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III. Inbreeding Depression and Heterosis

III. Inbreeding Depression and Heterosis

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QUANTITATIVE GENETICS



285



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).



B. HETEROSIS

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,

1973).

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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R. H. MOLL AND C. W. STUBER



result in greater heterosis in their hybrids, More recent studies have involved variety crosses of parents of different geographical origin, and show

that the association of increased heterosis with increased diversity extends

over a considerable range of maize types (Paterniani and Lonnquist, 1963;

Moll et al., 1962). However, as the range of diversity was expanded further, crosses of the most distantly related populations showed less heterosis

than crosses of populations assumed to be less distantly related. This would

suggest that maximum heterosis occurs at an optimal or intermediate level

of genetic diversity (Moll et al., 1965).

A similar pattern of heterosis and diversity has been observed in tobacco.

Hybrids between flue-cured varieties (Nicotiana tabacum L. ) and primitive

strains of Central and South America (the assumed center of origin of

N . tabucum) gave heterosis values similar to those observed in crosses

of flue-cured and Oriental varieties (Vandenberg and Matzinger, 1970;

Matzinger and Wernsman, 1968). The greatest heterosis was found in

crosses of flue-cured varieties to progenitor species, N . otophora and N .

tornentosiforrnis Goodsp. Crosses of flue-cured varieties with more distantly

related species resulted in less heterosis, which also suggested an optimum

degree of diversity for maximum heterosis (Matzinger and Wernsman,

1967).

2. Genetic Causes of Heferosis

There are three possible genetic causes of heterosis: partial to complete

dominance, overdominance, and epistasis. From the point of view of a

plant breeder, a basic issue is whether the best genotypes are homozygotes

or heterozygotes. If overdominance is important, the best genotype is a

heterozygote. With partial to complete dominance, the best genotype would

be a homozygote, and, rather than capitalize on heterosis directly, it might

be desirable to isolate transgressive segregates.

Evidence for heterozygote superiority in barley was reported by Jain

and Allard (1960). A bulk population, which had originated from intercrosses of 3 1 barley varieties and was heterozygous for several recognizable

mutants, was studied at intervals that encompassed 18 generations. The

proportion of heterozygotes at the marked loci did not decrease at the rate

expected, apparently because of the selective advantage of heterozygotes.

Overdominance was suggested as a possible explanation. However, no evidence for overdominance was found for four lethal chlorophyll mutants

of barley (Rasmusson and Byrne, 1972). The rate of elimination of the

recessive lethals for three of the loci was compatible with the rate expected

if there were complete dominance for fitness. The fourth allele showed

deviations from both complete dominance and overdominance models, and

behaved somewhat like a frequency-dependent phenomenon.

Apparent heterozygote superiority for forage yield of cocksfoot (Dac-



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tylis glornerata) was shown to result from genotype x environmental interactions (Breese, 1969; Knight, 1971). Through the application of the regression method of Finlay and Wilkinson (1963), the linear adjustments

for environmental differences resulted in estimates of dominance in the

partial dominance range.

The relative importance of dominant versus overdominant gene

action has been studied most intensively in maize. Extensive data reviewed

by Gardner ( 1963), Moll et al. ( 1964), and Moll and Robinson ( 1967)

provide evidence that if overdominance occurs in maize, it is either infrequent in occurrence or small in magnitude. The evidence clearly shows,

however, that linkage between loci with partial to complete dominance

does result in heterozygous effects that mimic effects of overdominance

for several generations after a cross. The issue of whether overdominance occurs to some extent in maize is not entirely resolved, and the

possibility of the existence of effects like overdominance must be recognized. For example, comparisons involving changes in heterosis after recurrent selection for hybrid performance are similar to changes expected if

overdominant gene action were increased in importance by selection (Moll

and Stuber, 197 1 ) .

Epistasis, particularly, epistasis that involves dominance effects, may also

contribute to heterosis, as was shown for certain traits in interspecific

crosses of cotton (Marani, 1968). Epistasis has also been shown to

occur in crosses of certain inbred lines of maize (Sprague and Thomas,

1967; Eberhart and Hallauer, 1968; Stuber and Moll, 1971; Stuber et al.,

1973). On the other hand, epistasis does not appear to be a major component of genetic variability in varieties or variety hybrids (Castro et al.,

1968; Eberhart and Gardner, 1966; Eberhart et al., 1966; Chi et al., 1969;

Stuber et al., 1966). The curvilinear relationship between heterosis and

genetic diversity noted previously might be a result of epistasis. However,

Cress (1966) has pointed out that multiple alleles would result in negative

dominance effects among some of the combinations, and could account

for the observed results in the absence of epistasis.



