CORRECTING FOR INBREEDING IN PARENT-OFFSPRING REGRESSION ESTIMATES OFHERITABILITY WITH NONADDITIVE AND GENOTYPE-X ENVIRONMENT EFFECTS PRESENT

Inbreeding, non-additive genetic effects, and genotype x environment i nteractions (GxE) cause parent-offspring (PO) regression estimates (b) of heritability obtained from one pair of PO generations to differ fr om those obtained from another pair of generations. If no non-additive genetic effects and no GxE are present, the influence of inbreeding i s 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 of line der ivation (t). When b is near unity, the correction is small even with c omplete inbreeding. However, h(2) is only slightly more than 0.5 b whe n b is small and F-t greater than or equal to 0.5 (any generation grea ter than F-2 or S-0 in a selfing series). This paper assesses the bias es from use of Nyquist's correction with GxE, and with non-additive ge netic effects with and without GxE. 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 GxE, gene frequencies of 0.5 result in b' values wi thin 0.1 absolute unit of b(001), regardless of non-additive effects o r degree of inbreeding. Gene frequencies in the range of 0.1 to 0.9 co mbined with additive epistasis, but with no dominance, produce no seve re biases, arbitrarily defined as \b' - b(001)\ greater than or equal to 0.1 and (\b' - b(001)\ / b(001)) greater than or equal to 0.2 occur ring jointly. Dominance, with or without additive epistasis, occasiona lly produces severely biased values of b', which generally overestimat e b(001) more strongly as inbreeding increases. Non-additive effects c ombined with GxE produce b' values that sometimes severely underestima te b(001), especially as inbreeding increases. Overall conclusions wer e 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 s e as an estimator of b(001) or b(012).