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breeding, crossbreeding, and selection are essential features of any plant

breeding program. A primary objective of quantitative genetic research is

an understanding of the genetic consequences of such manipulations.

A basic premise of quantitative genetics is that the genes that affect quantitative traits follow the same laws of transmission as genes that affect qualitative traits. Usually many loci with small individual effects are involved;

therefore, it is necessary to study these traits through statistics appropriate

for continuous variables, such as means, variances, and covariances. Fisher

( I 918) provided the initial framework for the study of quantitative inheritance. Since that time, his developments have been clarified, elaborated,

and extended by numerous geneticists and statisticians. Unfortunately, the

experimental aspects of quantitative genetics have lagged behind theory.

Because it is difficult to design quantitative genetic experiments with definitive alternative hypotheses, many of the experimental conclusions have

been reached from the experience of numerous individual empirical investigations that have shown similar results.

Most of our emphasis will be concentrated on reviewing and interrelating

recent research results in areas of most significance to plant breeders, such

as ( 1 ) kinds of genetic variability found, (2) effects of inbreeding and

crossbreeding, ( 3 ) genotype-environmental interaction, and (4) selection

methodology and response. It is not our purpose to present a detailed description of quantitative genetic theory. Cursory summaries (using nomenclature from Falconer, 1960) are included to provide background

for readers untrained in quantitative genetics and to aid in understanding

results from experimental research.


Genetic Variability


Evaluations of inheritance mechanisms in quantitative genetics research

depend on valid assessments of genotypic values. However, the genotypic

value of an individual must be ascertained from measurements made on

its phenotype. Phenotypic value then, is defined as the performance of

a particular genotype in the environment in which it is grown. The two

components of the phenotypic value (P)-genotypic value ( G ) and environmental deviation (E)-are

usually represented in the equation for

phenotypic value as: P = G E.

A genotype is considered as the particular assemblage of genes possessed

by an individual, and genotypic value for a given genotype is defined as

the average of all possible phenotypic values, expressed as a deviation from

the population mean. In other words, it is the average phenotypic value




when genotypes are grown over all possible environments (the mean environmental deviation is zero) . Diagrammatically, the relationship between

genotypes and genotypic values for a single locus may be represented as


Genotypic value




f a

In this representation, the origin, or zero point, is midway between the

value of the two homozygotes, and B , represents the allele that increases

the genotypic value. The value, d, of the heterozygote depends on the

degree of dominance. In order to determine the contribution of this locus

to the population mean, values of the genotypes must be weighted by their

respective frequencies. Contributions of each individual locus must be combined in the computation of the population mean.

Estimation of genetic effects and variances requires some type of family

structure. To analyze the properties of a population composed of various

family structures, it.is necessary to deal with concepts concerning transmission of value from parent to offspring. This cannot be done with only genotypic values, because parents pass on their genes, not their genotypes, to

the next generation. Genotypes are created anew by uniting gametes in

each generation. Therefore, a measure is required that allows the assignment of values associated with the genes carried by an individual and transmitted to its offspring, i.e., a measure is needed that reflects the average

effects of genes. The average effect of a gene at a locus is defined as the

average difference resulting from the substitution of one allele for the other.

For example, if B , genes could be changed at random in a population

to B , genes (see the diagram above), the resulting change in value is the

average effect of the gene substitution. Because the average effect of a gene

substitution depends on the gene frequency, it is a property of the population as well as of the gene.

Although the average effects of genes cannot be measured directly,

breeding values, which are weighted functions of average effects of genes,

can be measured experimentally. If an individual is mated with a number

of random individuals from the population, the breeding value is estimated

as twice the mean deviation of its progeny from the population. This deviation must be doubled because only one-half the genes in its progeny are

contributed by the individual being evaluated.

In addition to the breeding value, another component of the genotypic

value that must be considered is referred to as the dominance deviation.

For a single locus, it is defined as the difference between the genotypic

value and the breeding value. Although dominance deviations are within-



locus interactions, their importance depends on gene frequencies in the

population, so they are not simply measures of the degree of dominance.

Most quantitative traits are conditioned by genes at many loci. However,

the aggregate genotypic value may or may not be simply an additive combination of the genotypic values for individual loci. When this combination

is not additive, genes are said to interact or to show epistasis.

