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

*(English)*Zbl 1053.62124Summary: 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\(^\circledR\) 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.

##### MSC:

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

62E15 | Exact distribution theory in statistics |

92D10 | Genetics and epigenetics |

65C60 | Computational problems in statistics (MSC2010) |

##### Keywords:

genomic continuum model; genome surviving to the next generation; stopping time; exponential family##### Software:

Maple
PDF
BibTeX
XML
Cite

\textit{V. T. Stefanov}, J. Appl. Probab. 41, No. 2, 345--354 (2004; Zbl 1053.62124)

Full Text:
DOI

**OpenURL**

##### References:

[1] | Barndorff-Nielsen, O. (1978). Information and Exponential Families. John Wiley, Chichester. · Zbl 0387.62011 |

[2] | 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. · Zbl 0869.92012 |

[3] | 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. |

[4] | Donnelly, K. (1983). The probability that related individuals share some section of the genome identical by descent. Theoret. Pop. Biol. 23, 34–64. · Zbl 0521.92011 |

[5] | Jacod, J. and Shiryaev, A. N. (1987). Limit Theorems for Stochastic Processes . Springer, Berlin. · Zbl 0635.60021 |

[6] | Karr, A. (1991). Point Processes and Their Statistical Inference (Prob. Pure. Appl. 7 ), 2nd edn. Marcel Dekker, New York. · Zbl 0733.62088 |

[7] | Stefanov, V. T. (1991). Noncurved exponential families associated with observations over finite state Markov chains. Scand. J. Statist. 18, 353–356. · Zbl 0798.62096 |

[8] | Stefanov, V. T. (2000). Distribution of genome shared IBD by two individuals in grandparent-type relationship. Genetics 156, 1403–1410. |

[9] | 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. |

[10] | Widder, D. V. (1971). An Introduction to Transform Theory. Academic Press, New York. · Zbl 0219.44001 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.