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Stability Parameters for Comparing Varieties 1

Steve A. Eberhart, Wilbert A. Russell

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Abstract

The model, Y ij = μ 1 + β 1 I j + δ ij , defines stability parameters that may be used to describe the performance of a variety over a series of environments. Y ij is the variety mean of the i th variety at the j th environment, µ 1 is the i th variety mean over all environments, β 1 is the regression coefficient that measures the response of the i th variety to varying environments, δ ij is the deviation from regression of the i th variety at the j th environment, and I j is the environmental index. The data from two single‐cross diallels and a set of 3‐way crosses were examined to see whether genetic differences could be detected. Genetic differences among lines were indicated for the regression of the lines on the environmental index with no evidence of nonadditive gene action. The estimates of the squared deviations from regression for many hybrids were near zero, whereas extremely large estimates were obtained for other hybrids.

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The model, Y ij = μ 1 + β 1 I j + δ ij , defines stability parameters that may be used to describe the performance of a variety over a series of environments. Y ij is the variety mean of the i th variety at the j th environment, µ 1 is the i th variety mean over all environments, β 1 is the regression coefficient that measures the response of the i th variety to varying environments, δ ij is the deviation from regression of the i th variety at the j th environment, and I j is the environmental index. The data from two single‐cross diallels and a set of 3‐way crosses were examined to see whether genetic differences could be detected. Genetic differences among lines were indicated for the regression of the lines on the environmental index with no evidence of nonadditive gene action. The estimates of the squared deviations from regression for many hybrids were near zero, whereas extremely large estimates were obtained for other hybrids.

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Available abstract

The model, Y ij = μ 1 + β 1 I j + δ ij , defines stability parameters that may be used to describe the performance of a variety over a series of environments. Y ij is the variety mean of the i th variety at the j th environment, µ 1 is the i th variety mean over all environments, β 1 is the regression coefficient that measures the response of the i th variety to varying environments, δ ij is the deviation from regression of the i th variety at the j th environment, and I j is the environmental index. The data from two single‐cross diallels and a set of 3‐way crosses were examined to see whether genetic differences could be detected. Genetic differences among lines were indicated for the regression of the lines on the environmental index with no evidence of nonadditive gene action. The estimates of the squared deviations from regression for many hybrids were near zero, whereas extremely large estimates were obtained for other hybrids.

Key concepts: Variety (cybernetics), Linear regression, Regression, Hybrid, Biology, Gene–environment interaction, Statistics, Regression analysis

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