History, Contribution, and Future of Quantitative Genetics in Plant Breeding: Lessons From Maize

ARNEL R. HALLAUER* History, Contribution, and Future of Quantitative Genetics in Plant Breeding: Lessons From Maize C. F. Curtiss Distinguished Professor in Agriculture, Emeritus. Dep. of Agronomy, Iowa State University, Ames, IA 50011-1010. Received 9 July 2007. *Corresponding author (hallauer@iastate.edu). Published in Crop Sci. 47(S3) S4 S19 (2007). doi: 10.2135/cropsci2007.04.0002IPBS Crop Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA

The time frame of the history of quantitative genetics is similar to Mendelian genetics. The rediscovery of Mendel s laws of inheritance in 1900 was the basis for determining the inheritance of quantitative traits and for developing plant breeding and selection methods. Because of the differences expressed by many of the leading geneticists relative to importance of continuous vs. discontinuous variation in evolution, the acceptance of the concepts for the study of quantitative genetics was delayed. R.A. Fisher, S. Wright, and J.B.S. Haldane were the primary early contributors for developing the theory and methods for studying the inheritance of quantitative traits. Greater interest in the inheritance of quantitative traits in plants occurred after 1946, primarily because of the heterosis expressed in maize (Zea mays L.) hybrids. During the past 50 yr, extensive research has been conducted to determine the relative importance of different genetic effects in the inheritance of quantitative traits for most cultivated plant species. Quantitative genetic research has contributed extensive information to assist plant breeders in developing breeding and selection strategies. Directly and/or indirectly, the principles for the inheritance of quantitative traits are pervasive in developing superior cultivars to meet the food, feed, fuel, and fiber needs the world demands. The principles of quantitative genetics will have continued importance in the future, but at different levels. Information from molecular genetics research will be integrated with our current knowledge at the phenotypic level to increase the effectiveness and efficiency of plant breeding. INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007 S-5

The time frame of the histories of quantitative genetics and modern plant breeding is similar to that of Mendelian genetics and disciplines that are based on Mendelian genetics: it began with the rediscovery of Mendelism in 1900. Before 1900, researchers conducted studies that examined and compared the traits of cultivars, crosses (F 1 s) between cultivars, and the selfed generation (F 2 s) of the crosses. They were interested in the contributions the parents made to the crosses, and they observed, in some instances, the recovery of the parental types in the selfed generations. Different suggestions and theories were made how the contributions of the male and female parents were expressed in the crosses for different traits. No general theory was offered, however, as to how different traits of the parents were transmitted and expressed in crosses and subsequent selfed generations at the time Darwin (1876) summarized his studies with plants. Two events that were to have profound effects for the future of genetics, plant breeding, biology in general, and other disciplines related to plant improvement were reported within a 6-yr period: Darwin s (1963) book on the Origin of Species in 1859 and Mendel s report on his genetic studies with peas (Pisium sativum L.) in 1865. Darwin s theory of natural selection received immediate and widespread acclaim (for and against the theory) whereas Mendel s research was not recognized and/or understood for 35 yr. Although Darwin and Mendel were contemporaries, it does not seem they ever met and discussed their respective research interests. It is speculation on my part, but Mendel may have been more aware of Darwin s theory of selection than Darwin of Mendel s genetic studies because of the greater public distribution of Darwin s book and the vigorous debates about the validity of Darwin s theory of natural selection. Mendel s paper had limited distribution and had not stimulated much interest from those who either had copies provided by Mendel or had attended the meetings where Mendel presented summaries of his research. If Darwin had read Mendel s paper, or had been made aware of his studies, they seemingly did not impact Darwin s thinking on the transmission of traits from parents to their offspring. The concepts of blending inheritance and gemmules are mentioned, but it seems Darwin did not think these concepts were the final answer to explain the variation among individuals. It is interesting to speculate how Darwin might have revised his thinking if he had been aware and understood Mendel s conclusions on the transmission, segregation, and independent assortment of traits from parents to their offspring. Summaries of the origin and rediscovery of Mendelism are given by Olby (1985) and Anonymous (1950). Abbreviations: GCA, general combining ability; MAS, markerassisted selection; QTL, quantitative trait locus; SCA, specific combining ability. Quantitative genetics did not have an easy beginning. At the time Mendelism was rediscovered, vigorous debates were ongoing either supporting or discrediting Darwin s theory of natural selection. The main point of contention was whether evolution of species was because of either continuous or discontinuous variation. Both viewpoints had very strong, forceful supporters. The debates were often so contentious that friendships and research were sometimes discontinued because of the opposing views. Rediscovery of Mendelism did not resolve the differences and, in some instances, reinforced the differences. Because Mendelism proposed particulate factors of inheritance, the group (Bateson, devries, Galton, etc.) that supported discontinuous variation saw this as supporting their view, whereas, for example, Weldon, Pearson, Yule, Fisher, etc. believed Mendelism was compatible with Darwin s ideas of continuous variation in evolution. Yule (1906) seems to have been one of the earliest to recognize that Mendelism was compatible with the inheritance of quantitative traits. Provine (1971) suggested that the antagonisms between individuals supporting the relative importance of continuous