IV.



Genotype-Environmental Interactions



Valid interpretations of mechanisms of inheritance as well as predictions

of performance in breeding programs depend on accurate assessments of

genotypic values (Section 11, A ) . These assessments must be made from

data on phenotypes that reflect both nongenetic and genetic influences on

plant development. Unfortunately for the geneticist and plant breeder, the

genetic effects are not independent of the nongenetic environmental effects.

For example, the relative rankings of genotypes often differ in different



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R. H. MOLL AND C. W. STUBER



environments. This interplay of genetic and nongenetic effects, genotypeenvironmental interaction, reduces the correlation between genotype and

phenotype, which in turn reduces confidence in inferences from experimental data relevant to both plant improvement and inheritance

mechanisms.

As Allard and Bradshaw (1964) indicated, the nature of genotype-environmental interactions is extremely complex. In their attempt to classify

types of interactions, they showed that for only 10 genotypes and 10 environments, there are

possible types of interactions. This number is

larger than the total number of plants that have ever existed on the earth.

Therefore, consideration of genotypes and environments separately may

provide the only reasonable means of gaining an insight into the nature

and significance of the interactions.

Environmental variations can be classified into two types, predictable

and unpredictable (Allard and Bradshaw, 1964; Allard and Hansche,

1964). Predictable variations include the more permanent features of environments, such as climate and soil type, as well as cyclic fluctuations such

as day length. In addition, factors that can be fixed at will (e.g., planting

date, plant density, fertility levels, and harvest methods) are considered

in this category. Unpredictable variations include fluctuations in weather

such as distribution and amount of rainfall, temperature changes, and insect

or disease infestations. Although distinctions between the two categories of

variation may not always be clear, they have distinctly different impacts

on breeding programs, both on the operational procedures of selection and

on the testing phases.

Performances of genotypes (varieties) may or may not change with environmental fluctuations, even when there are large differences in environmental factors. Although workers disagree on their concepts of stability (to

be discussed later), it is generally agreed that the more stable genotypes

can somehow adjust their phenotypic responses to provide some measure

of uniformity in spite of environmental fluctuations, Allard and Bradshaw

( 1964) and Allard and Hansche (1964) equated stability with the term

“well-buffered.” They defined two types of buffering, individual bdff ering

and populational buffering. A homogeneous variety must depend largely

on individual buffering to achieve stability over a range of environments,

whereas a heterogeneous variety may use both individual and populational

buffering for this purpose.

The significance of genotype-environmental interactions to the plant

breeder depends on his objectives. If he desires varieties that perform well

over a broad spectrum of environments, then his program is favored by

small genotype-environmental interactions and/or well-buffered varieties.

However, if he desires varieties that are adapted to very specific environ-



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ments that can be predicted or specified in advance, then his program may

benefit by large interactions, and buffering may be of little consequence.

A major objective of the quantitative geneticist is the ascertainment of

the magnitudes of genetic variances as the basis for predicting genetic improvement in selection programs. In this situation, genotype-environmental

interactions may significantly affect the reliability of the variance estimates.

Such interactions are the source of part of the random errors of variance

estimates and often introduce an upward bias. Discrepancies between realized and expected response to selection wiII undoubtedly occur if expectations of progress are calculated from biased estimates of genetic variances.

A. MEASUREMENT

OF GENOTYPE-ENVIRONMENTAL

INTERACTIONS

Several procedures are available for characterizing behavior of varieties,

lines, or genotypes in varying environmental conditions. One of the most

commonly used methods is the use of replicated performance tests over

a series of environments. These tests are often analyzed as follows:



Source of variation



d.f.



Environments

Genotypes

Genotype x environment

Error



e-1

g--1

(g - l ) ( e - 1)

ge(r - 1)



Mean

square



Expectation

of mean square



MS,

MSz



u2



MSI



u2



u2



+ ruse2+ reup2



+ rugc*



The above analysis provides the mean squares for a simple F test

(MSJMS, ) for evaluating the overall significant of genotype-environmental interactions. Also, the component of variation attributable to these interactions, uge2,can be estimated as (MS2-MS,)/r. This may be useful

when comparisons of vse2 with genotypic variances, us2, are desired. If

the experiment is designed so that the genotypic variance can be partitioned

into separate components (such as additive, dominance, and possibly epistatic variances), it is often desirable to partition the genotypic-environmental source of variation so that specific tests of each type of variance

can be made.

