Asymptotic Moments and Distribution of Nearest Marker Distances When Major Genes and Marker Polymorphisms are Unevenly Distributed

John Woolliams, Chris Haley, K. Lange

Research output: Contribution to journalArticlepeer-review

Abstract

The asymptotic mean and variance of the distance from a major gene to the nearest marker are derived for the case when the markers are distributed with density m(x) along the chromosome and the major gene with density g(x). The asymptotic distribution was derived by analogy with Poisson processes. For a given g(x), the density of markers that minimised the expected distance to the nearest marker was proportional to root g(x); expected squared distance was minimised when the density of markers was proportional to root g(x). Comparison with simulations showed the asymptotic moments and distribution to be accurate when the number of markers n greater than or equal to 100, but even for n greater than or equal to 20 the first moment was considerably better than that derived from assuming uniformly distributed marker loci.
Original languageEnglish
Pages (from-to)1245-1251
Number of pages7
JournalBiometrics
Volume49
Issue number4
Publication statusPublished - 1993

Keywords

  • asymptotic distributions asymptotic moments euler-lagrange equations genes markers poisson processes uneven distributions human genome

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