Identifying Linkage Groups by Nonlinearity/Non-monotonicity Detection

This paper presents and discusses direct linkage identiication procedures based on nonlinearity/non-monotonicity detection. The algorithm we propose checks arbitrary nonlinearity/non-monotonicity of t-ness change by perturbations in a pair of loci to detect their linkage. We rst discuss condition of the linkage identiication by nonlinearity check (LINC) procedure (Mune-tomo & Goldberg, 1998) and its allowable nonlinearity. Then we propose another condition of the linkage identiication by non-monotonicity detection (LIMD) and prove its equality to the LINC with allowable nonlin-earity (LINC-AN). The procedures can identify linkage groups for problems with at most order-k diiculty by checking O(2 k) strings and the computational cost for each string is O(l 2) where l is the string length.