The phenotypic value has been expressed as P = G E. Therefore,

the phenotypic variance, up2,may be expressed as:


up2 =


+ +

U E ~

~ U G E

where uG2= genotypic variance, uK2= environmental variance,

covariance of genotypic and environmental effects.

The genotypic partition may be further divided as follows:



where uA2= additive genetic variance, uD2= dominance variance, u12=

epistatic variance.

The additive variance, which is the variance of breeding values, is the

primary measure of the resemblance between relatives and is relevant to

the effectiveness of selection. The objective of selection is to increase the

frequency of favorable alleles in a population by substituting favorable

genes for unfavorable genes. The effectiveness of gene substitution in

changing the population mean is directly related to the average effects of

genes. Average effects, in turn, are reflected in breeding values. The average effect of a gene substitution is actually a weighted regression coefficient

(weighted by gene frequency). Therefore, additive genetic variance at a

single locus may be considered as variance caused by the weighted linear

regression of genotypic values on number of favorable alleles. Dominance

variance, then, is variance attributed to deviations from regression. If the

total variation over loci is larger than the summation of additive and dominance variances for individual loci, the differences will be variance caused

by epistasis.

Resemblance between relatives is reflected in similarities of expression

of quantitative traits. The degree of resemblance expected provides the

basis for estimating genetic variance components. Estimation procedures

require systematic mating schemes that result in different types of relatives.

Using appropriate experimental designs and statistical analyses, design variance components can then be calculated. Genetic interpretations of these

design components are facilitated by translating them into covariances

among relatives. Theoretical considerations of the genetic causes for resemblances between relatives permit the translation of these covariances into

functions of genetic variance components. For example, with the assump-

28 1


tions of no epistasis and an inbreeding level of zero in the population,

the covariance between a parent and its offspring produced from mating

at random in the population is 1/2 uA2,the covariance among half-sibs is

% uA2,and the covariance among full-sibs is '/2 uA2 1/4 uBZ,These relationships change with different levels of inbreeding.

A comprehensive summary of methods for estimating genetic variances

was presented by Cockerham (1963). He also discussed many of the problems and limitations inherent in the definition and estimation of genetic

variances when inbreeding is present. For most cross-pollinated species,

genetic variances can be estimated with mating designs that do not depend

on inbred relatives. However, in many self-pollinators, production of sufficient seed for replicated evaluation trials is nearly impossible without the

use of inbred generations. The development by Stuber (1970) of methods

using inbred relatives has facilitated the estimation of genetic variances

in self-pollinated species.

Diallels and modified diallels are often used to estimate genetic variances. In this type of design, general and specific combining ability components of variance are routinely estimated. The general combining ability

component is primarily a function of additive genetic variance. However.

if epistasis is present, it may include functions of additive types of epistasis.

The specific combining ability component is primarily a function of dominance variance, but it may include all types of epistatic components. The

relative proportions of genetic variances in the two combining ability components depends on the inbreeding level of the parents. Although diallels

can be generated with parents chosen at random from some random mating

reference population, this type of mating design generally has been used

for specific sets of parents. With specific sets, the variance estimates must

be interpreted as characteristic of only the set of parents involved and

should not be used to characterize more broadly defined reference







Excellent reviews of genetic variance estimates available before 1962

for important crop species are given by Gardner (1963) and Matzinger

(1963). Since 1962, a large number of experiments have been reported

which cover essentially all major crop species and many different kinds

of traits. Most of the data reported points to one general conclusion: genetic variability of important agronomic traits is predominantly additive

genetic variance. Nonadditive variance also exists in nearly all species and

for many important traits, but it is generally smaller than additive genetic





Quantitative inheritance of various traits of maize has been studied most

extensively, and studies reported in the literature deal with a wide range

of maize populations. Estimates of genetic variability summarized by

Gardner (1963) and Moll and Robinson (1967), as well as evidence in

several more recent reports, indicate that additive genetic variance exceeds

dominance variance in many different kinds of populations, including

open-pollinated varieties, synthetics, variety hybrids, and variety composites. Furthermore, when sampling errors of variance estimates are considered, it appears that locally adapted open-pollinated varieties have genetic variances of essentially the same order of magnitude. Important

differences in genetic variability seem to occur only between populations

of distinctly different kinds. For example, composite populations formed

by intermating a number of varieties tend to have greater variability than

the parental varieties themselves. Composites of more genetically diverse

populations have greater variances than composites of less diverse populations. Even so, estimates reported for such composites show additive variance to be larger than nonadditive variance for most traits.

