progeny at loci that do not needimprovement and allows increased gain in gene frequency at important loci. Theseconcepts support the generally accepted practice of identifying heterotic groupsand selecting testers from an opposite heterotic group (see HalIauer, et aI., 1988,for a discussion of heterotic groups). Extensive experimental data support thetheory behind choice of tester (Hallauer and Lopez-Perez, 1979).

b. Early vs Late TestingThe question of when to begin testing for combining ability was hotly debated

in the early days of com breeding. The principle of increased variance betweenlines and decreased variance within lines as inbreeding progressed applies here aswell as in development of inbreds for use as lines, per se. Jenkins (1935) andSprague (1946) concluded that high-combining lines could be identified by test­ing early in the inbreeding process and at least half of them could be discarded,thus alIowing more effort to be placed on testing the remaining lines later in theinbreeding process. Richey (1944) eloquently stated the case for selection for lineper se performance prior to selecting for combining ability in a poem (to this au­thor's knowledge, the only poem ever published in Agronomy Journal).

Bernardo (1992) developed theory for the genetic and phenotypic correlationsbetween testcross values of lines tested in a given selfed generation and their self­ed progeny. As selfing advances, the correlation increases. Bernardo showed thegenetic correlation between lines in different generations to be [(1 + Fn )/(1 + Fn .)]

where Fn and Fn , are inbreeding coefficients in generations nand n'. Heritabilityof testcross means also affect the correlation between early generation phenotyp­ic values and expected genetic values of progeny. Based on theory and simulationresults, Bernardo suggested saving approximately 25% of lines based on Sl or S2testing if heritability is 0.25 or 0.5 in the Sl generation. He also presented tablesshowing the probability of retaining lines in the upper a % of a distribution of ho­mozygous lines given that a line selected in a preceding generation (S) was in the

16 JOHN W DUDLEY

being tested, a is half the difference between homozygotes, d is the deviation ofthe heterozygote value from the midparent, and P and Q are frequencies of favor­able and unfavorable alleles, respectively, in the tester. If the tester is homozygous,then either P or Q = 1. Several points are apparent from this equation. If d = 0,i.e., there is no dominance, gene frequency in the tester does not affect aT~ andany tester will be satisfactory. If dominance exists, then the higher the frequencyof the recessive allele in the tester, the higher the testcross variance. Likewise, thegreater the inbreeding of the lines being tested, the greater the testcross variance.Thus, with complete dominance maximum aT~ will occur when the tester ishomozygous recessive and the lines being tested are homozygous.

Because interest is in increasing frequencies of favorable alleles at loci wherethe line to be used in combination with the line being developed has recessive al­leles, the tester should be closely related to the line to be used in the ultimate hy­brid. This minimizes genetic variability in testcross progeny at loci that do not needimprovement and allows increased gain in gene frequency at important loci. Theseconcepts support the generally accepted practice of identifying heterotic groupsand selecting testers from an opposite heterotic group (see Hallauer, et al., 1988,for a discussion of heterotic groups). Extensive experimental data support thetheory behind choice of tester (Hallauer and Lopez-Perez, 1979).

b. Early vs Late TestingThe question of when to begin testing for combining ability was hotly debated

in the early days of corn breeding. The principle of increased variance betweenlines and decreased variance within lines as inbreeding progressed applies here aswell as in development of inbreds for use as lines, per se. Jenkins (1935) andSprague (1946) concluded that high-combining lines could be identified by test­ing early in the inbreeding process and at least half of them could be discarded,thus allowing more effort to be placed on testing the remaining lines later in theinbreeding process. Richey (1944) eloquently stated the case for selection for lineper se performance prior to selecting for combining ability in a poem (to this au­thor's knowledge, the only poem ever published in Agronomy Journal).

Bernardo (1992) developed theory for the genetic and phenotypic correlationsbetween testcross values of lines tested in a given selfed generation and their self­ed progeny. As selfing advances, the correlation increases. Bernardo showed thegenetic correlation between lines in different generations to be [(1 + Fn)/(1 + Fn')]where Fn and Fn , are inbreeding coefficients in generations nand n'. Heritabilityof testcross means also affect the correlation between early generation phenotyp­ic values and expected genetic values of progeny. Based on theory and simulationresults, Bernardo suggested saving approximately 25% of lines based on Sl or Sztesting if heritability is 0.25 or 0.5 in the Sl generation. He also presented tablesshowing the probability of retaining lines in the upper a% of a distribution of ho­mozygous lines given that a line selected in a preceding generation (Sn) was in the

QUANTITATIVE GENETlCS AND PLANT BREEDING 17

upper a% of lines in the Sn generation. Empirical results previously published byJensen et al. (1983) agreed with these results. Hallauer and Miranda (1988) pro­vide an extensive review of the literature dealing with early testing in com. In gen­eral, most com breeders use some form of early testing (Bauman, 1981).

c. RECURRENT SELECTION

The objective of recurrent selection is to increase the frequency of favorable al­leles affecting a trait in order to enhance the value of the population. Increased fre­quency of favorable genes is advantageous for either population per se perfor­mance, as in the case of synthetic cultivars, or for inbreeding to produce improvedhomozygous lines. Hallauer (1985) demonstrated the theoretical advantages of in­creasing gene frequency prior to selection. Mechanically, recurrent selection in­volves repeated cycles of selection and recombination. Four major steps includeselection of the starting population, development of progenies, evaluation of prog­enies, and recombination of selected individuals. The importance of selection ofthe starting population is detailed under the section on selection of parents. Com­parisons among recurrent selection procedures can be made on a theoretical basisusing the prediction Eq. (1). Hallauer (1985) details the types of progenies thatmay be used and the various forms of recurrent selection and provides examplesfrom a number of species. Prediction equations appropriate for a number of dif­ferent recurrent selection procedures are given in Empig et al. (1972) and Hallauerand Miranda (1988).

