Estimates of Variety ✕ Environmental Interactions in Yield Tests of Three Small Grains and Their Significance on the Breeding Programs1

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Abstract
The purpose of this study was to obtain estimates of the relative magnitudes of the various types of variety ✕ environment interactions in variety tests, and to consider the significance of these interactions on variety evaluation procedures. Ten varieties of winter wheat at 13 locations, 4 varities of winter barley at 10 locations, and 5 spring oat varieties at 5 locations were evaluated in Kansas for a 3‐year period. The variety ✕ year interactions were small and nonsignificant, but the second‐order interactions of variety ✕ location ✕ year were of considerable magnitude and highly significant. The significant three‐factor interaction was not accounted for by grouping locations, and in general, must be regarded as an error variance to be controlled by the number of locations used and number of years of testing. Significant variety ✕ location interactions were obtained for wheat and barley, indicating the state could be divided into subareas. By grouping appropriate locations together, a reduction of the magnitude of variety ✕ location mean square was generally observed. However, it is suggested that each subarea should be considered as an independent unit in testing the significance of variety ✕ location interaction because the decrease or increase in the magnitude of variety ✕ location mean squares of subareas compared to that of the state as a whole does not always provide the true picture of its significance.

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