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a Dep. of Plant Science, Nova Scotia Agricultural College, P.O. Box 550, Truro, NS, B2N 5E3 Canada
b Dep. of Plant Sciences, Univ. of Saskatchewan, Saskatoon, SK, S7N 0W0 Canada
c Atlantic Food and Horticulture Research Centre, Agric. and Agri-Food Canada, 32 Main Street, Kentville, NS, B4N 1J5 Canada
d SCPFRC, Agric. and Agri-Food Canada, 43 McGilvray St., Univ. of Guelph, Guelph, ON N1G 2W1 Canada
gatlin{at}cadmin.nsac.ns.ca
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ABSTRACT |
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2GS) relative to the genotypic variance (2G). 2GS is the portion of the genotype x location interaction (2GL) caused by local adaptation, rather than by random site-to-site variability in genotype means. Subdivision can increase heritability through the addition of 2GS to the numerator of Hi, but this may be offset by reduced replication across locations within the subregion. Modeling using variance estimates from several cereal programs indicated that, unless 2GL is large relative to 2G and at least 30% of 2GL is due to 2GS, subdivision is unlikely to increase response. These results help explain the success of breeding programs that test broadly.
Abbreviations: GE, genotype x environment • GS, genotype x subregion
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONTheoryMethodResultsDiscussionREFERENCES |
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Many current methods for the analysis of genotype x environment (GE) interaction use classification (Fox and Rosielle, 1982; Cooper et al., 1993b) or ordination (Gauch and Zobel, 1997) to group environments on the basis of similarity of cultivar response. Cooper and DeLacy (1994) review these methods and clarify the relationships among them. Current models do not, however, indicate if greater response to selection will result from dividing a target region into subregions to exploit local or specific adaptation (Basford and Cooper, 1998). This trade-off was described by Comstock and Moll (1963), who noted that partitioning of a target population of environments into several more homogeneous subdivisions could increase within-subdivision genetic variance, but recognized that increased testing effort would be required if a single large breeding program were to be replaced by several smaller ones. The effect of subdivision depends not only on the magnitude of genotype x subregion (GS) interaction but also on the precision with which means are estimated within the newly created subregions, relative to the precision of their whole-region estimates. Curnow (1988) noted that when GS interaction is relatively small and error variances are relatively large, greater gains within a subregion may be achieved by selecting on the basis of mean yield across the undivided region than within a single subregion.
The purpose of this study is to present a model for predicting the effect of dividing a large region into more homogeneous subregions on selection response, taking into account both the magnitude of local adaptation and the division of testing resources that normally accompanies the division of a target region. We model the impact of subdivision on selection response using published variance component estimates that represent much of the range of GE interaction likely to be encountered in plant breeding programs.
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Theory |
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TOPABSTRACTINTRODUCTIONTheoryMethodResultsDiscussionREFERENCES |
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 | (1) |
Equation [1] may be used to determine if division of a target region into smaller subregions is likely to increase response to selection. Stated in terms of the Falconer model, the problem is to determine if response in the subregion is likely to be greater as a result of direct selection within the subregion only, or as result of indirect selection in the undivided target region. In this case, we can denote the genetic correlation between line means in the subregion and the entire undivided region as rG', the genetic correlation among means estimated in different subregions as rG(ii'), the repeatability of means estimated in subregions as Hi, and the repeatability of means estimated in the undivided region as H. The correlated response in Subregion i to indirect selection in the undivided target region expressed as a proportion of direct response to selection in the subregion only can therefore be predicted as:
 | (2) |
Direct relationships exist among rG', rG(ii'), H, Hi, and the genotype x location (GL) variance component in the standard model used to decompose the phenotypic variance.
The Relationship between Heritability (H) in an Undivided Target Region and Heritability in a Subregion (Hi)
If a target region is divided into subregions, then the model for an observation may be described as:
 | (3) |
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In this discussion, all effects in the model except subregions are considered random, and no constraints are applied either to the fixed or the random terms. An explanation of the decision to treat genotypes and environments as random is warranted because they are often considered fixed effects in the GE literature. The trial locations are properly considered to be a random sample of the environments in which the tested genotypes are likely to be grown. Likewise, years are a random sample (or as random as possible) of production years.
For the purpose of analyzing the performance of a testing system under various allocations of resources, genotypes must also be considered to be random effects. This is because inferences are made not about particular genotypes, but about the relative selection response expected under different allocations of testing resources among locations, years, and replications within trials. These inferences are meant to extend beyond the group of genotypes included in the particular set of trials from which the data are collected.
The effect of subregion is fixed because inferences are to be made about the specific partition of the target region being studied; subregions are not considered to be random samples of the region, but have been specifically constituted on the basis of environmental differences or genotypic response. Locations are nested within subregions because they represent a sample of test environments within the subregion.