The development of recurrent selection procedures was given major impetus bythe controversy over the genetic causes of heterosis. Based on the data that sug­gested early testing should be effective, Jenkins (1940) outlined a procedure thatcame to be known as recurrent selection for general combining ability. In this pro­cedure, selection was based on half-sib family selection and took advantage of ad­ditive effects. Hull (1945) considered overdominance to be of major importancein controlling grain yield in com and suggested a recurrent selection scheme us­ing an inbred tester that emphasized specific combining ability and would take ad­vantage of loci showing overdominance. Comstock et al. (1949) suggested recip­rocal recurrent selection based on half-sib families to take advantage of bothgeneral and specific combining ability. The procedure was designed to maximizeprogress regardless of whether dominance or overdominance was important in hy­brid performance. Hallauer and Eberhart (1970) outlined reciprocal full-sib selec­tion, which increased emphasis on nonadditive effects and provided an efficientmethod of simultaneously improving population cross performance and develop­ing new inbreds. Details of these procedures and their use are provided in Hallauerand Miranda (1988).

Recurrent selection principles, developed in cross-pollinated crops, have been

18 JOHN W DUDLEY

utilized in self-pollinated crops (see Hallauer, 1985, for a review). A major limi­tation is the difficulty of making crosses to provide recombination between cycles.Brim and Stuber (1973) outlined a method of using genetic male sterility to facil­itate recurrent selection in soybeans. They developed prediction equations for se­lection among and within half-sib families. Burton and Carver (1993) comparedthe effectiveness of S l' selfed half-sib, and selfed full-sib families for recurrent se­lection using male sterile genes in soybeans and wheat. The advantage of usingselfed half-sib or full-sib families was an increase in the amount of seed availablefor testing. No consistent advantage to using S I families was found. Although thequantitative genetic basis for effective use of recurrent selection in self-pollinatedspecies is the same as that for cross-pollinated species and procedures are avail­able for overcoming the difficulties of recombination, use of recurrent selection inself-pollinated species has been limited (Hallauer, 1985).

D. MARKER-AsSISTED SELECTION

The quantitative genetic principle behind marker-assisted selection on a singlelocus basis is relatively simple. Gain from selection based on marker genotype isa form of indirect selection in which the heritability of the marker is 1.0 (Dudley,1993). However, for quantitative traits several markers are usually involved. Thisintroduces the complication of how to weight each marker's contribution when se­lections are made. One method is to determine the marker genotype of each indi­vidual or line being tested, sum the additive effects of the marker loci showing asignificant marker effect, and use the sum as an index value for the individual be­ing considered for selection. This procedure has the advantage of taking into con­sideration the difference in magnitude of effects of the loci being included in se­lection. As reviewed by Dudley (1993), gain from marker-assisted selection willbe greatest when the proportion of the additive variance accounted for by markereffects is greater than the heritability of the trait. This suggests selection based onmarkers has its greatest advantage when heritability of a trait is low. However,identification of marker-QTL associations requires precise experiments in whichheritability is as high as possible (Dudley, 1993). Thus, maximum benefit frommarker-assisted selection may occur when marker-QTL associations are identifiedunder conditions of high heritability and selection is done when the trait of inter­est cannot be measured.

In a survey reported by Lee (1995), the most common use of marker-assistedselection was to assist in transferring native monogenic factors or transgenes. Al­though the survey did not specifically request the information, Lee concluded thatthe primary breeding method involved was backcrossing. At least seven re­searchers indicated use of markers for transferring QTL. Thus, marker-assisted se­lection is in use in some plant breeding programs.

18 JOHN W DUDLEY

utilized in self-pollinated crops (see Hallauer, 1985, for a review). A major limi­tation is the difficulty of making crosses to provide recombination between cycles.Brim and Stuber (1973) outlined a method of using genetic male sterility to facil­itate recurrent selection in soybeans. They developed prediction equations for se­lection among and within half-sib families. Burton and Carver (1993) comparedthe effectiveness of S l' selfed half-sib, and selfed full-sib families for recurrent se­lection using male sterile genes in soybeans and wheat. The advantage of usingselfed half-sib or full-sib families was an increase in the amount of seed availablefor testing. No consistent advantage to using SI families was found. Although thequantitative genetic basis for effective use of recurrent selection in self-pollinatedspecies is the same as that for cross-pollinated species and procedures are avail­able for overcoming the difficulties of recombination, use of recurrent selection inself-pollinated species has been limited (Hallauer, 1985).

