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Correcting for Inbreeding in Parent-Offspring Regression Estimates of Heritability with Non-Additive and Genotype x Environment Effects Present

Dep. of Plant and Soil Science, Southern Illinois Univ. at Carbondale, IL 62901-4415

^* Corresponding author (pgibson{at}siu.edu).

Inbreeding, non-additive genetic effects, and genotype x environment interactions (GxE) 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 GxE are present, the influence of inbreeding is removed by the correction of Nyquist, h² = 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, h² is only slightly more than 0.5 b when b is small and F_t 0.5 (any generation greater than F₂ or S₀ in a selling series). This paper assesses the biases from use of Nyquist's correction with GxE, and with non-additive genetic effects with and without GxE. When considering individual-plant heritabilities, values of b' were compared with boot, defined as the parent-offspring regression coefficient of S₁ on S₀ (or F₃ on F₂). In the absence of GxE, gene frequencies of 0.5 result in b' values within 0.1 absolute unit of b₀₀₁, 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' – b₀₀₁| 0.1 and (|b' – b₀₀₁|/b₀₀₁) 0.2 occurring jointly. Dominance, with or without additive epistasis, occasionally produces severely biased values of b', which generally overestimate b₀₀₁ more strongly as inbreeding increases. Non-additive effects combined with GxE produce b' values that sometimes severely underestimate b₀₀₁, especially as inbreeding increases. Overall conclusions were the same for family-mean heritabilities in which b' was compared to b₀₁₂, defined as S₂ on S₁ family mean (or F₄ on F₃) regression. Despite some cases of severe bias, b' is generally superior to b per se as an estimator of b₀₀₁ or b₀₁₂.

Received for publication August 12, 1994.