| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
Dep. of Plant Sci., North Dakota State Univ., Fargo, ND 58105
* Corresponding author (ted.helms{at}ndsu.edu)
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
|---|
Abbreviations: G x E, genotype-by-environment
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
|---|
Comstock and Moll (1963) show that a large sample of locations and years must be used to estimate the components of variance without bias. As the number of environments increases, the G x E covariances approach an expectation of zero. They show that when the components of variance are estimated from only two locations in a single year, G x E covariances between locations will bias the estimates of the components of variance.
The predicted genetic gain formula is derived using a model where both genotypes and environments are random effects and G x E covariances average to zero. These assumptions are valid when genotypes are tested in a very large number of environments and selection is based on the mean of these sites. In practice, plant breeders have limited seed amounts and limited resources for the first year of yield evaluation. Nonzero G x E covariances would be expected between pairs of selection environments, especially when the selection environments are a sample of locations within the same year.
Allen et al. (1978) developed the concepts of test and target environments. Genotypes are selected in the test environments with a goal of identifying those genotypes that will have superior performance in future target environments. A genetic correlation exists between the test and target environments. A second requirement of the idealized genetic gain formula is that the test environments are representative of the target environments. However, because selection is only conducted in a single year, the correlation between test and target environments will be less than unity. They also state that estimates of heritability or genetic gain, based on a single environment "may be seriously deficient as criteria for environments in which selection would be effective."
If the usual assumptions used to develop the predicted genetic gain formula are not valid when the number of selection sites is small, a different formula needs to be developed. A formula that has been specifically developed for the usual situation where genotypes are tested at a limited number of sites may provide insight into the best allocation of resources for the applied breeding situation. Our objectives were to (i) develop a heritability formula that included covariances between G x E effects for the same genotype evaluated in different environments, and (ii) show how these G x E covariances influence resource allocation strategies to maximize genetic gain.
|
MATERIALS AND METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
|---|
Later maturing soybean genotypes tend to yield more than early maturing genotypes. To select for yield, it is necessary to consider the maturity of the lines. We used maturity as a covariate to adjust yield (Miller and Fehr, 1979). The maturity covariate was the date that 95% of the pods reached the mature pod color of brown or gray. The formula used was
 |
Selection sites were chosen based on the pair-wise G x E component of variance. The 1995 Mantador, ND, and 1995 Rosemount, MN, sites were chosen because the G x E component of variance was small between these two environments. The 1995 Mantador and 1996 Rosemount sites were chosen because the G x E component of variance was relatively large between these two environments. This was done to compare realized gain when the G x E component of variance between selection sites is small vs. when the G x E component of variance is large.
Lines were selected based on the mean performance for ADJYLD in the 1995 Mantador site averaged across two replicates. Lines were also selected based on the mean performance in the 1995 Mantador and 1995 Rosemount sites, averaged across two replicates per site. The third selection criterion was based on the mean at the 1995 Mantador and 1996 Rosemount sites, averaged across two replicates per site. Realized gain from selection was determined by averaging the performance of the selected lines across four target sites. The four target sites included 1995 Casselton, ND; 1995 Morris, MN; 1996 Casselton, ND; and 1996 Mantador, ND.
Comstock and Moll (1963) show that with a linear model:
 |
The G x E interaction effect is expressed as a deviation of phenotype from the sum of the main effects due to environment, genotype, and residual effects.
 |
Hanson (1964) showed that when years and locations are presumed random, but are correlated, the G x E interaction component of variance was biased. He showed that
 | [1] |
e2 is the residual variance (plot to plot error); GE2 is the G x E component of variance; b is the number of replicates; D = k1
y + k2l; k1 is the number of locations minus 1; k2 is the number of years minus 1; y is the correlation among years; l is the correlation among locations. When the number of years equals unity and the number of locations equals 2, then
 | [2] |
GY2 is the genotype x year interaction component of variance and GE2 = GY2 + GL2 + GYL2.
Fehr (1991) provides the traditional heritability formula on an entry-mean basis. This formula is
 | [3] |
Af2 is the additive genetic variance among families or inbred lines, e2 is the plot-to-plot error, and Gf2 is the genetic component of variance among families. The total genetic variance among families (Gf2) is equal to the sum of the additive genetic (Af2), dominance genetic (Df2), and epistatic genetic (Ef2) variances among families:
 | [4] |
The associated genetic gain formula is
 | [5] |
G equal the expected genetic gain and k equal the standardized selection differential (Falconer and Mackay, 1996).
Allen et al. (1978) developed the predicted gain equation for the target environments when selection was conducted in one test environment:
 | [6] |
y is the variance among genotypes in the target environments; and 
is the square root of the heritability in the test environment. The y symbol of Allen et al. (1978) represents the square root of Af2 in the target environments, where Af2 is our symbol for the genetic variance among families.
