Resultants in Genetic Linkage Analysis
Ingileif B. Hallgrimsdottir, Bernd Sturmfels
Abstract
Statistical models for genetic linkage analysis of k-locus diseases are k-dimensional subvarieties of a (3k-1)-dimensional probability simplex. We determine the algebraic invariants of these models with general characteristics for k=1, in particular we recover, and generalize, the Hardy-Weinberg curve. For k = 2, the invariants are presented as determinants of 32x32-matrices of linear forms in 9 unknowns, a suitable format for computations with numerical data.
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