vs. discontinuous variation in evolution caused a delay of more than a decade in recognizing that the concepts of Darwin and Mendel were complementary. Provine (1971) has summarized the early history in the development of population genetics. Genetic studies on different organisms were immediately implemented (or modified if started before 1900) in Europe and the United States with the experimental results being interpreted by the concepts of Mendelism. It became obvious, however, that not all traits could be classified in discrete classes, based on phenotypic differences. The number of genetic factors became greater as further research was conducted (e.g., Nilsson-Ehle, 1909, studies in wheat [Triticum aestivum L.] and oat [Avena sativa L.]). It was obvious that a different approach was needed to provide genetic information useful to plant improvement for many economically important traits that were quantitatively inherited. R.A. Fisher, Sewall Wright, and J.B.S. Haldane developed the theory necessary for the study of quantitative traits. The mathematical and statistical skills needed to comprehend and understand the theory, however, were limited to a relatively small group of individuals. Plant breeders were effectively developing improved cultivars by mass selection, pedigree selection, and progeny testing methods because large number of individuals could be grown and evaluated in a limited area. This was not the case for animal breeders. They had larger individual selection units that required more extensive facilities and care than plants. Hence, animal breeders and geneticists embraced the concepts sooner than the plant scientists. At that time, the majority of the plant breeders were either not trained or did not have an appreciation of the impact that the theory could have on plant breeding methods. Under the leadership and training of W. Castle, S. Wright, J. L. Lush, and others, ani- S-6 INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007

mal breeders employed the theory to study the inheritance of traits and developed breeding methods to enhance selection. Lush (1945, 1994) and Li (1976) also provided texts that made the theory of population genetics more understandable for the animal breeders. The basic concepts for the inheritance of quantitative traits developed by Fisher, Wright, and Haldane introduced new terms that are basic in today s vocabulary; for example, average effect of an allele, average effect of an allele substitution, covariance of relatives, additive genetic variance, variance due to dominance deviations, nonadditive variance, inbreeding coefficients, path coefficients, and epistasis. Some of the terms were similar to those used in the study of classical Mendelian studies, but they were defined in a different manner. The terms used in quantitative genetic analyses were based on statistical models via the regression of phenotype on genotype. Consequently, skills in mathematics and statistics were necessary to comprehend the basic concepts presented by Fisher, Wright, and Haldane. But the basic concepts for both classical genetics and quantitative genetics were based on Mendelism. Although there were differences among Fisher, Wright, and Haldane on the relative importance of specific items (e.g., epistasis and dominance) in evolution, these three individuals provided the basic framework for determining the relative importance of different genetic effects on the inheritance of quantitative traits. Selection, natural or by humans, was based on continuous variation with replacement of unfavorable alleles by more favorable alleles and accumulation of modifiers in support of the more important alleles. Quantitative Genetics Plants Greater interest in determining the types of genetic effects important in the inheritance of quantitative traits of plants occurred after World War II. This effort was generated initially by scientists in the United Kingdom and at North Carolina State University followed later by scientists at Iowa State University and the University of Nebraska. The delay, or limited interest, in quantitative genetic studies in the United States was, in my judgment, because of emphasis given to developing breeding methods for maize hybrids. In 1922, the U.S. Department of Agriculture and state agricultural experiment stations initiated comprehensive hybrid maize breeding programs throughout the United States. Interest was great in developing the new type of maize cultivars during the 1920s and 1930s. By 1950 nearly 100% of the U.S. maize area was planted to doublecross hybrids. Empirical methods were used to determine the more efficient methods for identifying inbred lines that became parents of the successively better hybrids. Formal quantitative genetic studies were not important factors in developing the inbred-hybrid concept, but the terms additive and nonadditive effects were used for interpreting hybrid prediction models (Jenkins, 1934), characterization of inbred lines performance in hybrids for general (GCA) and specific (SCA) combining ability (Sprague and Tatum, 1942), and types of testers that would emphasize selection for GCA (Jenkins, 1940) and SCA (Hull, 1945) in recurrent selection programs. The interest in maize hybrids and breeding methods to develop inbred lines and hybrids captivated the plant breeding community during the 1920s and 1930s because of the extensive number of breeding programs and the new type of cultivars (i.e., hybrids) for the maize producers. Maize continued to have an important role of increasing the level of interest in quantitative genetics during the 1950s: (i) maize hybrids had become a reality, but what was the genetic basis of heterosis expressed in crosses produced from inbred lines; and (ii) maize breeders realized that if continued genetic advances were to be achieved, other methods were needed to upgrade the germplasm sources used to derive inbred lines. Because future maize breeding efforts were dependent on these two questions, research and discussions centered on trying to resolve these issues. A conference held at Iowa State University in 1950 summarized the different view points on the types of genetic effects that were important in the expression of heterosis, mating designs to estimate the relative importance of different genetic effects in maize populations, and selection schemes to enhance