Statistical methods for polyploid radiation hybrid mapping.

Radiation hybrid mapping is a somatic cell technique for ordering genetic loci along a chromosome and estimating physical distances between adjacent loci. This paper presents a model of fragment generation and retention for data involving two or more copies of the chromosome of interest per clone. Such polyploid data can be generated by initially irradiating normal diploid cells or by pooling haploid or diploid clones. The current model assumes that fragments are generated in the ancestral cell of a clone according to an independent Poisson breakage process along each chromosome. Once generated, fragments are independently retained in the clone with a common retention probability. On the basis of this and less restrictive retention models, statistical criteria such as minimum obligate breaks, maximum likelihood ratios, and Bayesian posterior probabilities can be used to decide locus order. Distances can be estimated by maximum likelihood. Likelihood computation is particularly challenging, and computing techniques from the theory of hidden Markov chains prove crucial. Within this context it is possible to incorporate typing errors. The statistical tools discussed here are applied to 14 loci on the short arm of human chromosome 4.