D. MARKER-AsSISTED SELECTION

The quantitative genetic principle behind marker-assisted selection on a singlelocus basis is relatively simple. Gain from selection based on marker genotype isa form of indirect selection in which the heritability of the marker is 1.0 (Dudley,1993). However, for quantitative traits several markers are usually involved. Thisintroduces the complication of how to weight each marker's contribution when se­lections are made. One method is to determine the marker genotype of each indi­vidual or line being tested, sum the additive effects of the marker loci showing asignificant marker effect, and use the sum as an index value for the individual be­ing considered for selection. This procedure has the advantage of taking into con­sideration the difference in magnitude of effects of the loci being included in se­lection. As reviewed by Dudley (1993), gain from marker-assisted selection willbe greatest when the proportion of the additive variance accounted for by markereffects is greater than the heritability of the trait. This suggests selection based onmarkers has its greatest advantage when heritability of a trait is low. However,identification of marker-QTL associations requires precise experiments in whichheritability is as high as possible (Dudley, 1993). Thus, maximum benefit frommarker-assisted selection may occur when marker-QTL associations are identifiedunder conditions of high heritability and selection is done when the trait of inter­est cannot be measured.

In a survey reported by Lee (1995), the most common use of marker-assistedselection was to assist in transferring native monogenic factors or transgenes. Al­though the survey did not specifically request the information, Lee concluded thatthe primary breeding method involved was backcrossing. At least seven re­searchers indicated use of markers for transferring QTL. Thus, marker-assisted se­lection is in use in some plant breeding programs.

QUANTITATIVE GENETICS AND PLANT BREEDING 19

V. FUrURE ROLE OF QUANTITATIVE GENETICSIN PLANT BREEDING

Predicting the future is a hazardous occupation. However, certain aspects areevident. The principles of quantitative genetics are an integral part of plant breed­ing and will continue to be for the foreseeable future. Thus, training ofplant breed­ers will continue to require exposure to quantitative genetic principles and theiruse in plant breeding programs.

During the past several years, the most exciting development related to quanti­tative genetics and plant breeding has been the development and availability oflarge numbers of molecular markers that allow marking relatively small segmentsof chromosome. At the same time, transformation procedures that allow the intro­duction into cultivated plants of genes from other species have become available.The availability of molecular markers has enabled investigators to attack quanti­tative genetic questions such as number of genes affecting a quantitative trait, thelocation of such genes, the type of gene action associated with them, the impor­tance of epistasis, and the effect of environment on each gene. To date, the tech­nology allows dealing only with chromosome segments and not individual genes,but further advances may allow this type of refinement. As transformation be­comes more common, questions such as the importance of genetic background forthe introduction of new genes will be important. Evaluation of questions such asthis will require use of quantitative genetics.

Because of the importance of molecular markers, increasing emphasis on link­age and its manipulation will be required both in training of students and in re­search. A question of primary interest to plant breeders is how can favorable link­age blocks be held together while introducing new favorable alleles into anexisting genotype? Perhaps the combination of molecular marker technology,transformation, quantitative genetics, and the science of plant breeding can com­bine to answer this question.

In the future, to perhaps a greater degree than in the past, integration of quanti­tative genetics into plant breeding programs will be a team effort. Involved in thiseffort will be knowledge of molecular biology principles, plant breeding princi­ples, and quantitative genetic expertise. This combination of expertise is muchmore likely to be found in a team, each of whose members is an expert in one ormore of these disciplines and can and is willing to communicate with other teammembers, than in one individual.

REFERENCES

Allan, R. E. (1987). Wheat. III "Principles of Cultivar Development" (w. R. Fehr, ed.), Vol. 2,pp. 699-748. Macmillan, New York.

QUANTITATIVE GENETICS AND PLAt"J'T BREEDING 19

V. FUrURE ROLE OF QUANTITATIVE GENETICSIN PLANT BREEDING

Predicting the future is a hazardous occupation. However, certain aspects areevident. The principles of quantitative genetics are an integral part of plant breed­ing and will continue to be for the foreseeable future. Thus, training of plant breed­ers will continue to require exposure to quantitative genetic principles and theiruse in plant breeding programs.

During the past several years, the most exciting development related to quanti­tative genetics and plant breeding has been the development and availability oflarge numbers of molecular markers that allow marking relatively small segmentsof chromosome. At the same time, transformation procedures that allow the intro­duction into cultivated plants of genes from other species have become available.The availability of molecular markers has enabled investigators to attack quanti­tative genetic questions such as number of genes affecting a quantitative trait, thelocation of such genes, the type of gene action associated with them, the impor­tance of epistasis, and the effect of environment on each gene. To date, the tech­nology allows dealing only with chromosome segments and not individual genes,but further advances may allow this type of refinement. As transformation be­comes more common, questions such as the importance of genetic background forthe introduction of new genes will be important. Evaluation of questions such asthis will require use of quantitative genetics.