germplasm (Gowen, 1952). Information presented, both theory and data, was either directly or indirectly related to the types of genetic effects important in heterosis and breeding methods related to developing lines and hybrids. No information, for example, was presented on the relative importance of additive and nonadditive variances in maize populations. There were differences of opinion, but the conference set the research agenda in maize for next 30 yr. An update on the status of research related to heterosis and its genetic basis for plants in general was held in Mexico City in 1997 (Coors and Pandey, 1999). After 50 yr the genetic basis for the expression of heterosis in crosses was similar to 1950: interactions of alleles either within the same loci or among loci were necessary. Issues related to dominance vs. overdominance were emphasized at the 1950 conference whereas epistasis was emphasized at the 1997 conference. Although maize continued to be emphasized in quantitative genetic studies, K. Mather at Birmingham and H. F. Robinson at North Carolina State University generated greater interest in the study of quantitative traits in different plant species. The methods used by the two were different, but they were leaders at their respective organizations. Biometrical Genetics by Mather (1949) is the first book that I am aware of that emphasized the estimation of genetic components of variance for plant populations. Biometrical Genetics was a concise primer for explaining the basis of quantitative genetic analyses and included data to INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007 S-7

demonstrate the estimation of genetic components of variance, average level of dominance, heritability, heterosis, and number of effective factors affecting the inheritance of traits. The 1949 edition and subsequent editions (1971, 1982) of Biometrical Genetics never received the credit, in my judgment, that they deserved. The main criticism was that Biometrical Genetics was not general; it was applicable for only the special case of equal allele frequencies; i.e., p = q = 0.5. The so-called special case, however, is applicable for the most widely used breeding method for cultivar development, that is, pedigree selection. Pedigree selection usually, but not always, is initiated within F 2 populations generated from crosses of pure-line parents: allele frequencies would be p = q = 0.5 for all segregating loci. Although Biometrical Genetics lacked generality it certainly was a readable and useful source in the 1950s for students of plant genetics and breeding. H.F. Robinson was the driving force in the establishment of an extensive center for quantitative genetic studies at North Carolina State University in the 1950s. He was an aggressive administrator who recruited an excellent faculty and forcefully monitored all aspects of the programs. Robinson s original interests were in maize, but he encouraged geneticists and plant breeders in all crop species to conduct quantitative genetic studies to understand the mode of inheritance for the major traits of their respective crop species. His impact on the interest of quantitative genetics in plant sciences was because of his leadership in what he considered its importance for future improvements needed for plant breeding methods to develop improved cultivars. Robinson also was the leader in organizing the first international plant quantitative genetic symposium held at Raleigh, NC, in February 1961 (Hanson and Robinson, 1963). Another important factor for providing a greater understanding the basis of quantitative genetics for plant breeders was the book Introduction to Quantitative Genetics written by Falconer (1960). The early works by Fisher, Wright, and Haldane were published in scientific journals that were not easily available and in a form that was not easily understood by practicing plant breeders. An earlier book by Kempthorne (1957) was available, but it included primarily a rigorous mathematical treatment of the theory for the topics related to quantitative genetics. Falconer s (1960) book included topics important to an understanding of quantitative genetics without rigorous proof, data illustrating important points, and discussion of research related to the topics. Falconer s (1960) book and succeeding editions have become the standard text for plant scientists who are not mathematically inclined to have a better appreciation of the various topics related to the inheritance of quantitative traits. The golden era for interest in quantitative genetics was from 1950 to 1975. Classes were developed that emphasized the methods for study of quantitative traits and were well attended by students majoring in plant and animal breeding. The graduate students enrolled in the classes were to form the future cadre of plant breeders. In several instances, they were very fortunate to be exposed to some very talented instructors who had contributed to the developing theory and techniques for the study of quantitative traits. Personally, I can recall the stimulating and informative classes taught by C.C. Cockerham, J.E. Legates, and R.H. Moll at North Carolina State University and by J.L. Lush, O. Kempthorne, and G.F. Sprague at Iowa State University. Each individual was an important contributor to the study of quantitative genetics and was enthusiastic about how the topic could contribute to the future of animal and plant breeding. Quantitative Genetics and Plant Breeding The ultimate goal of plant breeding is to develop cultivars that have consistently good performance for the primary traits of interest. Primary traits will vary among crop species over time, but the ultimate goal remains the same. To attain this goal, it is essential that plant breeders use all of the information and techniques that are at their disposal. Many of the traits that are important in cultivar development are quantitative; for example, grain and forage yields. Although progress had been made in cultivar development in most crop species since the rediscovery of Mendelism, further genetic progress required more information on the inheritance of the primary traits and associations with other traits needed in improved cultivars. Quantitative geneticists believed they could enhance breeding methods if the inheritance of quantitative traits was better understood. Generally, the