Although a number of extensive variability studies have been reported,

epistatic variability has not been shown to be an important component

of genetic variances of maize populations (Chi et al., 1969; Eberhart el

al., 1966; Stuber et al., 1966). Studies of inbred line hybrids of various

kinds, however, frequently reveal significant epistatic effects (Wright et

al., 1971; Russell and Eberhart, 1970; Stuber and Moll, 1971; and others).

Joint consideration of these two kinds of evidence leads to the conclusion

that epistatic interactions must occur in maize populations, but they contribute very little variability beyond that accounted for by additive and

dominance variances.

The patterns seen in variance estimates in many other cross-pollinators

is similar to that reported for maize; however, the data are much less extensive. Although sugarcane presents difficulties for quantitative genetic

studies because of irregular meiosis and mating incompatibilities, estimates

reported by Hogarth (1 97 1 ) indicate that additive genetic variance exceeds

dominance variance, Variance estimates in alfalfa also provide evidence

that additive genetic variance exceeds nonadditive variance, but there is

some evidence for variance caused by trigenic, quadragenic, or epistatic

effects (Dudley et al., 1969). Hill et al. (1972) also report a preponderance of variance caused by general combining ability (which wouId be

largely additive genetic variance) and, although variance caused by specific

combining ability was detected, it was relatively small in magnitude. Significant general combining ability has also been found in several forage

grasses, including Bromus inermis Leyss. (Mishra and Drolsom, 1972;

Dunn and Wright, 1970), Dactylis glumerata L. (Kalton and Leffel,

1955), and Lolium perenne L. (Hayward and Lawrence, 1972).



A series of studies of genetic variability in flue-cured tobacco (a selfpollinator) have also shown that additive genetic variance is predominant

for a number of traits in several different populations. There appears to

be some epistatic variability in certain populations for certain traits, especially plant height and leaf measurements. Dominance variance tends to

be small and usually nonsignificant (Matzinger, 1968; Matzinger et al.,

1960, 1966, 1971). Changes in means after several generations of random

mating were interpreted as evidence for epistasis. Segregation of epistatic

gene complexes may have caused a breakdown of internal balance by

forced intercrossing in a naturally self-pollinated species (Humphrey et

al., 1969).

Genetic variability for a number of traits of soybeans has also been

shown to be predominantly additive, but nonadditive variability is significant for many of the traits (Brim and Cockerham, 1961; Hanson et al.,

1967; Weber et al., 1970). A series of diallel studies involving a number

of pulse crops, such as mungbean, cowpeas, blackgram, and lentil, have

shown significant general combining ability for a number of traits. Specific

combining ability appears to be important for certain traits, but it is usually

less important than general combining ability (Singh and Jain, 1971, 1972;

K. B. Singh and Singh, 1971; T. P. Singh and Singh, 1972). Diallel studies

in small grains, particularly in wheat and oats, and in sorghum have also

indicated that general combining ability for yield and related traits is more

important than specific combining ability, even though specific combining

ability is statistically significant in some instances (Collins and Pickett,

1972; Lee and Kaltsikes, 1972; Ohm and Patterson, 1973a,b; Gyawali et

al., 1968; Walton, 1972; Widner and Lebsock, 1973; and others).

A genetic study of pearl millet by Bains (1971), which used the analysis

proposed by Kearsey and Jinks (1968), found that additive genetic variance was important for three agronomic traits, but epistasis also appeared

to be prevalent. In diallel studies, however, Gupta and Singh (1971) found

the additive component to be nonsignificant for grain yield and ear number

in a study of eight diverse lines of pearl millet. General combining ability

was either smaller than specific combining ability or nearly the same size

in four traits studied by Ahluwalia et al. ( 1962).

Although many diallel studies in cotton indicate that additive variance

is more important than nonadditive types, there are several examples of

deviation from this pattern. For example, Gupta and Singh (1970) reported dominance variance to be larger than additive variance in several

seed and fiber traits. Their study involved eight diverse strains of upland

cotton. Baker and Verhalen (1973) reported similar results in a study of

10 selected upland cotton lines. They also presented an extensive literature

review in which they documented several instances in which additive variances predominated and several in which dominance predominated.




Inbreeding Depression and Heterosis

Inbreeding results from matings between related individuals. The degree

of inbreeding is measured by the inbreeding coefficient, which is the probability that two genes at a locus (in a diploid) are identical by descent.