We assumed that the covariances between G x E effects, summed across genotypes equal zero for two different genotypes evaluated in two different environments. We also assumed that covariances between G x E effects equal zero for two different genotypes evaluated in the same environment. Also, that covariances between G x E effects equal GE when the same genotype was evaluated in two different environments and that covariances between G x E effects equal GE2 when the same genotype is evaluated in the same environment. On the basis of these assumptions,
 | [7] |
GE equal the expectation of the covariance among G x E interaction effects.
We developed an operational heritability equation on an entry-mean basis that included covariances between G x E effects across two selection sites.
 | [8] |
Then, substituting Eq. [8] into Eq. [6], the operational genetic gain formula is given by Eq. [9].
 | [9] |
When only two locations within a single year are used to estimate the EMS(G), then GE2 of the idealized genetic gain formula is biased, as shown in Eq. [2]. Because of the small number of environments, the assumption of the idealized genetic gain formula that covariances between G x E effects average to zero is no longer true. Hanson (1964) showed that as the number of target environments increases, this bias becomes smaller. Both Comstock and Moll (1963) and Hanson (1964) concluded that this bias would not be a meaningful violation of the assumptions of the idealized gain formula when genotypes are selected, averaged across several locations within each of several years.
However, the reality of the selection process is actually much more complex than just the problem of a bias in estimating the GE2 term in the idealized genetic gain formula. The selection environments may not be representative of the target environments. If the expectation of GE2 in the selection environments equaled the expectation of GE2 in the target environments, then the genetic correlation between them would be unity. We did not assume that the expectation of GE2 was the same magnitude in both selection and target environments. For practical purposes, the selection environments may represent a more limited geographical area and will certainly represent a more limited number of years than the conceptual population of target environments.
When a breeder wants to determine whether one or two selection sites should be used, a genetic gain formula that assumes that a large number of selection sites will be used is not the correct formula for the situation. The conceptual population of selection environments may not be the same as the conceptual population of target environments. Also, the problem is not one of estimating GE2 in the idealized genetic gain formula, it is that the interaction of environment and genotype may be similar at two sites when the influence of the environment on the genotypes for each of the two selections sites are similar. This causes G x E covariances among selection sites.
Allen et al. (1978) showed that the correlated response to selection was proportional to r. Their heritability formula was developed for a single environment. We modified the heritability formula of the test environments which was proposed by Allen et al. (1978) to include the situation where selection was based on the mean of two environments. Our heritability formula for the test environments includes covariances between G x E effects. We considered genetic gain in the target environments to be a correlated response to selection in the test environments the same as Allen et al. (1978). Allocation of resources for testing purposes will alter the heritability and may change the correlation between test and target environments.
|
RESULTS AND DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
|---|
|
The operational genetic gain formula shows that the improvement in genetic gain cannot be determined using a formula, when comparing selection at multiple environments vs. at one environment. The components of variance used in the idealized heritability formula should be estimated from components of variance developed using a large sample of locations and years. However, this formula is not applicable to selection practiced using two environments. The idealized genetic gain formula (Eq. [5]), assumes that the GE2 is of the same magnitude for any pair of selection environments. The operational genetic gain formula (Eq. [9]), does not assume that GE2 is a constant between any pair of selection environments.
The idealized genetic gain formula is based on an estimate of GE2 using a large sample of years and environments. However, for any two specific selection sites, the GE2 component between those two sites may be larger or smaller than the estimate of GE2 used in the idealized genetic gain formula. If the G x E component of variance is small between two selection sites, the additional selection site may not provide information regarding the performance of lines under various environmental conditions. Comstock and Moll (1963) state that "Suppose, for example that the s locations in which data are collected happen to be very similar ones. In the extreme one can imagine them so similar that for practical purposes they are the same. Then the result would be as if there were rs replications at one location instead of r replications at each of s locations...." The point is that the estimate of GE2, based on a large number of years and locations, will not be useful for estimation of genetic gain when selection is based on only two or three sites.
The covariances of G x E effects between the same genotype at two different environments are specific to that particular data set and are not repeatable. The G x E covariances should be considered as random error. Therefore, increasing the number of selection environments, within the same year, may not increase the genetic gain in target environments as much as the idealized genetic gain formula would predict.
The reason that the idealized formula does not apply when selection is conducted, based on two environments, is that the expectation of the G x E covariances does not average to zero when only two or three environments are used for selection. Therefore, the problem with using the idealized heritability formula for selection at two environments is not one of estimating the components of variance, the problem is that the idealized heritability is the wrong formula for the situation.