Because of the importance of molecular markers, increasing emphasis on link­age and its manipulation will be required both in training of students and in re­search. A question of primary interest to plant breeders is how can favorable link­age blocks be held together while introducing new favorable alleles into anexisting genotype? Perhaps the combination of molecular marker technology,transformation, quantitative genetics, and the science of plant breeding can com­bine to answer this question.

In the future, to perhaps a greater degree than in the past, integration of quanti­tative genetics into plant breeding programs will be a team effort. Involved in thiseffort will be knowledge of molecular biology principles, plant breeding princi­ples, and quantitative genetic expertise. This combination of expertise is muchmore likely to be found in a team, each of whose members is an expert in one ormore of these disciplines and can and is willing to communicate with other teammembers, than in one individual.

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20 JOHN W DUDLEY

Bailey, T. B., Jr., and Comstock, R. E. (1976). Linkage and the synthesis of better genotypes in self­fertilizing species. Crop Sci. 16,363-370.

Baker, R. J. (1984). Quantitative genetic principles in plant breeding. In "Gene Manipulation in PlantImprovement" (J. P. Gustafson, ed.), pp. 147-175. Plenum Press, New York.

Baker, R. J. (1988). Tests for crossover genotype-environmental interactions. Can. J. Plant Sci. 68,405--410.

Bauman, L. F. (1981). Review of methods used by breeders to develop superior inbreds. Proc. 36thAnnu. Corn Sorghum Ind. Res. Con!, 199-208.

Bernardo, R. (1990a). An alternative statistic for identifying lines useful for improving parents of elitesingle crosses. Theor. Appl. Genet. 80(1), 105-109.

Bernardo, R. (1990b). Identifying populations useful for improving parents of a single cross based onnet transfer of alleles. Theor. Appl. Genet. 80(3),349-352.

Bernardo, R. (1991). Retrospective index weights used in multiple trait selection in a maize breedingprogram. Crop Sci. 31,1174-1179.

Bernardo, R. (1992). Retention of genetically superior lines during early-generation testcrossing ofmaize. Crop Sci. 32,933-937.

Bernardo, R. (1994). Prediction of maize single-cross performance using RFLPs and information fromrelated hybrids. Crop Sci. 34,20-25.

Bernardo, R. (1996). Best linear unbiased prediction of maize single-cross performance. Crop Sci. 36,50-56.

Brim, C. A. (1966). A modified pedigree method of selection in soybeans. Crop Sci. 6,220.Brim, C. A., and Stuber, C. W. (1973). Application of genetic male sterility to recurrent selection

schemes in soybeans. Crop Sci. 13,528-530.Burton, J. w., and Carver, B. F. (1993). Selection among S, families vs. selfed half-sib or full-sib fam­

ilies in autogamous crops. Crop Sci. 33,21-28.Busbice, T. H. (1970). Predicting yield of synthetic varieties. Crop Sci. 10,265-269.Busch, R. H., Janke, J. C., and Frohberg, R. C. (1974). Evaluation ofcrosses among high and low yield­

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Campbell, K. W., and White, D. G. (1995). Inheritance of resistance to Aspergillus ear rot and aflatoxinin com genotypes. Phytopathology 85, 886-896.

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Cockerham, C. C. (1963). Estimation of genetic variances. In "Statistical Genetics and Plant Breed­ing" (W. D. Hanson and H. F. Robinson, eds.), pp. 53-94. NAS~RCPub\. 982, Washington, DC.

Comstock, R. E. (1978). Quantitative genetics in maize breeding. In "Maize Breeding and Genetics"(D. B. Walden, ed.), pp. 191-206. Wiley, New York.

Comstock, R. E., and Moll, R. H. (1963). Genotype--environment interaction. In "Statistical Geneticsand Plant Breeding" (W. D. Hanson and H. F. Robinson, eds.), pp. 164-197. NAS-NRC Pub\. 982,Washington, DC.

Comstock, R. E., Robinson, H. F., and Harvey, P. H. (1949). A breeding procedure designed to makemaximum use of both general and specific combining ability. Agron. J. 41,360-367.

Crabb, A. R. (1947). "The Hybrid Corn Makers, Prophets of Plenty." Rutgers Univ. Press, NewBrunswick, NJ.

Dudley, J. W. (1982). Theory for transfer of alleles. Crop Sci. 22,631-637.

20 JOHN W DUDLEY

Bailey, T. B., Jr., and Comstock, R. E. (1976). Linkage and the synthesis of better genotypes in self­fertilizing species. Crop Sci. 16,363-370.

Baker, R. J. (1984). Quantitative genetic principles in plant breeding. In "Gene Manipulation in PlantImprovement" (J. P. Gustafson, ed.), pp. 147-175. Plenum Press, New York.

Baker, R. J. (1988). Tests for crossover genotype-environmental interactions. Can. J. Plant Sci. 68,405--410.

Bauman, L. F. (1981). Review of methods used by breeders to develop superior inbreds. Proc. 36thAnnu. Corn Sorghum Ind. Res. Con!, 199-208.

Bernardo, R. (1990a). An alternative statistic for identifying lines useful for improving parents of elitesingle crosses. Theor. Appl. Genet. 80(1), 105-109.