The main differences between the conventional analysis of variance (ANOVA) model for the analysis of cultivar trials repeated over locations and years and the subregion model is the partitioning of the genotype x location effect into a genotype x subregion interaction and a genotype x location interaction nested within subregions, and the decomposition of the genotype x location x year effect into a genotype x subregion x year interaction and a genotype x location x year interaction nested within subregions. This results in the partitioning of 2GL and 2GYL in the conventional model as follows:
 | (4) |
 | (5) |
When a target region is subdivided for the purpose of genotype recommendation and genotype effects are estimated from within-subregion means only, the genotype and genotype x subregion effects specified in Eq. [3] are confounded. The overall effect of Genotype m in the undivided region was defined as Gm in Eq. [3]. Its variance, 2G, is the variance of the across-region genotypic effect. Following Comstock and Moll (1963), the effect of the same genotype in Subregion i is
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Expressed in terms of Eq. [3], and assuming that Gm and GSmi are uncorrelated, the variance of within-subregion means is
 | (7) |
In terms of the ANOVA across subregions, the result of subdivision is that 2GS is removed from 2GL and becomes part of the within-subregion genetic variance. The variance component 2GYS, on the other hand, remains part of the within-subregion phenotypic variance.
The effect of these changes on potential selection response can be assessed by comparing the broad-sense heritability of genotype means over the undivided target region (H), with the heritability of means estimated within one subregion only (Hi). For H, we have
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 | (9) |
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2GS to the numerator of Hi. However, this may be offset by the reduction in replication across locations that is a consequence of subdivision. The reduction increases the phenotypic variance.
The Genetic Correlation (r'G) between Line Means Measured in a Large Target Region and a Subdivision of the Region
The overall effect of Genotype m in the undivided region was defined as Gm in Eq. [3]. The effect of the same genotype in Subregion i was defined in Eq. [6] as
.
Assuming that Gm and GSmi are uncorrelated, the covariance between genotypic effects in the undivided target region and in a subregion is therefore:
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The correlation between genotypic effects in the undivided region and in the target can therefore be expressed as:
 | (11) |
Assuming independence of genotype x subregion effects in different subregions, the covariance between genotypic effects in Subregions i and i' is:
 | (12) |
From Eq. [7] and [12], it follows that the genetic correlation between line means in different subregions (rG(ii')) is:
 | (13) |
The relationship between rG' and rG(ii') can be clarified as follows:
 | (14) |
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Method |
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TOPABSTRACTINTRODUCTIONTheoryMethodResultsDiscussionREFERENCES |
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. It should be noted that the purpose of the modeling exercise was to consider the effect of subdivision of a target region for various levels of this ratio, and assuming a range of hypothetical values of
, rather than to make explicit recommendations about the testing systems in question. To facilitate comparison, variance component estimates (Table 1)
have been standardized by expressing them as a proportion of the phenotypic variance (2P) for a selection unit consisting of a single plot in a single trial, where:
 | (15) |
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The effect of the size of 2GS as a proportion of 2GL on Hi, rG', and CR/DR was modeled for a subregion containing two, four, or six trial locations out of an original testing network of 12 locations across the undivided region. For the calculation of H and Hi, Eq. [8] and [9] were used. Genetic variances were assumed to be identical in all subregions. Values of 2GS ranging from 0.1(2GL) to 0.5(2GL) in increments of 0.2 (2GL) were assumed in the calculation of H and Hi. Inspection of Eq. [9] indicates that Hi must decrease as 2GYS increases as a proportion of 2GYL in the conventional model. A value of 0 was therefore assumed for 2GYS, because this condition is most likely to favor subdivision. rG' was calculated by Eq. [11]. Heritabilities were calculated assuming 1 or 2 yr of testing and three replicates per trial. Eq. [2] was used to predict correlated response in a subregion to indirect selection in the undivided region, expressed as a proportion of direct response to selection in the subregion. It should be noted that, in this study, response to selection among pure lines or families is considered, after Comstock and Moll (1963), to be the difference that would be observed between the means of selected and unselected families in a set of trials conducted independently of the trials upon which selection was based.
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Results |
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2GS/2GL and 2GL/2G on rG'2GL relative to 2G tended to be high unless 2GL was large or 2GS was assumed to be a large part of 2GL (Table 2) . For winter wheat cultivars evaluated in eastern Canada, where 2GL was only 8% of the magnitude of 2G (Table 1), predicted values for rG' were close to 1.0 regardless of the extent to which 2GL was presumed to be caused by differential adaptation to subregions. For spring wheats tested in western Canada, where 2GL was 37% of 2G, predicted rG' remained above 0.9 even under the assumption that half of 2GL was due to specific adaptation of genotypes to subregions. However, for the case of spring wheat in Australia, where 2GL was 267% of 2G, predicted rG' was low enough to suggest that direct selection within subregions would be warranted.