The G x E component of variance (GE2) cannot be estimated separately from the G x E covariance (GE) when mean squares are equated to expected mean squares in the ANOVA. For this reason, the breeder cannot determine the magnitude of the G x E component of variance between the selection sites. Therefore, the breeder cannot determine the degree to which testing at an additional site will increase the genetic gain in the target environments.
Equation [1] shows that the expectation of the G x E component of variance will always be biased, when estimation is based on two locations within 1 yr. In practice, the first yield tests must be a sample of locations within the same year. Selection sites within a single year might be expected to result in covariances between G x E effects, because these locations would share a common year effect. Also, the components of variance that are estimated from a large sample of locations and years would not apply to the operational model, because the operational model does not assume that the covariances of G x E effects sum to zero. Therefore, the assumptions of the idealized heritability formula are not valid when selection is conducted based on two or three locations in a single year. For this reason, the idealized genetic gain formula cannot be used to determine the optimum allocation of resources for the first year yield evaluation.
Schutz and Bernard (1967) discuss the fact that the G x E interactions include both a difference in genotypic variances between sites, as well as the genetic correlation between the two sites. They state that when the breeder wants to select the best genotypes, the difference in genetic variances between the two sites is of relatively minor importance. They suggest the genetic correlation between selection sites is a more important component of the G x E component of variance than the difference in genetic variances between selection sites. They also provide evidence that approximately one-third of the G x Y interaction is due to differences in genetic variances from year to year. They conclude that "for selection purposes, the importance of the strain x year interaction appears to be somewhat exaggerated."
Jones (1988) reported that it is desirable for test locations to have a low correlation. They used data that had been standardized to develop least significant difference formulas that included testing across different environments. They state that "If the correlation coefficients all equal 1.0, no reduction in standard error results from additional testing because no additional information is generated." In conclusion, selection will be most effective when the correlation between test environments is low (Comstock and Moll, 1963; Jones, 1988) and the correlation between test and target environments is high (Allen et al., 1978).
Even if the G x E component of variance between two selection sites is relatively large, this might be due to interactions of magnitude between the relative performance of lines in the two environments, rather than due to crossover interactions. A cultivar that performs consistently across target environments is desirable (Huhn et al., 1993). However, a lack of rank changes between selection sites would not be desirable because this would mean that the second selection site was not providing any additional information. Baker (1988) stated that "Genotype–environmental interaction is of consequence in plant or animal improvement only if it involves change in genotype rank from one environment to another."
Another reason why the realized genetic gain was not increased when selection was conducted at two environments vs. one environment is that the correlation between the test and target environments was not increased. Allen et al. (1978) showed that realized gain should be considered a correlated response between the test and target environments (Eq. [6]). Increasing the heritability by using more replicates per site or selection in more than one site may not be of significant value if the correlation between the test and target environments is low.
We compared the rank correlation between means of selection environment(s) and the mean of the four target environments using all 300 lines. The Kendall rank correlation between the 1995 Mantador selection site and the mean of the four target environments was r = 0.28 (P = 0.001). Including additional selection data, due to including the 1995 Mantador and 1995 Rosemount mean correlated to the mean of the four target environments, resulted in a Kendall rank correlation of r = 0.36 (P = 0.001). The Kendall rank correlation between the mean of the 1995 Mantador and 1996 Rosemount selection sites with the mean of the four target environments was r = 0.27 (P = 0.001). These results show that there was little additional information provided by averaging across two selection sites as opposed to selection based on one site.
The conventional wisdom is that selection using more replicates or more environments will increase genetic gain. Selection using more replicates at a single selection site will provide greater precision at that site. However, using more replicates at a single selection site will not provide additional information on the performance of lines in the target environments, due to G x E interaction between the test and target environments.
One difficulty in using the idealized genetic gain formula (Eq. [5]), is that the G x E interaction component of variance is underestimated (Hanson, 1964) and the genetic component of variance is overestimated, based on an ANOVA using two locations within a single year (Casler, 1982). Another problem with using the idealized genetic gain formula for resource allocation decisions is that the portion of the G x E interaction component that is due to differences in the genetic variances between environments cannot be determined (Schutz and Bernard, 1967). The change in rank of genotypes among environments is not considered in this formula. However, even if the G x E interaction and genetic components of variance could be estimated without bias, the idealized genetic gain formula does not allow for covariances between G x E effects for two locations within a single year and does not consider the correlation between test and target environments.
The operational genetic gain formula (Eq. [9]) is complex, but provides a theoretical basis for a discussion of the concepts involved in first year selection. However, the breeder cannot estimate the various components of the formula. For these reasons, the operational genetic gain formula cannot be used in practice to determine the best allocation of resources. Equation [9] is useful to more fully understand quantitative genetic selection theory.
