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Classical statistical genetics models of a quantitative trait depending on an autosomal gene indicate that father-to-daughter and mother-to-son correlations should be the same. If phenotypes are not sex-dependent, father-to-son and mother-to-daughter correlations also share this common value. On the other hand, if the gene is sex-linked, then the father-to-son correlation is zero. Such models do not explain genetic variation in pulmonary artery pressure (PAP) of cattle -- important because cattle with high PAP are known to develop Brisket Disease, pulmonary heart disease and congestive heart failure when taken to high altitudes. Data on 966 calves at a ranch in Colorado showed positive correlation (0.2) between sire PAP and male calf PAP, but slightly negative correlation (-0.01) between sire PAP and female calf PAP; the dam to male calf and dam to female calf correlations are both about 0.1. The model presented here postulates an autosomal gene with reduced penetrance (i.e. the trait may remain at a normal level even when the genotype suggests abnormality), and that, in males, the rate of penetrance is related to an abnormality in the Y chromosome, and is therefore passed on from father to son. Then under plausible selective breeding assumptions, the pairwise correlation between fathers and daughters can become zero or negative. Explicit formulas are computed for the model covariances, and numerical computations indicate that plausible parameter values can be chosen for the model. (to appear in BIOMETRICS)

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