The Poisson-skip model of crossing-over

Annals of Applied Probability

Volumn 7, Issue 2, 1997, Pages 299-313

  Lange, Kenneth ^a   Zhao, Hongyu ^b   Speed, Terence P ^c  

^a UNIVERSITY OF MICHIGAN   (United States)

^b YALE UNIVERSITY SCHOOL OF MEDICINE   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Genetic recombination; Interference; Markov chain; Poisson process; Reliability theory; Renewal process

Indexed keywords

EID: 0031287502     PISSN: 10505164     EISSN: None     Source Type: Journal    
DOI: 10.1214/aoap/1034625332     Document Type: Article

References (37)

1. BARLOW, R. E. and PROSCHAN, F. (1975). Statistical Theory of Reliability and Life Testing. Holt, Rinehart and Winston, New York.
2. BAUM, L. E. (1972). An inequality and associated maximization technique in statistical estimation for probabilistic functions of Markov processes. Inequalities 3 1-8.
3. BLANK, R. D., CAMPBELL, G. R., CALABRO, A. and EUSTACHIO, P. D. (1988). A linkage map of mouse chromosome 12: localization of Igh and effects of sex and interference on recombination. Genetics 120 1073-1083.
4. CARTER, T. C. and ROBERTSON, A. (1952). A mathematical treatment of genetical recombination using a four-strand model. Proc. Roy. Soc. London Ser. B 139 410-426.
5. COBBS, G. (1978). Renewal process approach to the theory of genetic linkage: case of no chromatid interference. Genetics 89 563-581.
6. DEVIJVER, P. A. (1985). Baum's forward-backward algorithm revisited. Pattern Recognition Lett. 3 369-373.
7. FISHER, R. A., LYON, M. F. and OWEN, A. R. G. (1947). The sex chromosome in the house mouse. Heredity 1 335-365.
8. FOSS, E., LANDE, R., STAHL, F. W. and STEINBERG, C. M. (1993). Chiasma interference as a function of genetic distance. Genetics 133 681-691.
9. FOSS, E. and STAHL, F. W. (1995). A test of a counting model for chiasma interference. Genetics 139 1201-1209.
10. GOLDGAR, D. E. and FAIN, P. R. (1988). Models of multilocus recombination: nonrandomness in chiasma number and crossover positions. Amer. J. Hum. Genet. 43 38-43.
11. GOLDSTEIN, D. R., ZHAO, H. and SPEED, T. P. (1995). Relative efficiencies of several statistical models of recombination for exclusion mapping and gene ordering. Genomics 27 265-273.
12. KARLIN, S. and LIBERMAN, U. (1979). A natural class of multilocus recombination processes and related measure of crossover interference. Adv. in Appl. Probab. 11 479-501.
13. KARLIN, S. and LIBERMAN, U. (1983). Measuring interference in the chiasma renewal formation process. Adv. in Appl. Probab. 15 471-487.
14. KING, J. S. and MORTIMER, R. K. (1990). A polymerization model of chiasma interference and corresponding computer simulation. Genetics 126 1127-1138.
15. MATHER, K. (1935). Reduction and equational separation of the chromosomes in bivalents and multivalents. J. Genet. 30 53-78.
16. MATHER, K. (1938). Crossing over. Biol. Rev. 13 252-292.
17. MCPEEK, M. S. and SPEED, T. P. (1995). Modeling interference in genetic recombination. Genetics 139 1031-1044.
18. MORGAN, T. H., BRIDGES, C. B. and SCHULTZ, J. (1935). Report of investigations on the constitution of the germinal material in relation to heredity. Carnegie Institute of Washington 34 284-291.
19. MULLER, H. J. (1916). The mechanism of crossing over. Amer. Nat. 50 193-207.
20. NEUTS, M. F. (1981). Matrix-Geometric Solutions in Stochastic Models. Johns Hopkins Univ. Press.
21. OWEN, A. R. G. (1950). The theory of genetical recombination. Adv. Genet. 3 117-157.
22. PAYNE, L. C. (1956). The theory of genetical recombination: a general formulation for a certain class of intercept length distributions appropriate to the discussion of multiple linkage. Proc. Roy. Soc. London Ser. B 144 528-544.
23. PERKINS, D. D. (1962). Crossing-over and interference in a multiply marked chromosome arm of Neurospora. Genetics 47 1253-1274.
24. PRESS, W. H., TEUKOLSKY, S. A., VETTERLING, W. T. and FLANNERY, B. P. (1992). Numerical Recipes in Fortran: The Art of Scientific Computing, 2nd ed. Cambridge Univ. Press.
25. RISCH, N. and LANGE, K. (1979). An alternative model of recombination and interference. Ann. Hum. Genet. 43 61-70.
26. ROSS, S. M. (1983). Stochastic Processes. Wiley, New York.
27. SPEED, T. P., MCPEEK, M. S. and EVANS, S. N. (1992). Robustness of the no-interference model for ordering genetic markers. Proc. Nat. Acad. Sci. U.S.A. 89 3103-3106.
28. STAM, P. (1979). Interference in genetic crossing over and chromosome mapping. Genetics 92 573-594.
29. STRICKLAND, W. N. (1961). Tetrad analysis of short chromosome regions of Neurospora crassa. Genetics 46 1125-1141.
30. STURTEVANT, A. H. (1915). The behavior of the chromosomes as studied through linkage. Z. Indukt. Abstammungs. Vererbungsl. 13 234-287.
31. TODD, J. A., AITMAN, T. J., CORNALL, R. J., GHOSH, S., HALL J. R. et al. (1991). Genetic analysis of autoimmune type 1 diabetes mellitus in mice. Nature 351 542-547.
32. WEEKS, D. E., OTT, J. and LATHROP, G. M. (1994). Detection of genetic interference: simulation studies and mouse data. Genetics 136 1217-1226.
33. WEINSTEIN, A. (1935). The theory of multiple strand crossing over. Genetics 21 155-199.
34. ZHAO, H. (1995). Statistical Analysis of Genetical Interference. Ph.D. dissertation, Univ. California, Berkeley.
35. ZHAO, H. and SPEED, T. P. (1996). On genetic map functions. Genetics 142 1369-1377.
36. ZHAO, H., SPEED, T. P. and MCPEEK, M. S. (1995a). Statistical analysis of crossover interference using the chi-square model. Genetics 139 1045-1056.
37. ZHAO, H., MCPEEK, M. S. and SPEED, T. P. (1995b). Statistical analysis of chromatid interference. Genetics 139 1057-1065.