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. 2021 Feb 15;22:119. doi: 10.1186/s12864-021-07414-7

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© The Author(s) 2021

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated in a credit line to the data.

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Fig. 3 — A flow diagram of three coefficient of determination (CD) statistics. The group average CD (CD_{_}GrpAve) is shown in A. A1: A relationship matrix of seven individuals. A2: Calculate the mean relationships within and between units. A3: Group average CD is calculated by scaling group average PEVD (PEVD_{_}GrpAve) by the quantity obtained from the PEVD equation using the within and between unit means. The individual average CD (CD_{_}IdAve) is shown in B. B1: A relationship matrix of seven individuals. B2: Calculate pairwise relationship differences of individuals between the units. Subscripts i and j refer to the ith and jth individuals in units 1 and 2, respectively. B3: Individual average CD is calculated by scaling indvidual average PEVD (PEVD_{_}IdAve) with the average of pairwise relationship differences of individuals. The CD of contrast (CD_{_}Contrast) is shown in C. CD_{_}Contrast is calculated by scaling the prediction error variance of the differences (PEVD) of contrast with the product of the transpose of the contrast vector (x), the relationship matrix (K), and the contrast vector