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Correcting for Inbreeding in Parent‐Offspring Regression Estimates of Heritability with Non‐Additive and Genotype × Environment Effects Present
Author(s) -
Gibson P. T.
Publication year - 1996
Publication title -
crop science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.76
H-Index - 147
eISSN - 1435-0653
pISSN - 0011-183X
DOI - 10.2135/cropsci1996.0011183x003600030012x
Subject(s) - inbreeding , biology , additive function , heritability , epistasis , genetics , statistics , offspring , linear regression , zoology , population , mathematics , demography , gene , pregnancy , mathematical analysis , sociology
Inbreeding, non‐additive genetic effects, and genotype × environment interactions (G×E) cause parent‐offspring (PO) regression estimates ( b ) of heritability obtained from one pair of PO generations differ from those obtained from another pair of generations. If no non‐additive genetic effects and no G×E are present, the influence of inbreeding is removed by the correction of Nyquist, h 2 = b = b /[1 + F t (1 − b )], where F t is the inbreeding coefficient in the generation line derivation ( t ). When b is near unity, the correction is small even with complete inbreeding. However, h 2 is only slightly more than 0.5 b when b is small and F t ≥ 0.5 (any generation greater than F 2 or S 0 in a selling series). This paper assesses the biases from use of Nyquist's correction with G×E, and with non‐additive genetic effects with and without G×E. When considering individual‐plant heritabilities, values of b ′ were compared with b 001 , defined as the parent‐offspring regression coefficient of S 1 on S 0 (or F 3 on F 2 ). In the absence of G×E, gene frequencies of 0.5 result in b ′ values within 0.1 absolute unit of b 001 , regardless of non‐additive effects or degree of inbreeding. Gene frequencies in the range of 0.1 to 0.9 combined with additive epistasis, but with no dominance, produce no severe biases, arbitrarily defined as | b ′ − b 001 | ≥ 0.1 and (| b ′ − b 001 |/ b 001 ) ≥ 0.2 occurring jointly. Dominance, with or without additive epistasis, occasionally produces severely biased values of b ′, which generally overestimate b 001 more strongly as inbreeding increases. Non‐additive effects combined with G×E produce b ′ values that sometimes severely underestimate b 001 , especially as inbreeding increases. Overall conclusions were the same for family‐mean heritabilities in which b ′ was compared to b 012 , defined as S 2 on S 1 family mean (or F 4 on F 3 ) regression. Despite some cases of severe bias, b ′ is generally superior to b per se as an estimator of b 001 or b 012 .