Multilocus ordering strategies based on sperm typing

Sperm typing is a promising new approach for fine‐structure human gene mapping. We examine three‐locus sperm typing and its implications for the estimation of recombination fractions and for locus ordering. In particular, we compare some sequential stopping rules for three‐locus order assignment and develop methods for approximating their mean stopping times and error probabilities. A stopping rule recently described by Thompson and Boehnke et al. appears to be nearly optimal. Under this rule, one stops sampling as soon as the number of sperm of the least frequent recombinant type is s fewer than the number of sperm of the next least frequent type. We develop a random‐walk algorithm and some heuristic formulas for assessing the performance of this rule.

[1]  K. Lange,et al.  Single-sperm typing: determination of genetic distance between the G gamma-globin and parathyroid hormone loci by using the polymerase chain reaction and allele-specific oligomers. , 1989, Proceedings of the National Academy of Sciences of the United States of America.

[2]  P. Jones,et al.  Bayesian sequential methods for choosing the best multinomial cell: some simulation results , 1988 .

[3]  D. Aldous.  Probability Approximations via the Poisson Clumping Heuristic , 1988 .

[4]  Henry A. Erlich,et al.  Amplification and analysis of DNA sequences in single human sperm and diploid cells , 1988, Nature.

[5]  K. Mullis,et al.  Primer-directed enzymatic amplification of DNA with a thermostable DNA polymerase. , 1988, Science.

[6]  J. Gitschier,et al.  An improved method for prenatal diagnosis of genetic diseases by analysis of amplified DNA sequences. Application to hemophilia A. , 1987, The New England journal of medicine.

[7]  Henry A. Erlich,et al.  Analysis of enzymatically amplified β-globin and HLA-DQα DNA with allele-specific oligonucleotide probes , 1986, Nature.

[8]  K. Mullis,et al.  Enzymatic amplification of beta-globin genomic sequences and restriction site analysis for diagnosis of sickle cell anemia. , 1985, Science.

[9]  D. Siegmund.  Sequential Analysis: Tests and Confidence Intervals , 1985 .

[10]  Mauro Cerasoli.  Poisson randomization in occupancy problems , 1983 .

[11]  D. Botstein,et al.  Construction of a genetic linkage map in man using restriction fragment length polymorphisms. , 1980, American journal of human genetics.

[12]  Y. Kan,et al.  Polymorphism of DNA sequence adjacent to human beta-globin structural gene: relationship to sickle mutation. , 1978, Proceedings of the National Academy of Sciences of the United States of America.

[13]  Khursheed Alam,et al.  On Selecting the Most Probable Category , 1971 .

[14]  W. Hoeffding.  Probability inequalities for sum of bounded random variables , 1963 .

[15]  W. Feller.  An Introduction to Probability Theory and Its Applications , 1959 .

[16]  F. Collins,et al.  Fine-structure genetic mapping of human chromosomes using the polymerase chain reaction on single sperm: experimental design considerations. , 1989, American journal of human genetics.

[17]  D. Bishop.  The information content of phase-known matings for ordering genetic loci. , 1985, Genetic epidemiology.

[18]  David Siegmund,et al.  The Sequential Probability Ratio Test , 1985 .

[19]  E A Thompson,et al.  Information gain in joint linkage analysis. , 1984, IMA journal of mathematics applied in medicine and biology.