Bernardo, R. (1990b). Identifying populations useful for improving parents of a single cross based onnet transfer of alleles. Theor. Appl. Genet. 80(3),349-352.

Bernardo, R. (1991). Retrospective index weights used in multiple trait selection in a maize breedingprogram. Crop Sci. 31,1174-1179.

Bernardo, R. (1992). Retention of genetically superior lines during early-generation testcrossing ofmaize. Crop Sci. 32,933-937.

Bernardo, R. (1994). Prediction of maize single-cross performance using RFLPs and information fromrelated hybrids. Crop Sci. 34,20-25.

Bernardo, R. (1996). Best linear unbiased prediction of maize single-cross performance. Crop Sci. 36,50-56.

Brim, C. A. (1966). A modified pedigree method of selection in soybeans. Crop Sci. 6,220.Brim, C. A., and Stuber, C. W. (1973). Application of genetic male sterility to recurrent selection

schemes in soybeans. Crop Sci. 13,528-530.Burton, J. w., and Carver, B. F. (1993). Selection among S, families vs. selfed half-sib or full-sib fam­

ilies in autogamous crops. Crop Sci. 33,21-28.Busbice, T. H. (1970). Predicting yield of synthetic varieties. Crop Sci. 10,265-269.Busch, R. H., Janke, J. C., and Frohberg, R. C. (1974). Evaluation ofcrosses among high and low yield­

ing parents of spring wheat (Triticum aestivum L.) and bulk prediction of line performance. CropSci. 14,47-50.

Campbell, K. W., and White, D. G. (1995). Inheritance of resistance to Aspergillus ear rot and aflatoxinin corn genotypes. Phytopathology 85, 886-896.

Carson, M. L., and Hooker, A. L. (1981). Inheritance ofrsistance to anthracnose leafblight in five in­bred lines of corn. Phytopathology 71, 488--49 I.

Chase, S. S. (1974). Utilization of haploids in plant breeding, breeding diploid species. In "Haploidsin Higher Plants" (K. J. Kasha, ed.), pp. 211-230. Univ. of Guelph Press, Guelph, Canada.

Choo, T. M., Reinbergs, E., and Kasha, K. J. (1985). Use of haploids in breeding barley. Plant Breed­ing Rev. 3,219-252.

Cockerham, C. C. (1954). An extension of the concept of partitioning hereditary variance for analysisof covariances among relatives when epistasis is present. Genetics 39, 859-882.

Cockerham, C. C. (1963). Estimation of genetic variances. In "Statistical Genetics and Plant Breed­ing" (W. D. Hanson and H. F. Robinson, eds.), pp. 53-94. NAS~RCPub!. 982, Washington, DC.

Comstock, R. E. (1978). Quantitative genetics in maize breeding. In "Maize Breeding and Genetics"(D. B. Walden, ed.), pp. 191-206. Wiley, New York.

Comstock, R. E., and Moll, R. H. (1963). Genotype--environment interaction. In "Statistical Geneticsand Plant Breeding" (W. D. Hanson and H. F. Robinson, eds.), pp. 164-197. NAS-NRC Pub!. 982,Washington, DC.

Comstock, R. E., Robinson, H. F., and Harvey, P. H. (1949). A breeding procedure designed to makemaximum use of both general and specific combining ability. Agron. J. 41,360-367.

Crabb, A. R. (1947). "The Hybrid Corn Makers, Prophets of Plenty." Rutgers Univ. Press, NewBrunswick, NJ.

Dudley, J. W. (1982). Theory for transfer of alleles. Crop Sci. 22,631-637.

QUANTITATIVE GENETICS AND PLANT BREEDING 21

Dudley, J. W. (1984a). Identifying parents for use in a pedigree breeding program. In "Proceedings ofthe 39th Annual Corn and Sorghum Research Conference," pp. 176-188. American Seed TradeAssociation, Washington, DC.

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Dudley, J. W. (1984c). A method for identifying populations containing favorable alleles not presentin elite germplasm. Crop Sci. 24, 1053-1054.

Dudley, J. W. (1987a). Modification of methods for identifying populations to be used for improvingparents of elite single crosses. Crop Sci. 27,940-944.

Dudley, J. W. (l987b). Modification of methods for identifying inbred lines useful for improving par­ents of elite single crosses. Crop Sci. 27,945-947.

Dudley, J. W. (1988). Evaluation of maize populations as sources of favorable alleles. Crop Sci. 28,486-491.

Dudley, 1. W. (1993). Molecular markers in plant improvement, Manipulation of genes affecting quan­titative traits. Crop Sci. 33, 660-668.

East, E. M. (1910). A Mendelian interpretation of variation that is apparently continuous. Am. Natl. 44,65-82.

Eberhart, S., and Russell. W. A. (1966). Stability parameters for comparing varieties. Crop Sci. 6,36-40.

Eberhart. S. A., and Russell. W. A. (1969). Yield and stability for a lO-line diallel of single-cross anddouble-cross maize hybrids. Crop Sci. 9,357-361.

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York.Finlay, K. w.. and Wilkinson, G. W. (1963). The analysis of adaptation in a plant breeding programme.

