Hostname: page-component-7479d7b7d-pfhbr Total loading time: 0 Render date: 2024-07-13T12:03:51.138Z Has data issue: false hasContentIssue false
  • English
  • Français

Distribution of the amount of genetic material from a chromosomal segment surviving to the following generation

Part of: Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Valeri T. Stefanov
Valeri T. Stefanov*
Affiliation:
University of Western Australia
*
∗ Postal address: School of Mathematics and Statistics, University of Western Australia, Crawley, WA 6009, Australia. Email address: stefanov@maths.uwa.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

A method is provided for numerical evaluation, with any given accuracy, of the probability that at least p% of the genetic material from an individual's chromosomal segment survives to the next generation. Relevant MAPLE® V codes, for automated implementation of such evaluation, are also provided. The genomic continuum model, with Haldane's model for the crossover process, is assumed.

Keywords

Genomic continuum modelgenome surviving to the next generationstopping timeexponential family

MSC classification

Primary: 92D10: Genetics 62E15: Exact distribution theory
Secondary: 60E10: Characteristic functions; other transforms
Type
Research Papers
Information
Journal of Applied Probability , Volume 41 , Issue 2 , June 2004 , pp. 345 - 354
Copyright
Copyright © Applied Probability Trust 2004 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Barndorff-Nielsen, O. (1978). Information and Exponential Families. John Wiley, Chichester.Google Scholar
Bickeboller, H., and Thompson, E. A. (1996a). Distribution of genome shared IBD by half-sibs: approximation by the Poisson clumping heuristic. Theoret. Pop. Biol. 50, 66–90.Google Scholar
Bickeboller, H., and Thompson, E. A. (1996b). The probability distribution of the amount of an individual's genome surviving to the following generation. Genetics 143, 1043–1049.Google Scholar
Donnelly, K. (1983). The probability that related individuals share some section of the genome identical by descent. Theoret. Pop. Biol. 23, 34–64.CrossRefGoogle ScholarPubMed
Jacod, J., and Shiryaev, A. N. (1987). Limit Theorems for Stochastic Processes. Springer, Berlin.CrossRefGoogle Scholar
Karr, A. (1991). Point Processes and Their Statistical Inference (Prob. Pure. Appl. 7), 2nd edn. Marcel Dekker, New York.Google Scholar
Stefanov, V. T. (1991). Noncurved exponential families associated with observations over finite state Markov chains. Scand. J. Statist. 18, 353–356.Google Scholar
Stefanov, V. T. (2000). Distribution of genome shared IBD by two individuals in grandparent-type relationship. Genetics 156, 1403–1410.Google Scholar
Stefanov, V. T. (2002). Statistics on continuous IBD data: exact distribution evaluation for a pair of full(half)-sibs and a pair of a (great-) grandchild with a (great-) grandparent. BMC Genetics 3, No. 7.CrossRefGoogle Scholar
Widder, D. V. (1971). An Introduction to Transform Theory. Academic Press, New York.Google Scholar