basic concepts were accepted and incorporated with the previously used breeding methods. But there were skeptics. Some of the assumptions (random mating populations, linkage equilibrium, two alleles per locus, no epistasis, etc.) used by the quantitative geneticists in developing the theory and methods of estimation did not seem realistic to practicing plant breeders. Initially, greater efforts were given to studies related to types of gene action important in maize populations because of the inbred-hybrid maize breeding methods; how does information relate to other crop species? Although the theory for the study of quantitative traits was based on Mendelism, it seemed to many that the assumptions used in their derivations were not realistic for the plant breeding. Consequently, there were those who questioned if the information derived from quantitative genetic studies was applicable to the development of improved cultivars. To paraphrase Dudley and Moll (1969), plant breeding includes three stages: identify or create pools of germplasm, select superior individuals from the chosen germplasm, and develop a superior cultivar from the selections. And, a fourth stage would be to intermate the superior individuals to upgrade the original germplasm pool (i.e., some type of S-8 INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007

cyclical selection). Estimates of the relative importance of the types of genetic variation and heritabilities are of value in making decisions for all stages. Dudley and Moll (1969), Moll and Stuber (1974), and Dudley (1997) have emphasized that information on the inheritance of quantitative traits have application to planning breeding strategies for cultivar development. Quantitative genetic studies, therefore, were conducted to answer specific questions relative to germplasm sources, what types of genetic effects were important, and how can selection methods be modified to enhance cultivar development and upgrade our germplasm pools. Several of the earlier quantitative genetic studies were conducted with maize populations. Why? Two questions were of primary concern: (i) what is the relative importance of additive, dominance, and epistatic effects in the expression of heterosis; and (ii) why does it seem a yield plateau has been attained with the use of double-cross hybrids. Although extensive research has been reported for the past 50 yr, definitive answers to the first question are still not resolved (Gowen, 1952; Coors and Pandey, 1999). And probably never will be generally. Each hybrid is a unique cross between two or more parents. The relative importance of the different genetic effects are probably different, or unique, for each cross. We know that interactions of alleles at each locus (dominance) and between loci (epistasis) must be important because in maize predictability of hybrids, based on inbred line performance, tends to be poor or inconsistent. For the second question, it was found that estimates of additive genetic variance were two to four times greater than estimates of variance due to dominance deviations in maize (Hallauer and Miranda Fo, 1988). Hence, selection should be effective. The problem was that the maize breeders were resampling the same germplasm pools and one would not expect any significant genetic changes if adequate sample sizes were used initially. Hence, recycling methods were suggested to increase the frequency of favorable alleles for the primary traits of interest (Jenkins, 1940; Hull, 1945; Comstock et al., 1949). Interest and appreciation of the tenets of quantitative genetics, however, expanded rapidly in field crops, forestry, and horticultural species (Stalker and Murphy, 1992). Terms that were foreign to plant breeders before 1940 were included in the lexicon of plant breeding research by 1970. Important topics in plant breeding and selection methods that were either directly or indirectly impacted by either theory or data of quantitative genetic studies included nearly all aspects of plant breeding. Some information may have had greater impact for specific crop species but most was applicable for nearly all plant species. Details among plant species varied because of mode of reproduction, ploidy levels, and traits of greater importance, but adjustments were made to adapt to specific situations. A few examples where information from quantitative genetic studies contributed to increasing the effectiveness and efficiency of plant breeding are briefly discussed. Heritability Lush (1945) defined heritability (h 2 ) either as the ratio of the additive genetic variance (σ 2 ) to the phenotypic variance (σ 2 ) or as the ratio of the total genetic variance P (σ2 ) G A to the σ 2. The ratio, P σ2 A /σ2, was designated as P h2 in the narrow sense, whereas σ 2 G /σ2 was designated as P h2 in the broad sense. These definitions provide information for specific situations (e.g., mass selection) but they have limited generality in plant breeding. Because of the range of possible situations in different plant species, estimates of heritability are applicable for specific breeding methods. Types of progeny (individuals, half-sib, full-sibs, S 1, S 2, etc.) and extent of testing (number of replications and environments) would impact the estimates of heritability. All estimates of heritability are specific for each population for the combination of genetic and phenotypic variance estimates. Hanson (1963), Nyquist (1991), and Holland et al. (2003) have discussed the factors that are important in determining estimates of h 2 in plant populations. Estimates of h 2 can be obtained from mating designs imposed on a population that provide estimates of variances; these estimates can be used to calculate estimates of h 2 for different combinations of progenies and testing conditions. Estimates of h 2 also can be obtained from evaluation trials where progenies developed from a population that is under some type of recurrent selection. The estimates of h 2 are based on progeny means from the ANOVA. An example that illustrates how estimates of h 2 can vary is with the evaluation of different types of progenies that can be used in recurrent selection (Lamkey, 1992). For grain yield in maize, assume progenies are a random sample from a population evaluated in two replications at four locations within 1 yr for different possible types of progenies. Progeny-mean