The effect of inbreeding upon the population mean can be shown to be

a function of the gene frequency, dominance effects, and the coefficient

of inbreeding. If dominance is directional, i.e., the majority of loci show

dominance for the favorable allele, inbreeding will result in a decrease in

the mean proportional to the inbreeding coefficient.

Heterosis, which results from crossing unrelated strains, is the reverse

of inbreeding depression. It also depends upon directional dominance for

its expression. Therefore, inbreeding depression and heterosis both refer

to differences in mean performance directly related to differences in

heterozygosity, and in diploids the level of heterozygosity is directly related

to the coefficient of inbreeding. Inbreeding depression is the decline in trait

expression with decreased heterozygosity, and heterosis is the enhancement

of trait expression with increased heterozygosity.




The relationship between the mean expression and the coefficient of inbreeding tends to be linear for most traits of maize, and yield of grain

shows a steeper rate of depression than other agronomic traits (Sing et

al., 1967). Papers by Levings (1964) and Busbice (1969) show that in

autotetraploids the loss of heterozygosity is not directly related to the inbreeding coefficient, and is much slower than in diploids. Levings et al.

( 1967) reported that the relationship between heterozygosity and performance in autotetraploid maize was linear for three quantitative traits. The

decrease in ear weight relative to the inbreeding coefficient was slightly

less than half as rapid in the autotetraploid as it was for yield of ear corn

in diploid maize studied by Sing et al. ( 1967). Comparison of these results

agrees qualitatively, at least, with theoretical expectations.

A direct comparison of inbreeding effects in crested wheatgrass [Agropyron cristatum (L. ) Gaertn.] suggests that inbreeding depression is

greater than expected at higher levels of ploidy (Dewey, 1966). Forage

yields of self-pollinated progeny for diploids, tetraploids,, and hexaploids

were 35.9, 50.4, and 67.4%, respectively, less than yields of noninbred

progenies. Also contrary to theoretical expectations, diploid and tetraploid

sugar beets (Beta vulgaris L.) were reported to show the same rate of

inbreeding depression (Hecker, 1972). In a study involving diploid and



autotetraploid rye (Secale cereale L.), Lundqvist (1969) found less inbreeding depression in the autotetraploids than in the diploids, but not

as much less as expected from genetic theory.

Inbreeding in alfalfa is accompanied by impaired reproductive fertility,

as well as by loss of vigor and productivity. The relationship between inbreeding coefficient and inbreeding depression was linear for several traits,

and most drastic for yield and spring vigor. The inbreeding rates for yield

and spring vigor approach a theoretical curve for tetragenic inheritance,

whereas plant height approximates the curve for duplex inheritance

(Aycock and Wilsie, 1968).


1 . Genetic Diversify and Heterosis

Heterosis, in quantitative genetic terminology, is usually measured as

the superiority of a hybrid over the average of its parents, and has been

reported for a wide range of crop species, which include both self- and

cross-pollinators.The expression of heterosis is greatly influenced by the

magnitude of genetic differences for some traits, but not for others. For

example, several recent reports of diallel crosses among strains of wheat

show greater heterosis associated with crosses of more distantly related

parents (Fonesca and Patterson, 1968; Widner and Lebsock, 1973; Sun

et d.,

1972). On the other hand, Gyawali et al. (1968) found no evidence

for an increase in heterosis associated with interclass differences between

soft red and hard red parents. A study of crosses of nine strains of tall

fescue (Festuca arundinaceae Schreb) suggests that heterosis increased

with genetic divergence with respect to morphological traits and flowering

time, and also with respect to geographical origin of the parents (Moutray

and Frakes, 1973).

Comparisons of inter- and intraspecific hybrids of alfalfa and cotton

show greater heterosis associated with greater diversity (Sriwatanapongse

and Wilsie, 1968; Marani, 1963, 1968). Heterosis in lint yield of cotton

tended to be associated with a greater number of bolls rather than boll size,

especially in interspecific hybrids, in which boll size was often less than

the average of the parents. A relationship of heterosis to diversity is also

reported for several traits of cotton relating to plant growth, such as plant

height, leaf area index, and dry matter accumulation (Marani and Avieli,


Studies involving interracial crosses of maize and interspecific crosses

of tobacco indicate that the relationship between diversity and heterosis

may not be linear over very wide ranges of diversity. There is considerable

evidence that increased genetic differences between inbred lines of maize

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