Another measure of genotype-environmental interactions that has some

appeal to empirical plant breeders involves the correlation of performances

of an array of genotypes in one environment with their performances in

other environments (Stuber et al., 1973). Large positive values for this



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R. H. MOLL AND C. W. STUBER



type of correlation coefficient indicate little effect of genotype-environmental interactions, whereas the converse is true when evaluating the magnitudes of variance components attributed to such interactions.

Although genotype-environmental interaction effects appear to vary

somewhat in different species, no general pattern has been noted that could

be associated with specific types of mating systems or with specific types

of traits. Results from numerous experiments with maize indicate that estimates of genotype-environmental interaction variance components are significant for most traits evaluated and are relatively large when compared

with estimates of genetic variances (Gardner, 1963; Moll and Robinson,

1967; Stuber and Moll, 1971). Both additive and nonadditive effects show

significant interactions with environments. Second-order interactions

(i.e., genotype-year-location) tend to be much greater than either genotypeyear or genotype-location effects.

Both genotype-environmental interaction effects and epistatic genetic

effects may contribute to biases when standard methods are used for predicting three-way and double-cross hybrids from single-cross performances.

Studies with maize by Otsuka et al. (1972) and Stuber et al. (1973) indicated that genotype-environmental interaction effects produce greater

biases than epistatic effects when predictions are made from data obtained

in a single environment. When several environments are used for prediction

values, biases from the two types of effects are nearly equal.

Data from yield traits in three autogamous species-cotton, soybeans,

and tobacco-showed highly significant variances attributable to secondorder interactions (Matzinger, 1963). Except for tobacco, these variance

components tend to be large in comparison with total genetic variances.

More recent studies in cotton (Lee et al., 1967; Bridge et al., 1969; Baker

and Verhalen, 1973) produced similar results, with the additive component

of variance for lint yield showing particularly large interactions with environments. Cotton quality traits, in general, show relatively little genotype-environrnental interaction.

Baker ( 1969) found highly significant genotype-environmental effects

for grain yield in hard spring wheat, with the second-order interaction component of variance nearly as large as the genotypic component of

variance. In a durum wheat study, Widner and Lebsock (1973) reported

that genotypic-environmental interaction mean squares were significant for

Fl’s and parents, but not for Fz‘s in their grain yield data.



B. EVALUATION

OF STABILITY

Although, in general, genetic effects are not independent of environmental effects, a number of authors (Yates and Cochran, 1938; Finlay and



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Wilkinson, 1963; Rowe and Andrew, 1964; Eberhart and Russell, 1966;

Perkins and Jinks, 1968; Johnson et d.,1968; Breese, 1969; Baker, 1969)

have observed that the relation between the performance of different genotypes in various environments and some measure of these environments

is often linear, or nearly so. From these observations, Freeman and Perkins

(1971) concluded that there is strong evidence indicating a genuine underlying linear relation between performances of specific genotypes and environmental conditions, even though this relation does not always account

for all of the interaction observed.

Because of this linear relationship, several authors have used regression

techniques to characterize responses of genotypes in varying environmental

conditions. In particular, regression analyses have been used to provide

measures of phenotypic stability. Many of the regression analyses used for

this purpose do not entirely satisfy rigorous statistical requirements. Even

so, the regressions computed have been shown to be useful predictors of

stability, and would appear to be particularly meaningful in practical plant

improvement work.

One of the basic statistical objections to many of the papers cited above

is the improper choice of sums of squares and degrees of freedom from

which to subtract the regression components. In fact, one author, Baker

(1969), divided the genotype-environmental sum of squares, with (g - 1 )

(e - 1) degrees of freedom, into a separate partition associated with each

genotype. The total degrees of freedom for these partitions is g(e - 1 ) .

This, of course, is statistically invalid, because any sum of squares has

a unique number of degrees of freedom irrespective of the partitioning

scheme used.

A method for partitioning sums of squares, as presented by Freeman

and Perkins (1971 ), avoids the difficulties cited above. Their analysis, in

which all the terms are orthogonal, and in which comparisons are possible

with F tests, is as follows:



Source of variation



d.f.