heritabilities usually are 0.45 to 0.55 for half-sibs, 0.50 to 0.65 for full-sibs, 0.70 to 0.85 for S 1 progenies, and 0.80 to 0.92 for S 2 progenies. The relative magnitudes of the h 2 estimates reflect the σ 2 A among the half-sib [(1/4)σ 2 ], full-sib A [(1/2)σ2 ], S A 1 (σ2 ), A and S 2 [(3/2)σ 2 ] progenies. The relative A h2 estimates also would vary if different combinations of replications and environments were used. The range of the h 2 estimates for the same progenies tested in two replications at four locations reflects the differences among years when progenies were tested (e.g., different cycles of selection), in which there are differences in estimates of experimental errors and genotype by location interactions. Estimates of h 2 for maize grain yield on an individual plant basis at one location are usually less than 0.10. Summaries of the basic definitions to estimate h 2 in plant populations are given by Nyquist (1991) and Holland et al. (2003). INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007 S-9

Prediction of Genetic Gain Predicting genetic gain (Δ G ) is of interest to determine what future gains can be anticipated within a given program and for making comparisons among different selection methods for a specific set of genetic and environmental parameters. Genetic gain is determined as h 2 (X X ), where h 2 is the heritability estimate and (X X ) s s is the selection differential or difference between the mean of the selections (X ) and the population mean (X ). Similar to h 2 estimation, several factors can affect Δ G s because h 2 is an important component. If a specific mating design is imposed on a population, the estimates of genetic and environmental variances can be used to determine Δ G for different sets of conditions with use of different types of progenies. Data from the combined ANOVA of the evaluation trials also can be used to calculate h 2 for the selection method being used (Smith et al., 1981), which then is used to predict Δ G for the next cycle of selection. If one is initiating a selection program and desires to determine which type of progenies to use in selection, estimates of variances for the population of interest would be needed. Because of the different types of progenies that can be used in selection, the types of progenies used for recombination between cycles of selection and the number of years required to complete each cycle of selection can affect Δ G. Eberhart (1970) and Empig et al. (1972) developed comprehensive Δ G formulae that could be used to make valid comparisons among different selection methods. Eberhart (1970) proposed that Δ G = (kcσ 2 )/yσ, where k is a function of selection intensity, c is parental control, σ 2 is addi- G P G tive genetic variation among progenies, y is the number years per cycle of selection, and σ P is the square root of phenotypic variance. With the use of Eberhart s formula, direct comparisons can be made among selection systems. But estimates of genetic and environmental variances would be needed to calculate h 2. Types of Hybrids The inbred-hybrid concept proposed by Shull (1910) had a profound effect on breeding methods for maize as well as for other plant species. Shull proposed the use of single-cross hybrids. Because of the limitations of poor vigor and grain yields of the inbred lines and cultural practices at that time, use of single-cross hybrids did not seem feasible. After the suggestion of Jones (1918) to produce double-cross hybrids, maize research emphasized use of double-cross hybrids which were grown on nearly 100% of the U.S. maize area by 1950. By 1960, there was some interest in use of single-cross hybrids because it seemed grain yields of double crosses had plateaued. Also, because of recycling of inbred lines via pedigree selection, inbred lines were more vigorous, easier to maintain, and had greater grain yields than the initial lines developed from open-pollinated cultivars. With the more vigorous inbred lines and developments in cultural practices and equipment, it seemed production of single-cross hybrids at costs acceptable to the growers was more feasible than in 1910. A few single-cross hybrids (e.g., B37 Oh43) were tested, produced, and grown in late 1950s and early 1960s. Empirically, it seemed that breeding methods would be simpler for single crosses than for double crosses. At the time discussions were being made for a change in type of hybrids, Cockerham (1961) showed theoretically that selection among single crosses would be twice as effective as selection among double crosses if only additive genetic effects were considered. If nonadditive effects (dominance and epistasis) were important in the genetic variances among types of hybrids, the advantage of selection among single crosses rather than among double crosses would be even greater. Rapid changes were made in types of hybrids provided to the growers, and by 1980 nearly 100% of the U.S. maize acreage was planted to single-cross hybrids. The theoretical information on genetic variances among types of hybrids supported the empirical evidence in breeding programs that caused a rapid, and significant, change in providing better hybrids to the producers. The use of recycling breeding methods for improvement of inbred lines to produce single crosses has resulted in consistent genetic advance of U.S. maize hybrids since 1960 (Troyer, 2006). Estimation of Epistasis Interactions between alleles at different loci were detected in early genetic studies and were designated as epistasis. For quantitative traits it was obvious that epistatic effects had to exist because of the large number of loci assumed for their expression. Cockerham (1954, 1956, 1961) developed the theory of including epistatic effects in the covariances of relatives and mating designs and analyses for the estimation of the epistatic components of variance. Estimates of the relative importance of epistatic variances to additive and dominance variances, however, have been generally futile in maize (Eberhart et al., 1966; Chi et al., 1969; Wright et al., 1971; Silva and Hallauer, 1975; Wolf and Hallauer, 1997). Silva and Hallauer (1975) used the Cockerham (1956) model in a study that included 800 full-sib progenies developed from parents at two levels of inbreeding (F) using the North Carolina Design 1 (F = 0, 480 fullsibs) and Design 2 (F = 1, 320 full-sibs) mating designs within the Iowa Stiff Stalk Synthetic maize population. The 800 full-sibs were evaluated in two replications at six environments. Estimates of epistatic variances were in most instances unrealistic (often large, negative estimates). The estimates of additive and dominance variances accounted for more than 90% of the total genetic variance for most traits. Our inability to estimate genetic components of epistatic variance in maize does not imply that epistatic effects are either absent or unimportant in the inheritance of quantitative traits. There is evidence that epistatic S-10 INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007