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leles. I. Theoretical results. Theor. Appl. Genet. 76, 209-216.Goulden, C. H. (1941). Problems in plant selection. In "Proceedings of the 7th International Genetics

Congress," pp. 132-133. Cambridge Univ. Press, Cambridge. UK.Griffing, B. (1956). Concept of general and specific combining in relation to dialle! crossing systems.

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Hallauer. A. R.. and Eberhart, S. E. (1970). Reciprocal full-sib selection. Crop Sci. 10,315-316.Hallauer, A. R., and Lopez-Perez, E. (1979). Comparison among testers for evaluating lines of corn.

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provement" (G. F. Sprague and J. W. Dudley, eds.), pp. 463-564. American Society of Agrono­my, Madison. WI.

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QUANTITATIVE GENETICS AND PLANT BREEDING 21

Dudley, J. W. (1984a). Identifying parents for use in a pedigree breeding program. In "Proceedings ofthe 39th Annual Corn and Sorghum Research Conference," pp. 176-188. American Seed TradeAssociation, Washington, DC.

Dudley, J. W. (I 984b). A method of identifying lines for use in improving parents of a single cross.Crop Sci. 24,355-357.

Dudley, J. W. (1984c). A method for identifying populations containing favorable alleles not presentin elite gennplasm. Crop Sci. 24, 1053-1054.

Dudley, J. W. (1987a). Modification of methods for identifying populations to be used for improvingparents of elite single crosses. Crop Sci. 27, 940-944.

Dudley, J. W. (1987b). Modification of methods for identifying inbred lines useful for improving par­ents of elite single crosses. Crop Sci. 27,945-947.

Dudley, J. W (1988). Evaluation of maize populations as sources of favorable alleles. Crop Sci. 28,486---491.

Dudley, J. W. (1993). Molecular markers in plant improvement, Manipulation of genes affecting quan­titative traits. Crop Sci. 33, 660-668.

East, E. M. (1910). A Mendelian interpretation of variation that is apparently continuous. Am. Natl. 44,65-82.

Eberhart, S., and Russell, W. A. (1966). Stability parameters for comparing varieties. Crop Sci. 6,36---40.

Eberhart, S. A., and Russell, W. A. (1969). Yield and stability for a IO-line diallel of single-cross anddouble-cross maize hybrids. Crop Sci. 9,357-361.

Empig, L. T., Gardner, C. 0., and Compton, W. A. (1972). "Theoretical Gains for Different PopulationImprovement Procedures." Nebraska Agr. Exp. Sta. Misc. Pub. 26 (revised).

Falconer, D. S. (1989). "Introduction to Quantitative Genetics." Wiley, New York.Fehr, W. R (1987). "Principles of Cultivar Development: Theory and Technique." Macmillan, New

York.Finlay, K. W, and Wilkinson, G. W. (1963). The analysis of adaptation in a plant breeding programme.

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Trans. R. Soc. Edinburgh 52, 399---433.Galton, F. (1889). "Natural Inheritance." MacMillan, London.Gerloff, J. E., and Smith, O. S. (1988). Choice of method for identifying germplasm with superior al­

leles. I. Theoretical results. Theor. Appl. Genet. 76, 209-216.Goulden, C. H. (1941). Problems in plant selection. In "Proceedings of the 7th International Genetics

Congress," pp. 132-133. Cambridge Univ. Press, Cambridge, UK.Griffing, B. (1956). Concept of general and specific combining in relation to diallel crossing systems.

Aust. J. BioI. Sci. 13, 463---493.Griffing, B. (1994). Historical perspectives on contributions of quantitative genetics to plant breeding.

In "Historical Perspectives in Plant Science" (K. J. Frey, ed.), pp. 43-86. Iowa State Univ. Press,Ames.

Hallauer, A. R (1985). Compendium of recurrent selection methods and their application. Crit. Rev.Plant Sci. 3, 1-30.

Hallauer, A. R, and Eberhart, S. E. (1970). Reciprocal full-sib selection. Crop Sci. 10,315-316.Hallauer, A. R, and Lopez-Perez, E. (1979). Comparison among testers for evaluating lines of corn.

Proc. 34th Annu. Hybrid Corn Ind. Res. ConJ, 57-75.Hallauer, A. R, and Miranda Fo, J. B. (1988). "Quantitative Genetics in Maize Breeding." Iowa State

Univ. Press, Ames.Hallauer, A. R, Russell, W. A., and Lamkey, K. R. (1988). Com breeding. In "Corn and Corn Im­

provement" (G. F. Sprague and J. W. Dudley, eds.), pp. 463-564. American Society of Agrono­my, Madison, WI.

Hayes, H. K. (1963). "A Professor's Story of Hybrid Corn." Burgess, Minneapolis, MN.

22 JOHN W. DUDLEY

Henderson, C. R (1988). Progress in statistical methods applied to quantitative genetics since 1976.In "Proceedings of the Second International Conference on Quantitative Genetics" (B. S. Weir,E. J. Eisen, M. M. Goodman, and G. Namkoong, eds.), pp. 85-90. Sinauer, Sunderland, MA.

