The conditional independences between variables derived from two independent identically distributed Markov random fields when pairwise order is ignored.

A result for the equivalence of conditional independence graphs of ordered and unordered vector random variables from first-order Markov models is extended to arbitrary forests. The result is relevant to estimating graphical models for linkage disequilibrium between genetic loci. It explains why, in terms of the conditional independence structure, it sometimes does not matter whether you consider haplotypes or genotypes.