Genotypes (C)

Environments ( E )

Combined regression

Residual

Interaction (C X E )

Heterogeneity of regressions

Residual

Error (between replicates)



g-1



1

e-2

g-1



(9



- I)(e - 2)

ge(r - 1)



292



R. H. MOLL AND



C . W. STUBER



In this analysis, the “combined regression” term partitions the variation

associated with fitting a single line over all genotypes. The term “heterogeneity of regressions” partitions the sum of squares associated with the

differences of the individual regression lines for the different genotypes

from the combined regression line. Tai ( 1971 ) partitioned the ‘‘interaction” term in a similar manner.

Eberhart and Russell (1966) used an analysis which (although it was

developed earlier) might be considered as a modification of the FreemanPerkins analysis. It is as follows:

Source of variation



d.f.



Genotypes (G)

Environments ( E )

Interaction (C X E )

Environments (linear)

G X E (linear)

Pooled deviations

Genotype 1

Genotype 2



9 - 1



Genotype g

Pooled error



s(e - 1)



1

g-1

g(e - 2)

e - 2



e-e



e-52



49 -



- 1)



The above analysis differs from the Freeman-Perkins analysis by considering the total variation among genotypes as a single component by combiing

“environments” and “interaction” sums of squares. The two “residual”

sums of squares from the Freeman-Perkins analysis form the “pooled deviations” partition in this analysis, which can then be further subdivided to

provide individual genotype (or variety) partitions.

Another basic objection to many of the regression analyses cited is the

choice of measurement of environmental effects on which the regression

is made. Some type of environmental measurement independent of the

experimental organism would be highly desirable. It would be even better

if environmental values could be measured without error. These requirements cannot be met, and the best measure of the combined environmental

effects is probably provided by the organism itself.,

Several of the authors cited earlier have used the mean of all the genotypes (varieties) grown in a specific environment as the value assigned

to the environment (i.e., variety performance is regressed on the mean

of all varieties grown at a specific environmental site). This does not pro-



QUANTITATIVE GENETICS



293



vide an independent measure of environmental effects and, therefore, does

not satisfy the requirements of a regression analysis as rigorously as one

would like. However, it appears to provide sufficiently reliable estimates

to be useful. Some independent measures that are possible include: (1)

division of the replicates of each genotype into two groups, using one group

to measure the environment and the other to evaluate interactions, or (2)

use of one or more genotypes as standards to assess the environment. Although these measures provide the desired independence between environmental and genetic effects, they require additional experimental costs or

the discarding of some data from the interaction analyses, and are inefficient with regard to minimizing sampling errors.

Perkins and Jinks (1973) compared the use of the usual dependent assessment of environments with three independent measures in a study of

82 lines of Nicotiuna rusticu L. In their analyses of significance of heterogeneity of regressions and the ranking of inbred lines based on their linear

regression coefficients, they found that it made little difference whether they

used dependent or independent environmental measures. In fact, the increased size of the sampling variances, because fewer experimental units

were available for the independent environmental assessments, was probably more serious than the lack of independence that resulted when all

the experimental material was used for the environmental assessment.

Although the regression analyses appear to be very useful in providing

stability measures, there is not complete agreement on the best definition

for the term stability. In a study of 277 barley varieties, Finlay and Wilkinson ( 1 943) (basing their analyses on methods developed by Yates and

Cochran, 1938) regressed variety mean yield on site mean yield, using

a logarithmic scale. They indicated that a regression coefficient of: (1)

unity indicates average stability, (2) greater than unity indicates below

average stability, and (3) less than unity indicates above average stability.

Absolute phenotypic stability would be expressed by a coefficient of zero.

Although their definition implied that a stable cultivar performs relatively

well in poor environments and relatively poorly in favorable environments,

they defined an ideal variety as one with maximum yield potential in the

most favorable environment and with maximum phenotypic stability. Using

these definitions, their barley data showed that the varieties with high

phenotypic stability all had low mean yields and were unable to exploit

highly favorable environments. They then concluded that the breeder must

compromise in his search for an ideal variety.