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2GL is small relative to 2G. In such regions, or in more diverse regions when
is less than 0.2, the correlation between genotypic value in the subregion and the undivided target region is likely to approach or exceed 0.90. It should be noted that, according to Eq. [14], this value of rG' corresponds to a between-subregion genetic correlation (rG(ii')) of 0.81; thus, even a moderate genetic correlation across subregions will result in a high rG'. The phenotypic correlations between means in different subregions may be considerably lower still, and yet be associated with a high value for rG'. This is because the phenotypic correlation between means estimated in different subregions is the product of within-subregion repeatability (Hi) and rG(ii'). Using the winter wheat variance components in Table 1, the predicted repeatability of means from trials conducted at two sites over 2 yr, with three replicates per trial, is 0.75. Assuming rG(ii') of 0.81, the expected phenotypic correlation between sets of means estimated from two such series of trials in different subregions is expected to be only 0.61 Thus, even low levels of phenotypic correlation among trials in different subregions can still be associated with a value for rG' of 0.9 or greater. Low phenotypic correlations among trials are therefore not sufficient evidence that target regions should be subdivided.
The Effect of Subdivision of the Target Region on Hi
For subdivision of the target region to increase the selection response, increases in the contribution to 2P of the random variances 2GL
, 2GS, 2GY, 2GYS, 2GYL, and 2 resulting from reduced environmental replication should be counterbalanced by the increase in the genetic variance that results from the addition of 2GS to 2G upon subdivision. For winter wheat in eastern Canada, which exhibited little 2GL (Table 1), the increase in within-subregion 2G resulting from partition was insufficient to counterbalance the effect of the reduced number of locations per subregion, even when as much as half of 2GL was assumed to result from differential performance among subregions (Table 3)
. For spring wheat in western Canada, for which
, subdivision was only predicted to increase Hi relative to H if 2GS accounted for at least 50% of 2GL, and if testing was conducted at six sites within the subregion. For spring wheat in Australia, where 2GL was reported to greatly exceed 2G, subdivision resulted in an increase in Hi relative to H when 2GS accounted for at least 30% of 2GL and testing was conducted at four or more locations within the subregion. In general, subdivision appears likely to significantly increase the repeatability of genotype means only if at least four locations are retained within the subregion,
is 0.3 or greater, and 2GS , the component of the genotype x location interaction associated with local adaptation, accounts for at least 30% of 2GL.
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, and the size of
. For winter wheat testing networks in eastern Canada, which exhibit relatively little genotype x location interaction (
), subdivision was not predicted to increase response to selection unless 2GS accounts for 50% of 2GL, and testing occurs at six locations over 2 yr (Table 4)
. For spring wheat in western Canada, which was reported by Baker (1969) to exhibit more genotype x location interaction (
), subdivision was predicted to increase selection response if
0.3 and if at least four trial sites were retained in the subregion. For cultivars tested across the major wheat-growing regions in Australia, where 2GL was estimated to be nearly three times the magnitude of 2G, subdivision was predicted to result in increased response if as few as two test sites are retained in the subregion and if at least 30% of 2GL in the undivided region is caused by 2GS. In general, Table 4 indicates that subdivisions of a target region retaining four or fewer trial sites are unlikely to increase selection response unless 2GL is large (approximately 40% of 2G or greater) and at least 30% of 2GL is due to specific adaptation to subregions. In other situations, subdivision is likely to reduce selection response.
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Discussion |
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2GS relative to 2G and 2GL, and the precision with which genotype value can be estimated within the resulting subregions, must be taken into account. The decision should be made on the basis of a realistic assessment of available testing resources.
The geographical extent of breeding or recommendation target regions is usually determined empirically by agronomists, or by commercial, political, or logistical considerations, rather than on the basis of scientific analysis. For example, a testing network may be limited to a country, state, or province even though the soils and climate of adjacent areas are similar. The target regions represented in Table 1 are examples of such empirically or politically determined networks. Judging by the small estimates for 2GL observed in several of these networks, there often appears to be little specific adaptation to locations within regions delineated in this way. The results of this study indicate that, for many breeding programs, efforts to obtain greater selection response by attempting to produce genotypes with specific adaptation to local environments will fail unless the resources available for yield trials are multiplied when subregions are created. In three of the nine series of METs whose variance components are presented in Table 1, estimates of 2GL were less than 10% of the magnitude 2G. In these target regions, division into subregions is almost certainly unwarranted. In an additional five METs, estimates of 2GL ranged from about 30 to 100% of 2G; in these regions, subdivision might increase selection response if 2GS accounted for at least 30% of 2GL, and if four to six test sites were retained in each subregion. Only in the case of spring wheat cultivars tested across the entire Australian wheat belt, where 2GL was nearly three times the size of 2G, was the need for subdivision of the target region unequivocal.
