III. Inbreeding Depression and Heterosis
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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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287
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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QUANTITATIVE GENETICS
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)
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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
+
+
294
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.