Eberhart and Russell (1966) improved the regression technique for

evaluating stability by considering two empirical parameters, the slope

of the regression line and the deviations from the regression line. In their

pij, Yij is the ith variety mean at the jth enmodel, Y i j = pi piZi



+



+



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R. H. MOLL AND C. W. STUBER



vironment, pi is the ith variety mean over all environments, pi is the

regression coefficient that measures the response of the ithvariety to varying environments, &! is the deviation from regression, and If is the environmental index. They then defined a stable variety as one with a

regression coefficient of unity ( b = 1.0) and with a minimum deviation

from the regression line ( ~ d =

, ~ 0). Using their definitions, a breeder

would usually desire a variety with a high mean and one that meets the

above requirements for stability.

Data on corn inbreds and hybrids presented by Eberhart and Russell

( 1966) showed considerable variation for stability parameters. However,

the data suggested that both parameters, the regression coefficient and the

parameter measuring deviations from regression, are of prime importance

for varietal evaluations.

Regression techniques were used by Breese (1969) in a study of five

populations of Dactylis glornerata. He also concluded that a stability concept must include a measure of deviations from regression as proposed by

Eberhart and Russell (1966). Comparisons of performances of 12 varieties of hard red winter wheat (Triticum aestivum L.) grown in regional

performance nurseries produced regression coefficients that differed little

from unity (Johnson et al., 1968). Although they did not compute the

deviations from regression, comparisons with a standard wheat variety,

KHARKoF, also indicated that the deviations from regression should be considered when making varietal comparisons relating to stability.

In a study of sorghum yield stability parameters, Jowett (1972) compared evaluation methods of Eberhart and Russell (1966), Finlay and

Wilkinson (1963), and Wricke (1960), using empirical data. Wricke’s

method, based on a single parameter called ecovalence, was determined

to be the least informative of the three methods. Jowett concluded that

the Eberhart-Russell method, which uses an arithmetic scale, was probably

preferable because it is more explicit than the Finlay-Wilkinson procecdure, which uses a logarithmic scale. However, the logarithmic scale may

be preferable if varieties differ markedly. In the empirical analyses, Jowett

(1972) found that single cross and three-way cross sorghum hybrids were

more stable over environments than the inbred varieties.

In an analysis of regional potato trials, Tai ( 1971) considered stability

in a slightly different context and outlined a procedure that removes the

error deviate from the stability parameters defined by Eberhart and Russell

( 1966). This provided genotypic stability statistics which Tai compared

with the phenotypic statistics of Eberhart and Russell. He concluded that

with only a small number of varieties tested over a small number of environments, the phenotypic estimates may differ substantially from the genotypic estimates. However, in a potato experiment with eight entries and



QUANTITATIVE GENETICS



29 5



six environments, the estimates of genotypic statistics differed very little

from phenotypic estimates. Tai also found that the highest yielding experimental lines were unstable, and those with average stability yielded about

the same as the check varieties.

Until recently, hopes that genotype-environmental interactions could be

successfully accommodated in the study and manipulation of quantitative

traits have not been very optimistic. Sprague (1966) showed considerable

pessimism when he indicated that the possibility for reducing such interactions under field conditions seemed questionable. As Breese (1969) suggested, perhaps the attitude that we should seek to minimize genotype-environmental interactions has inhibited our approach to this problem. From

the studies discussed above, it now seems apparent that the combined

effects of genotype and environment do not behave in a disorderly fashion,

but might be envisioned as reasonably predictable responses to some type

of regulatory system.

In the past, workers also may have been deterred in the study of genotype-environmental concepts because they have been too concerned with

the identification of individual components of the environment. However,

Breese (1 969) reminded us that the phenotype is the product of the genotype and its environment. Therefore, it is just as appropriate to qualify

an environment by its mean expression over a range of genotypes as it

is to measure a genotype by its mean expression over a range of environments. We certainly cannot specify all the underlying biochemical and

physiological processes that characterize a genotype. Therefore, the fact

that we are unable to specify all the factors that contribute to an environmental expression should not be a deterrent to our study of quantitative

traits and their relationships to environmental conditions. In fact, the recent

evidence, strongly indicating a genuine underlying linear relationship between performances of specific genotypes and environmental conditions,

should provide new opportunities for quantitative genetic research, as well

as provide better tools for the plant breeder to predict response over varying environments.

V.



Response to Selection



The genetic potential of a plant population can be considered in two

different ways: (1) the mean performance of the population itself or (2)

the performance of the population in hybrid combination with other germplasm. Selection procedures have been devised for the direct improvement

of each kind of genetic potential. When the goal of the breeding program

is a superior variety or pure line, it would be logical to choose among

selection procedures designed to improve population performance itself.



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