Resultants in genetic linkage analysis

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 algebraic invariants are presented as determinants of 32×32-matrices of linear forms in nine unknowns, a suitable format for computations with numerical data.