Multipoint genetic mapping with trisomy data

Trisomy is the most common genetic abnormality in humans and is the leading cause of mental retardation. Although molecular studies that use a large n umber of highly polymorphic markers have been undertaken to understand the recombination patterns for chromosome abnormalities, there is a lack of mul tilocus approaches to incorporating crossover interference in the analysis of human trisomy data. In the present article, we develop two statistical m ethods that simultaneously use all genetic information in trisomy data. The first approach relies on a general relationship between multilocus trisomy probabilities and multilocus ordered-tetrad probabilities. Under the assum ption that no more than one chiasma exists in each marker interval, we desc ribe how to use the expectation-maximization algorithm to examine the proba bility distribution of the recombination events underlying meioses that lea d to trisomy. One limitation of the first approach is that the amount of co mputation increases exponentially with the number of markers. The second ap proach models the crossover process as a chi (2) model. We describe how to use hidden Markov models to evaluate multilocus trisomy probabilities. Our methods are applicable when both parents are available or when only the non disjoining parent is available. For both methods, genetic distances among a set of markers can be estimated and the pattern of overall chiasma distrib ution can be inspected for differences in recombination between meioses exh ibiting trisomy and normal meioses. We illustrate the proposed approaches t hrough their application to a set of trisomy 21 data.