effects are present. Fasoulas and Allard (1962), Russell and Eberhart (1970), and Russell (1971) used factorial analyses to estimate the epistatic effects of genetic markers at individual loci measured in their phenotypes. Gamble (1962), and others, compared different generations from crosses of pure lines detected significant estimates of epistatic effects for all traits. Bauman (1959), Moreno-Gonzalez and Dudley (1981), and Melchinger et al. (1986) compared different types of hybrids, based on their genetic expectations, and reported significant estimates of epistatic effects for all traits they studied. All of these studies used a generation mean type of analyses. The models used to estimate epistatic components of variance have either been inadequate or the wrong statistical analyses were used. It seems that because the coefficients of the epistatic components of variance are multiples of the coefficients of the additive and dominance components of variance that independent estimates of the epistatic components of variance are compromised, similar to situations discussed by Hayman (1960) for the estimation of genetic effects via generation mean analyses. It seems reasonable to assume because of the number of genes that affect quantitative traits that epistatic effects could be as important as the additive and dominance effects. Holland (2001) has presented a comprehensive discussion of the issues related to and how epistasis affects plant breeding and selection systems. Selection Indices Multiple-trait selection is the norm in plant breeding. Cultivar development must meet the demands (or needs) of the producer for target environments. Breeders of different crop species will have different strategies for the primary trait(s) of interest, but the main goal will be to balance the relative importance given in selection among the different traits. For example, a new cultivar may have superior yield to the cultivars used by the producers, but if the higher yielding cultivar has deficiencies (or acceptable levels) for resistance to common pests, poor heat and drought tolerance, and poor stalk and root strength and matures late relative to target environments, it may not be acceptable to the producers because of the risks involved in production. Initially, plant breeders closely observed their selections and by either intuition and/or experience (art of plant breeding) developed cultivars that approached their perceived matrix of traits that met their breeding objectives. Personal bias and the specific combination of environments used during breeding and selection may, however, lead to cultivars that may not have been acceptable generally. Ultimately, plant breeders strive to attain the proper combination of traits (Baker, 1986) and selection methods (Moreno-Gonzalez and Hallauer, 1982; Gallais, 1997) that result in cultivars that have superior, stable performance over time and space. The difficulty is the relative weights given to each trait during breeding and selection. Smith (1936) and Hazel (1943) suggested methods to increase the effectiveness and efficiency of multiple-trait selection. These indices required information on the genetic variability of traits, correlations between traits, and relative economic weights for the different traits (Lerner, 1958). Estimates of genetic variances for each trait and correlations between traits could be obtained for specific populations and the estimates (along with economic weights) used to construct selection indices, which would be applicable to the source populations. These types of indices have been constructed and used for specific situations, but they would depend on the gene frequencies for the specific populations from which the estimates of genetic variances and correlations were obtained. If, for example, selection was effective, one would expect changes in gene frequencies, and the initial index may not be applicable in future cycles of selection. Plant breeders work with several populations simultaneously and the construction of the complex indices for each population may not be applicable or possible. Simpler selection indices have been developed and used in plant breeding. Smith et al. (1981), for example, used h 2 estimates from the ANOVA of evaluation trials of recurrent selection experiments as weights in developing a simpler selection index. Smith et al. (1981) assumed correlations between the traits of interest had either small or zero correlations. In maize, for example, one type of index may be: Y = h 2 (X ) + 1 1 h2 ( X ) + 2 2 h2 ( X ) + 3 3 h 2 ( X ), where Y is the index value, 4 4 h2 values are heritability i estimates on progeny mean basis for yield (X 1 ), grain moisture at harvest (X 2 ), and root (X 3 ) and stalk (X 4 ) lodging, and X i s have coefficients of 1 for yield and 1 for the other traits. The goal is to identify selections that have greater yields, and the least grain moisture and root and stalk lodging. Other simpler selection indices have been used in plant breeding, including the multiplicative index by Elston (1963) [I = (X 1 k 1 )(X 2 k 2 ) (X i k i ), where X i are traits of interest and k i is the minimum acceptable value for each trait] and the rank summation index by Mulamba and Mock (1978) m I = R [1] j= 1 i( j) where R (i)j is the observed ranking of the jth trait for the ith family. Compton and Lonnquist (1982), for the multiplicative index, and Mulamba and Mock (1978), for the rank summation index, have discussed use of the two indices in maize selection programs. Baker (1986) has provided an excellent summary of the theory of selection indices, their construction and use, and the relative advantages and disadvantages of the different types of selection indices that have been suggested and used in plant breeding. Bernardo (1991a) also suggested use of retrospective index weights for use in plant selection. Early Testing It soon became evident to maize breeders that it was easier to develop inbred lines than to determine which inbred INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007 S-11