The following hypothetical example demonstrates why the breeder cannot estimate the genetic correlation between test and target environments. In practice, the test environments might include years with above-average rainfall, while the target environments might include years of drought or vice versa. A breeder might select in years of relatively high precipitation, only to have the weather change such that the released cultivar is grown in drier years. The estimate of the genetic correlation between test and target environments depends on the relatively small sample of years used for estimation. Also, the standard error of a genetic correlation is large.
If breeders choose to use the operational genetic gain formula, instead of the idealized genetic gain formula they must, of necessity, rely on empirical results to allocate testing resources. Two locations that are in close geographical proximity would be expected to share a similar soil type and experience similar weather conditions in the same year. Two locations that are separated by a wide distance would be expected to have different soil types and tend to experience different weather conditions. Therefore, a formula that assumes that the G x E component of variance between any two selection sites is a constant cannot be used to decide how to allocate testing resources.
Empirical evidence is available in the scientific literature to support the finding that the idealized genetic gain formula does not always result in the optimum allocation of resources. Helms et al. (2002) found that the realized gain of soybean lines selected based on the mean of one plot was equal to the realized gain of lines selected based on two replicates at each of two selection sites. Realized gain was determined using validation sites that were not the same as the selection sites. Baihaki et al. (1976) reported that the highest yielding soybean lines could be identified based on data from a single test location. They used validation environments that were not the same as the test environments.
Additional selection environments may provide additional information that will increase the realized gain in the target environments, but this will depend on whether rank changes exist between the two selection environments and on the correlation between test and target environments. If r = 0.3, as is the case in this study, then any increase in the heritability of the selection sites would be of limited effectiveness because the square root of the heritability of the selection site(s) would be multiplied by 0.3 to determine the resultant increase in the correlated response.
The reduction in the denominator of the heritability estimate due to dividing the G x E component of variance by the number of selection environments (n) cannot be determined because the estimate of the G x E component of variance (GE2) cannot be separated from the estimate of the G x E covariance (GE). There are not enough independent equations in the ANOVA to separately estimate these two components of the expected mean square for genotypes. For these reasons, the estimate of the operational heritability (Eq. [7]) in the selection environments is not useful for determining the correlated response to selection as the allocation of resources is varied. Thus, the operational heritability formula cannot be used to determine the value of using more than one test site. To determine the best selection strategy, breeders must conduct an empirical experiment that provides the realized gain in target environments when selection is conducted in one vs. two selection sites.
If selection for yield is of primary importance, the resources that might have been allocated to testing all experimental lines at a second site could instead be utilized to test twice as many experimental lines. In some breeding programs it may well be that the resources that could have been allocated to selection for yield at a second site would be better used to select for another trait. For example, the empirical results of this study suggest that the resources that would have been allocated to yield testing at a second site might be better allocated to use in selection for disease resistance or iron deficiency chlorosis tolerance. The best allocation of resources will vary from one breeding program to another, but cannot be determined based on the idealized genetic gain formula.
From a practical standpoint, breeders often test experimental lines using one replicate at each of two locations within a single year. This is because the risk of hail, flooding, or other hazards is reduced using this strategy. However, these two locations could be as close as 40 km to significantly reduce the risk of weather related hazards. Two testing sites that are this close together are not likely to result in changes of rank between experimental lines. It is more expensive to test genotypes at two sites that are further apart. The results of this study suggest that the extra expense of separating the first year testing sites by a large geographical distance may not be worthwhile. The idealized genetic gain formula will not provide insight into this question. The operational genetic gain formula explains the complexity of the first year selection process more fully than the idealized genetic gain formula.
The empirical results of this experiment do not prove that first year yield evaluation at a single selection site is the best allocation of resources. The results of this experiment show that in some situations, selection based on two sites is not superior to selection based on data from one site. These results support the theory developed by Comstock and Moll (1963), Allen et al. (1978), and Schutz and Bernard (1967). Theoretical considerations developed in this manuscripts show that the idealized genetic gain formula is not useful for determining the optimum allocation of testing resources for the operational model of first year yield evaluation.
Received for publication July 19, 2005.
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTS AND DISCUSSIONREFERENCES |
|---|
This article has been cited by other articles:
|
|
 |
|
  H.-P. Piepho and J. Mohring Computing Heritability and Selection Response From Unbalanced Plant Breeding Trials Genetics, November 1, 2007; 177(3): 1881 - 1888. [Abstract] [Full Text] [PDF]
|
|
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
| The SCI Journals | Agronomy Journal | Vadose Zone Journal | |||
| Journal of Natural Resources and Life Sciences Education |
Soil Science Society of America Journal | ||||
| Journal of Plant Registrations | Journal of Environmental Quality |
The Plant Genome | |||
