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Covariance between nonrelatives in maize


The covariance between relatives is a tenet in quantitative genetics, but the covariance between nonrelatives in crops has not been studied. My objective was to determine if a covariance between nonrelatives is present in maize (Zea mays L.). The germplasm comprised 272 maize lines that were previously genotyped with 28,626 single nucleotide polymorphism (SNP) markers. Pairs of unrelated lines were identified on the basis of their membership probabilities in five subpopulations. The covariance between nonrelatives was assessed as the regression of phenotypic similarity on SNP similarity between unrelated lines. Out of 77 regressions, seven were significant at a 5% false discovery rate: anthesis and silking dates in unrelated B73 and Oh43 lines; plant height and ear height in unrelated Oh43 and PH207 lines; oil in unrelated A321 and Mo17 lines; starch in unrelated B73 and PH207 lines; and protein in unrelated B73 and Mo17 lines. The latter covariance was negative, and this negative covariance between nonrelatives was attributed to the subpopulations having different linkage phases between the markers and underlying causal variants. Overall, the results indicated that a covariance between nonrelatives in maize is not ubiquitous but is sometimes present for specific traits and for certain groups of unrelated individuals. I propose that the covariance between nonrelatives and the covariance between relatives be combined into a generalized covariance between individuals, thus giving a unified framework for expressing the resemblance regardless of the degree of relatedness.

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Fig. 1
Fig. 2: Regression of nonrelative cross-products on across-genome marker similarity for different traits in the B73 group.

Data availability

The maize datasets analyzed in this study can be accessed in Dryad (


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The phenotypic and marker data analyzed herein were from the doctoral thesis experiments of my former Ph.D. student Christopher M. Schaefer. Thank you, Chris, for a most excellent dataset.

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The single author thought of the problem, analyzed the data, interpreted the results, and wrote this manuscript.

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Correspondence to Rex Bernardo.

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The author declares no competing interests.

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Associate editor: Chenwu Xu.

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Bernardo, R. Covariance between nonrelatives in maize. Heredity (2022).

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