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Abstract:
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The statistical genetics of quantitative traits have benefited deeply from analysis of variance methods, which carry assumptions of finite moments and normal kurtosis. Heavy tailed distribution methods violate these assumptions and can therefore lead to radically different behaviors. Our assertion is that the genetics of heavy-tailed traits is not merely Gaussian genetics with outliers; rather, these traits exhibit subtle heritability patterns, especially in polygenic traits, and show the classical distinction between heterogeneous Mendelian and blending forms of inheritance by a novel bifurcation argument. We derive closed form results using the Cauchy distribution, which we show to be a steady state in a broad family of population processes, and connect the distribution to evolvability via extreme value theory and process subordination arguments.
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