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Horner, E. S., Chapman, W. H., L~trick, M. C., and Lundy, H. W. (1969). Comparison of selectionbased on yield of topcross progenies and of S2 progenies in maize (Zea mays L.). Crop Sci. 9,539-543.

Hull, F. H. (1945). Recurrent selection and specific combining ability in com. J. Am. Soc. Agron. 37,134-135.

Jenkins, M. T. (1935). The effect of inbreeding and selection within inbred lines of maize upon hybridsmade after successive generations of selfing. Iowa State Coil. J. Sci. 6,429--450.

Jenkins, M. T. (1940). The segregation of genes affecting yield of grain in maize. J. Am. Soc. Agron.32,55-63.

Jensen, S. D., Kuhn, W. E., and McConnell, R L. (1983). Combining ability studies in elite U.S. maizegermplasm. Proc. 38th Ann. Corn and Sorghum Res. Con!, Am. Seed Trade Assoc. 38, 87-96.

Johannsen, W. (1903). "Uber Erblichkeit in Population und in Reinen Linien." Gustav Fischer, Jena.Johannsen, W. (1909). "Elemente der Exakten Erblichkeitslehre." Gustav Fischer, Jena.Johnson, B., Gardner. C. D., and Wrede, K. C. (1988). Application of an optimization model to multi­

trait selection programs. Crop Sci. 28,723-728.Kang, M. S. (ed.) (1990). "Genotype-by-Environment Interaction and Plant Breeding." Louisiana State

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Lamkey, K. R, Schnicker, B. J., and Melchinger, A. E. (1995). Epistasis in an elite maize hybrid andchoice of generation for inbred line development. Crop Sci. 35, 1272-1281.

Lee, M. (1995). DNA markers and plant breeding programs. Adv. Agron. 55,265-344.Lin, C. S., Binns, M. R, and Lefkovitch, L. P. (1986). Stability analysis, where do we stand? Crop Sci.

26, 894-900.Lush, J. L. (1935). Progeny test and individual performance as an indicator of an animal's breeding

value. J. Dairy Sci. 18,1-19.Mather, K., and Jinks, J. L. (1982). "Biometrical Genetics, The Study of Continuous Variation." Chap­

man & Hall, London.Metz, G. (1994). Probability of net gain of favorable alleles for improving an elite single cross. Crop

Sci. 34,668-672.Misevic, D. (1989). Identification of inbred lines as a source of new alleles for improvement of elite

maize single crosses. Crop Sci. 29, 1120-1125.Moll, R H., Thompson, D. L., and Harvey, P. H. (1963). A quantitative genetic study of the inheritance

of resistance to brown spot (Physoderma maydis) of corn. Crop Sci. 3, 389-391.Mumm, R H., and Dudley, J. W. (1994). A classification of U.S. Maize inbreds: I. Cluster analysis

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tions. Crit. Rev. Plant Sci. 10, 235-322.Duyang, Z., Mowers, R P., Jensen, A., Wang, S., and Zheng, S. (1995). Cluster analysis for genotype

X environment interaction with unbalanced data. Crop Sci. 35, 1300-1305.

22 JOHNW. DUDLEY

Henderson, C. R (1988). Progress in statistical methods applied to quantitative genetics since 1976.In "Proceedings of the Second International Conference on Quantitative Genetics" (B. S. Weir,E. J. Eisen, M. M. Goodman, and G. Namkoong, eds.), pp. 85-90. Sinauer, Sunderland, MA.

Hogan, R M., and Dudley, 1. W. (1991). Evaluation of a method for identifying sources of favorable

alleles to improve an elite single cross. Crop Sci. 31, 700-704.Horner, E. S., Chapman, W. H., LJ!trick, M. c., and Lundy, H. W. (1969). Comparison of selection

based on yield of topcross progenies and of S2 progenies in maize (Zea mays L.). Crop Sci. 9,539-543.

Hull, F. H. (1945). Recurrent selection and specific combining ability in com. J. Am. Soc. Agron. 37,134-135.

Jenkins, M. T. (1935). The effect of inbreeding and selection within inbred lines of maize upon hybridsmade after successive generations of selfing. Iowa State Coil. J. Sci. 6,429--450.

Jenkins, M. T. (1940). The segregation of genes affecting yield of grain in maize. J. Am. Soc. Agron.32,55-63.

Jensen, S. D., Kuhn, W. E., and McConnell, R L. (1983). Combining ability studies in elite U.S. maizegermplasm. Proc. 38th Ann. Corn and Sorghum Res. ConJ, Am. Seed Trade Assoc. 38, 87-96.

Johannsen, W. (1903). "Uber Erblichkeit in Population und in Reinen Linien." Gustav Fischer, Jena.Johannsen, W. (1909). "Elemente der Exakten Erblichkeitslehre." Gustav Fischer, Jena.Johnson, B., Gardner, C. D., and Wrede, K. C. (1988). Application of an optimization model to multi­

trait selection programs. Crop Sci. 28,723-728.Kang, M. S. (ed.) (1990). "Genotype-by-Environment Interaction and Plant Breeding." Louisiana State

University Agriculture Center, Baton Rouge.Kempthorne, D. (1954). The correlations between relatives in a random mating population. Proc. R.