lines had above average combining ability in hybrids. This was of particular importance when use of double-cross hybrids was emphasized. If, for example, one had 10 new inbred lines, there are 45 possible single crosses, 360 possible 3-way crosses, and 630 possible double crosses (excluding reciprocals). During inbreeding, selection was done for phenotypic traits deemed important, but no evaluation for combining ability in crosses was done until lines were relatively homozygous. Jenkins (1935) and Sprague (1946a) suggested testing for combining ability in earlier generations (S 1 or S 2 ) of inbreeding to reduce costs of continued inbreeding within lines that had below average combining ability. Inbreeding and selection would be continued only for those lines that exhibited above average GCA. Jenkins (1935) and Sprague (1946a) included empirical data in support of their concept of early testing. But the concept of early testing was not viewed favorably by all maize breeders. Bauman (1981), from a survey of 130 maize breeders, found that initial testing of generation inbred lines for combining ability was 51% for S 2 and S 3 generations and 49% for those who evaluated new lines for combining ability at the S 4 (27%), S 5 (9%), and later (13%) generations of inbreeding. Some maize breeders were concerned that lines may be discarded on the basis of early testing that would be acceptable after further inbreeding and selection, which may be true. Jenkins (1935) and Sprague (1946a) did not suggest, however, that the ranking of lines for GCA would be exact; they only wanted to emphasize selection on lines that expressed above average combining ability. Rodriguez and Hallauer (1991) also reported data that supported the concept of early testing. They tested a group of full-sib families from S 0 to S 4 generations. The 20% of greatest yielding S 0 crosses were not always in the 20% greatest yielding S 4 crosses, but the majority had above average yields. For the 20% poorest yielding S 0 crosses, none were above average for yield in the S 4 crosses. Hence, the poorest S 0 full-sib families did not have above average yield at the S 4 generation full-sib families. The debate relative to the effectiveness of early testing was usually one of the main topics of discussion at maize breeding workshops and conferences during the 1940s and 1950s. It seems, however, that early testing is an important strategy in present-day breeding programs, both for developing pure lines and hybrids. Early testing (S 0 and S 1 ) is used in recurrent selection programs and evidence suggests early testing has been effective in population improvement (Hallauer, 1992; Stalker and Murphy, 1992; Pandey and Gardner, 1993). Inbred lines (B14, B37, B73, B84, B97, B104, B110, etc.) were identified on the basis of early testing programs and the inbred lines have had a major role either as parents of hybrids or breeding germplasm in the U.S. Corn Belt and other temperate maize production areas. Bernardo (1991b, 1992) has shown that the effectiveness of early testing is limited mainly by nongenetic causes. He reported that the covariance between S n and S n testcrosses is equal to the genetic variance among S n testcrosses. The genetic correlations between S n and S n testcrosses (TC) becomes r GnGn = CovTC n, TC n /[(Var TC n )(Var TC n )] 0.5 or r GnGn = [(1 + F n )/(1 + F n )] 0.5. He reported that the genetic correlation between testcrosses of individual S 0 plants or S 1 progenies and their directly descended homozygous lines is 0.71. Correlations for most testcross comparisons exceeded r = 0.90. Lile and Hallauer (1994) practiced intense selection among and within maize progenies during inbreeding. Testcross trials were conducted at four locations at the S 2 and S 8 generations. Genetic correlations between the S 2 and later generations were 0.97 for BS13(S2)C1 and 0.86 for BSCB1(R)C7 populations, suggesting that early testing at the S 2 generation was effective in discriminating among these lines for relative combining abilities in later generations of inbreeding. It seems the concept of Jenkins and Sprague has been validated, and that testing before the S 3 generation is currently used in most present-day plant breeding programs. Diallel Mating Design The diallel mating scheme is probably the most frequently used mating design in plant research and is an excellent scheme to determine how parents perform in crosses. The diallel mating design has many useful purposes if analyzed and interpreted correctly (Hinkelmann, 1977; Baker, 1978). As the name implies, n(n 1)/2 crosses are produced between n parents, excluding reciprocals. If n = 10 there are there are 45 crosses; if n = 20 there are 190 crosses, and if n = 100 there are 4950 crosses. Because of the logistics in producing and evaluating the crosses between parents, the number of parents included in the diallel mating design usually includes less than 20 parents. There are options of the entries included in evaluation of the diallel mating design (Griffing, 1956; Hallauer and Miranda Fo, 1988). Usually, the main emphasis is to estimate the relative GCA effects of the parents in crosses and the SCA effects for specific crosses of the parents. In applied breeding programs, the estimation of the GCA and SCA effects can be very informative in the evaluation of, for example, inbred lines in hybrids (Sprague and Tatum, 1942). Another instance of effective use of the diallel crossing designs is to evaluate cultivars in crosses to identify possible new heterotic groups (Kauffman et al., 1982). The parents and crosses are evaluated to estimate GCA and SCA effects and heterosis of the parents vs. crosses (Gardner and Eberhart, 1966). Other combinations and analyses can be used depending crop species and objectives of the investigator. Estimates of genetic effects are appropriate for most diallel mating systems, but often investigators desire to extend estimation to include genetic components of variance and heritabilities. In most instances, the reference population either is not adequately sampled or the parents included are not from the same population. Estimation of components of genetic variances requires an adequate sample of individuals (n > 100) S-12 INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007

