Journal of Heredity Advance Access originally published online on December 23, 2004
Journal of Heredity 2005 96(1):78-79; doi:10.1093/jhered/esi003
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© 2005 The American Genetic Association
Computer Note |
GENSTAT Programs for Performing Muir's Alternative Partitioning of Genotype-by-Environment Interaction
From the Department of Primary Industries, PIRVic-Horsham, Natimuk Road, Private Bag 260, Horsham Victoria 3401, Australia
Address correspondence to L. C. Emebiri at the address above.
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Abstract |
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 Top Abstract Program DescriptionNumerical ValidationNew ApplicationsAvailabilityReferences |
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Genotype-by-environment (GE) interaction exists when different cultivars or strains have different phenotypic responses to environmental variation (Merila and Fry 1998). The phenomenon is of major concern in plant breeding, as it can limit gains in selecting superior cultivars. In animal breeding, the problem is also an important issue because breeding stocks are developed by a few companies but are used worldwide (Lin and Togashi 2002).
Genotype-by-environment interactions can arise from two possible sources: the difference in responses of the same set of genes to different environments, and the expression of different sets of genes in different environments (Cockerham 1963; Falconer 1952; Robertson 1959). Analysis of variance (ANOVA) serves to provide information on the existence of significant GE interactions, but is incapable of explaining the pattern of GE interaction, which is often the most important portion of the total variance that impacts on breeding strategies.
The GE interaction sum of squares may be partitioned into two components: one due to heterogeneity of variances among environments and one due to lack of perfect correlation of the same trait measured in two environments (Dickerson 1962; Robertson 1959; Yamada 1962). A significant GE interaction may take place because of one or both of these two components. Heterogeneous variances cause a change in scale (scaling effect), but do not alter the ranking of the cultivars (noncrossover GE interaction). On the other hand, a lack of perfect correlation (Muir et al. 1992) would result in reranking of cultivars (i.e., crossover GE interaction) (Baker 1988). This is the component that can complicate selection because it measures the degree to which performance in one environment fails to predict performance in the other.
In most studies where GE interaction is partitioned into these two components, only the total GE sum of squares is partitioned (e.g., Burdon 1977; Chapman et al. 2000; Krenzer et al. 1992; Moll et al. 1978; Wu and Stettler 1997). This allows inferences to be made at the trait level, but such trait-based analyses are not very helpful in selection since recommendations cannot be made among cultivars and testing environments. Specifically, they provide no insight into the contribution of each cultivar, environment, or combinations to the total GE sum of squares. Muir et al. (1992) described an algorithm for partitioning GE sum of squares into components assignable to individual cultivars and/or environments. The algorithm was applied by Grausgruber et al. (2000) to characterize cultivar stability for quality traits in Austrian-grown winter wheats, but the statistics are tedious and cumbersome to calculate manually. Herein we describe programs for routine implementation of the two methods that were written for use with the GENSTAT statistical software package.
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Program Description |
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TopAbstractProgram DescriptionNumerical ValidationNew ApplicationsAvailabilityReferences |
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Muir et al. (1992) described two methods for partitioning the GE sum of squares into components associated with heterogeneous variance and those due to imperfect correlation. Method 1 partitions the GE sum of squares into components ascribable to each environment, while method 2 calculates components contributed by each cultivar.
We have written two separate programs to allow routine implementation of both methods for any multienvironment dataset. The same array of GE data (e.g., Table 1) is used for both methods. The programs are available as .gen files which can be run on a PC licensed for GENSTAT, and these are executed by opening the .gen file and editing the required user inputs. These are (1) the number of samples, (2) the number of cultivars, (3) the number of environments, and (4) the data file. The required data file is stored in a text format that can be read by GENSTAT using the Open command in our program.
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The output file provides descriptive statistics of the GE matrix in terms of means, minimum and maximum values, and number of valid and missing data points. It also provides the total sum of squares associated with GE interactions and its decomposition into sources due to heterogeneity of variance and lack of perfect correlation. In addition, the output provides the contribution (in terms of sum of squares) made by any given cultivar or environment to the total GE sum of squares and a partition of this measure into sources due to heterogeneity of variance and lack of perfect correlation.
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Numerical Validation |
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TopAbstractProgram DescriptionNumerical ValidationNew ApplicationsAvailabilityReferences |
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For numerical validation of our program, we reanalyzed the original data used by Muir et al. (1992), which can be found in Table 9 of their article (Table 1 in this article). The required input parameters were the number of samples (which in this case was the number of years x number of plots, or 2 years x 3 plots = 6), the number of cultivars (5 cultivars), and number of environment (6 environments).
The results showed very good agreement with the published output of Muir et al. (1992). The Print command of GENSTAT provides the total for each component, which is very useful in quantifying the proportion each component made to the total GE sum of squares.
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New Applications |
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TopAbstractProgram DescriptionNumerical ValidationNew ApplicationsAvailabilityReferences |
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A unique and useful feature of our program is the output of a half-matrix of the GE sum of squares and products associated with any given pair of cultivars or environments. These data can be imported into any dendrogram drawing software to identify clusters of cultivars and/or environments with similar effects on the total GE sum of squares. As an example, when the output from analysis based on method 2 was imported into the MVSP software (Kovach Computing Service; available at http://www.kovcomp.com/), the results showed that Svansota and Velvet were very similar in their response and were more related to Manchuria than either Trebi or Peatland (Figure 1). Muir et al. (1992) identified Trebi as the least stable of the cultivars and Peatland as the most stable. Both cultivars were clearly distinguishable on the dendrogram.
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Availability |
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TopAbstractProgram DescriptionNumerical ValidationNew ApplicationsAvailabilityReferences |
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Both GENSTAT programs are freely available upon request by e-mail to Livinus.Emebiri{at}dpi.vic.gov.au. Detailed instructions, including the example dataset, will be distributed along with the programs.
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Acknowledgments |
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Financial support from the Grains Research & Development Corporation (GRDC) under project DAV395 is gratefully acknowledged.
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Footnotes |
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Corresponding Editor: Irwin Goldman
Received May 1, 2003
Accepted June 30, 2004
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References |
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