Soc. London B 143,103-113.Kempthorne, D. (1957). "An Introduction to Genetic Statistics." Iowa State Univ. Press, Ames.Kempthorne, D. (1977). The international conference on quantitative genetics, introduction. In "Pro­

ceedings of the International Conference on Quantitative Genetics" (E. Pollak, D. Kempthorne,and T. B. Bailey, Jr., eds.), pp. 3-18. Iowa State Univ. Press, Ames.

Lamkey, K. R, Schnicker, B. J., and Melchinger, A. E. (1995). Epistasis in an elite maize hybrid andchoice of generation for inbred line development. Crop Sci. 35, 1272-1281.

Lee, M. (1995). DNA markers and plant breeding programs. Adv. Agron. 55,265-344.Lin, C. S., Binns, M. R, and Lefkovitch, L. P. (1986). Stability analysis, where do we stand? Crop Sci.

26, 894-900.Lush, J. L. (1935). Progeny test and individual performance as an indicator of an animal's breeding

value. J. Dairy Sci. 18,1-19.Mather, K., and Jinks, 1. L. (1982). "Biometrical Genetics, The Study of Continuous Variation." Chap­

man & Hall, London.Metz, G. (1994). Probability of net gain of favorable alleles for improving an elite single cross. Crop

Sci. 34,668-672.Misevic, D. (1989). Identification of inbred lines as a source of new alleles for improvement of elite

maize single crosses. Crop Sci. 29, 1120-1125.Moll, R. H., Thompson, D. L., and Harvey, P. H. (1963). A quantitative genetic study of the inheritance

of resistance to brown spot (Physoderma maydis) of corn. Crop Sci. 3,389-391.Mumm, R H., and Dudley, J. W. (1994). A classification of U.S. Maize inbreds: I. Cluster analysis

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tions. Crit. Rev. Plant Sci. 10, 235-322.Duyang, Z., Mowers, R P., Jensen, A., Wang, S., and Zheng, S. (1995). Cluster analysis for genotype

X environment interaction with unbalanced data. Crop Sci. 35, 1300-1305.

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Sax. K. (1923). The association of size differences with seed coat pattern and pigmentation in Phase­olus vulgaris. Genetics 8, 552-560.

Schnell, F. W. (1983). Probleme der Eltemwahl-Ein Uberblick. In "Arbeitstagung der Arbeitsgemein­schaft der Saatzuchtleiter in Gumpenstein. Austria." pp. I-II. November 22-24, 1983. Verlag andDruck der Bundesanstalt fur alpenlandische Landwirtschaft. Gumpenstein. Austria.

Simmonds. N. W. (1984). Gene manipulation and plant breeding. In "Gene Manipulation in Plant Im­provement" (J. P. Gustafson. ed.), pp. 637-654. Plenum Press. New York.

Smith, D. C. (1966). Plant breeding':"'-Development and success. In "Plant Breeding" (K. J. Frey. ed.).pp. 3-54. Iowa State Univ. Press. Ames.

Smith, G. A. (J 987). Sugar beet. In "Genetic Contributions to Yield Gains of Five Major Crop Plants"(w. R. Fehr. ed.). pp. 577-625. CSSA Spec. Publ. No.7. ASA. CSSA. and SSSA, Madison. WI.

Smith. H. F. (1936). A discriminant function for plant selection. Ann. Eug. 7, 240.-250.Smith. O. S. (1986). Covariance between line per se and testcross performance. Crop Sci. 26,540.-543.Sprague. G. F. (1946). Early testing of inbred lines of com. J. Am. Soc. Agron. 38, 108-117.Sprague. G. F.. and Tatum. L. A. (1942). General vs. specific combining ability in single crosses of

com. J. Am. Soc. Agron. 34,923-932.Stuber. C. W. (1992). Biochemical and molecular markers in plant breeding. In "Plant Breeding Re­

views" (J. Janick, ed.). pp. 37-61. Wiley, New York.Stuber. C. W.. and Edwards. M. D. (1986). Genotypic selection for improvement of quantitative traits

in com using molecular marker loci. Proc. 41st Ann. Com and Sorghum Res. Can!. Am. SeedTrade Assoc. 41,40.-83.

Toledo. J. F. F. (1992). Mid parent and coefficient of parentage as predictors for screening among sin­gle crosses for their inbreeding potential. Rev. Brasil. Genet. 15,429--437.

Wallace. H. A., and Brown. W. L. (1956). "Com and Its Early Fathers." Michican State Univ. Press,East Lansing.

Williams, J. S. (1962). The evaluation of a selection index. Biometrics 18, 375-393.Wright, S. (1921). Systems of mating I. The biometric relations between parent and offspring. Genet­

ics6,111-123.Zanoni, U., and Dudley. 1. W. (1989). Comparison of different methods of identifying inbreds useful

for improving elite maize hybrids. Crop Sci. 29,577-587.Zirkle. C. (1952). Early ideas on inbreeding and crossbreeding. In "Heterosis" (1. W. Gowen, ed.).

pp. 1-13. Iowa State College Press, Ames.