The role of marriage rules in the structure of genetic relatedness

Joseph C. Watkins

doi:10.1016/j.tpb.2004.03.001

The role of marriage rules in the structure of genetic relatedness

Joseph C. Watkins

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

In this work, we take a forward in time approach to compute the probabilities of non-identity by descent for a population consisting of n sections obeying one of a class of marriage rules that is invariant under cyclical relabeling of sections. A perturbation method allows for exact asymptotics using the reciprocal of the section population as a small parameter. The analysis yields relatedness measures that generalize Wright's F-statistics.

Original language	English (US)
Pages (from-to)	13-24
Number of pages	12
Journal	Theoretical Population Biology
Volume	66
Issue number	1
DOIs	https://doi.org/10.1016/j.tpb.2004.03.001
State	Published - Aug 2004

Keywords

Circulant matrices
Marriage rules
Perturbation methods
Relatedness measures

ASJC Scopus subject areas

Ecology, Evolution, Behavior and Systematics

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10.1016/j.tpb.2004.03.001

Cite this

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title = "The role of marriage rules in the structure of genetic relatedness",

abstract = "In this work, we take a forward in time approach to compute the probabilities of non-identity by descent for a population consisting of n sections obeying one of a class of marriage rules that is invariant under cyclical relabeling of sections. A perturbation method allows for exact asymptotics using the reciprocal of the section population as a small parameter. The analysis yields relatedness measures that generalize Wright's F-statistics.",

keywords = "Circulant matrices, Marriage rules, Perturbation methods, Relatedness measures",

author = "Watkins, {Joseph C.}",

note = "Funding Information: The author thanks Klaus Lux for the early discussions that set a good course for the mathematical ideas and to members of the biocomplexity group at the University of Arizona—John T. Murphy, Kathryn McElveen, and Christopher G. Langdon—for their input on the issues both in genetics and in anthropology. In particular, J.C.W. thanks J. Stephen Lansing whose initial insights form the foundational ideas of this work. J.C.W. also acknowledges the National Science Foundation support through the Biocomplexity Research award BCS-0083524. ",

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doi = "10.1016/j.tpb.2004.03.001",

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PY - 2004/8

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N2 - In this work, we take a forward in time approach to compute the probabilities of non-identity by descent for a population consisting of n sections obeying one of a class of marriage rules that is invariant under cyclical relabeling of sections. A perturbation method allows for exact asymptotics using the reciprocal of the section population as a small parameter. The analysis yields relatedness measures that generalize Wright's F-statistics.

AB - In this work, we take a forward in time approach to compute the probabilities of non-identity by descent for a population consisting of n sections obeying one of a class of marriage rules that is invariant under cyclical relabeling of sections. A perturbation method allows for exact asymptotics using the reciprocal of the section population as a small parameter. The analysis yields relatedness measures that generalize Wright's F-statistics.

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KW - Marriage rules

KW - Perturbation methods

KW - Relatedness measures

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The role of marriage rules in the structure of genetic relatedness

Abstract

Keywords

ASJC Scopus subject areas

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