If
is small, it is possible that combining regions, rather than subdividing them, may increase selection response, because the increased number of trials that can be conducted over a larger area increases the precision of estimates of genotype means, and hence H. Geographically extensive testing networks are likely to produce genotypes with broad adaptation. Current plant breeding practice tends to confirm this view. Many breeding programs now test very broadly (Troyer, 1996), having observed that, in their particular circumstances, the gain in H resulting from extensive testing more than compensates for the inability to exploit specific adaptation to local environments.
It should be noted that the approach to assessing the extent of local adaptation we have proposed, i.e., defining a fixed subregion and then predicting the impact of subdivision on selection response using Eq. [2], may also be extended to investigate the effect of other approaches to subdividing the target environment. For example, locations in multiple-environment trials may be grouped according to management system, soil type, or planting date. Eq. [2] may then be used to determine if selection response will be increased by attempting to develop cultivars with specific adaptation to the environmental subsets, taking into account both the extent of specific adaptation and the reduction in testing resources resulting from subdivision.
By making explicit the relationships among 2GL, 2GS, rG', H, and Hi, the model presented in this paper permits a clear description of the trade-off between the exploitation of local adaptation and the precision with which differences in genotype means are estimated for the purposes of selection. Our results indicate that selection based on means resulting from testing over a wide geographical area will often produce a greater response within local subdivisions of that area than will selection based on within-subregion means only, unless 2GS accounts for a large proportion of 2GL. This view appears to contradict that of many other investigators of GE interaction (e.g., Gauch and Zobel, 1997; Ceccarelli, 1989), who argue that the existence of genotype x environment interaction usually means that breeding for local adaptation will be more effective than strategies based on wide testing.
In our opinion, there are several reasons for this difference of views. One is that analyses that focus only on GE interaction do not take into account the effect of the reduced precision that necessarily results from division of testing resources. Even if 2GL is significantly greater than 0, as it was in most of the studies reported in Table 2, division of the target region may reduce Hi because of the splitting of testing resources among the subregions. This reduction in precision may be greater than any benefit that can be gained from selection for local adaptation.
Another reason is that many analyses of cultivar trials over environments fail to disaggregate the effects of locations and years. This results in confounding of the 2GL, 2GY, and 2GYL components in a single GE term, and may lead to mistaken conclusions of the importance of local adaptation. Of the three components of GE variance recognized by the conventional GEI model, 2GYL is usually the largest (Table 2), but only 2GL can contribute to specific adaptation to subregions. Both 2GY and 2GYL are random "noise" terms which obscure the estimation of genotypic value; their effects can only be minimized through environmental replication.
Finally, inappropriate designation of locations as fixed effects in the analysis of cultivar trials has resulted in a general overestimation of the magnitude of local adaptation. Because inferences about genotype performance are not restricted to the specific farms where trials are conducted, but are meant to apply to the surrounding area, it is usually more realistic to consider trial locations as a random sample of production sites within the target region. Regardless of how finely a target region is divided, it is still possible that random 2GL will exist among sites within the subdivisions. Only 2GS, the component of the overall 2GL variance associated with differential genotype response across subregions, can contribute to selection response resulting from the exploitation of specific adaptation. Recent reports on the strong correlation of wheat and barley (Hordeum vulgare L.) genotype response across widely separated areas (Atlin et al., 2000; Braun et al., 1992; Cooper et al., 1993a; Peterson and Pfeiffer, 1989) indicate that 2GS is likely to be small relative to 2GL in many target regions. We need to recognize explicitly that there is a random component (2GL) of site-to-site variability in genotype response within regions when GE models are used in designing cultivar trials and plant breeding programs.
These results help explain the widespread success of breeding strategies based on selection for broad adaptation as applied by commercial breeding programs (Troyer, 1996) and international agricultural research centers (Braun et al., 1996). This strategy is likely to continue to lead to extensive adoption of a small number of widely adapted genotypes supplied by large-scale breeding programs. Alternate strategies aimed at reducing genetic uniformity through the establishment of decentralized, small-scale breeding programs geared to the development of locally adapted genotypes have been proposed (Witcombe et al., 1996). Such programs will probably need to test genotypes over at least four sites within their target region if they must compete directly with large-scale breeding programs.
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ACKNOWLEDGMENTS |
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Received for publication July 1, 1998.
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