The effect of linkage on the calculation of DNA match probabilities for siblings and half siblings

The loci in many forensic multiplexes are often selected to avoid linked loci. However as the multiplices used increase in the number of loci represented instances are occurring of loci that are loosely linked. As yet little attention has been paid to the likely consequence of this. We begin the process of developing formulae to give the match probability at two linked loci for full and half siblings. The methodology proceeds from the previously published joint IBD states for two linked loci [B.K. Suarez, J. Rice, T. Reich, The generalized sib pair IBD distribution: its use in the detection of linkage, Ann. Hum. Genet. Lond. 42 (1978) 87; J.K. Haseman, R.C. Elston, The investigation of linkage between a quantitative trait and a marker locus, Behav. Genet. 2 (1972) 3-19]. Our formulation has the drawback of assuming linkage equilibrium. This assumption may be tenable as a first order approximation. We hope to stimulate work on developing better treatments.