from a reference population to obtain estimates with reasonable standard errors (Marquez-Sanchez and Hallauer, 1970). A group of pure-line cultivars (say n = 10) may be included in diallel crosses that have different origins (in some instances origin may not be known) and the reference population for the interpretations of the components of genetic components would be nebulous, unless one considers that the estimates apply to the entire crop species. The expectations for GCA (covariance half-sibs) and SCA (covariance full-sibs minus two covariance half-sibs) include the covariances of relatives which have genetic components of variances. The options for use of the diallel mating design to estimate components of genetic variance would be either to include different sets of diallels whose parents are sampled from the same population and data are pooled over sets or use of the partial diallel where a greater number of parents can be included but not all possible crosses (Kempthorne and Curnow, 1961). If a cross classification mating design is preferred, then the North Carolina Design II would be a good option for estimation of components of variance (Cockerham, 1963); a greater number of parents is included to produce a fewer number of crosses, compared with a diallel mating design. The diallel mating systems are good designs. They have been used in plant research more frequently than any other mating design, but often genetic components of variance, genetic correlations, heritabilities, and predicted gains have been reported for instances of either inadequate sample sizes or parents were selected that did not represent a specific population. Estimates of GCA and SCA effects are appropriate and very useful genetic parameters of the parents and their crosses. No apologies are needed if one is unable to estimate correctly genetic components of variance. Recurrent Selection Methods Most of the economically important traits emphasized in plant breeding require breeding strategies that employ a range of techniques to determine the relative genetic worth of progenies via different screening techniques to develop and improve germplasm sources. Recurrent selection methods were designed for the genetic improvement of quantitative traits. Because it is assumed quantitatively inherited traits are affected by an unknown number of genetic factors, each having a small effect on trait expression, and whose effects are affected by environmental effects, methods to increase the frequency of the favorable alleles were needed. Recurrent selection, as the name implies, is a breeding method that is conducted repetitively. The time frame of recurrent selection methods is not predetermined. They are conducted for the lifetime of a breeding program to provide systematic genetic improvement of the programs germplasm resources (Hallauer, 1985). Quantitative genetic studies have had a major role in the development of recurrent selection methods. Because of the nature of the traits, selection within populations has been of interest to determine the nature of the genetic changes and how effective the selection methods are in modifying allele frequencies. The original suggestions of Jenkins (1940), Hull (1945), and Comstock et al. (1949) were based on what each author considered were the more important genetic effects in selection within and between maize populations. The concepts of recurrent selection, however, have been modified and adapted for different traits in a number of field crops, horticulture crops, and forestry (Gilmore, 1964; Hallauer and Eberhart, 1970; Brim and Stuber, 1973; Fehr and Ortiz, 1975; Rowe and Hill, 1981; Marquez-Sanchez, 1982; Sorrells and Fritz, 1982; Frey et al., 1988). The major goal remains the same in all instances; increase the frequency of favorable alleles for the primary trait(s) of interest for the target environments of the breeding program. Recurrent selection programs have been conducted to determine relative effectiveness of different selection methods (e.g., Doggett and Eberhart, 1968; Tanner and Smith, 1987), effectiveness of individual plant selection based on evidence that additive genetic variance of major importance (e.g., Gardner, 1977), direct and correlated responses of traits considered important in cultivar development (Hallauer et al., 2004), the relative importance of different genetic effects, etc. Recurrent selection systems can contribute to cultivar development, both directly and indirectly (Eberhart, 1972). Although recurrent selection systems have been conducted to obtain basic information relative to the types of genetic effects that can be emphasized to improve quantitative traits, cultivar development remains the primary goal of all plant breeding research. Eberhart (1964) and Smith (1979) have provided methods to enhance the genetic information we can derive from long-term recurrent selection studies. Documented evidence of the recycling within pedigree selection systems used within most breeding programs is limited (Duvick, 1977), but the genetic improvements made in cultivar development via pedigree selection methods during the past 60 yr have been significant in nearly all crops. When and where appropriate, the more effective use of cyclical selection systems (germplasm improvement and pedigree selection) is to integrate them within breeding programs rather than treat them as separate entities. Cyclical selection methods are used, and needed, to genetically improve quantitative traits. Quantitative geneticists have contributed to the theory of recurrent selection systems and plant breeders have applied the theory to develop systems for their specific situations. In nearly all instances, recurrent selection systems have been effective to improve germplasm resources and cultivars for use by the growers (Stalker and Murphy, 1992). Heterosis The expression of heterosis in hybrids has been exploited in many different plant species (Coors and Pandey, 1999). Because of the interests in determining the types of genetic INTERNATIONAL PLANT BREEDING SYMPOSIUM DECEMBER 2007 S-13