Multiobjective Genetic Marker Selection

A genetic mapping project, typically implemented during a search for genes responsible for a disease, requires the acquisition of a set of data from each of a large number of individuals. This data set includes the values of multiple genetic markers. These genetic markers occur at discrete positions along the genome, which is a collection of one or more linear chromosomes. Typing the value of a marker in an individual carries a cost; one seeks to minimize the number of markers typed without excessively jeopardizing the probability of detecting an association between a marker and a disease phenotype. The probability of detecting an association between a marker and a disease phenotype decreases with distance between the marker and the actual position of the gene responsible for the phenotype. Thus, one can maximize the probability of detecting disease linkage by choosing markers as closely spaced as possible. In general, the decrease in probability of detecting association is not linear with distance; this probability tends to be relatively constant across patches of the genome known as ”haplotype blocks”. Thus one can save considerably on the cost of a mapping project by choosing no more than one marker from each haplotype block. Generally, the exact boundaries of haplotype blocks are not known prior to project execution, but it is often possible to assume that all haplotype blocks are of the same constant length s. One typically searches for a marker-disease linkage within a given locus, or possibly set of locuses, of the genome. For purposes of this paper, a ”locus” is any linear segment of the genome; in practice, a locus is typically fifty kilobases (kb) to several megabases (Mb). Each locus can be considered independently. The locations of genetic markers are known prior to project initiation. In general, the number of known genetic markers exceeds the number necessary and/or affordable for a project. Thus, prior to project initiation, one is faced with the task of selecting a subset of markers from this initial library of markers. This paper presents algorithms for the solution of this selection task. Markers in the library will have been previously characterized to a lesser or greater extent. A marker may be listed in error such that there is not in reality a marker at that position in the genome. A marker may be present in