DOI: 10.2307/1427919. Stationary distributions under mutation-selection balance: structure and properties

Stationary distributions under mutation-selection balance: structure and properties

10.2307/1427919

Crossref journal-article

Cambridge University Press (CUP)

Advances in Applied Probability (56)

Abstract

A general model for the evolution of the frequency distribution of types in a population under mutation and selection is derived and investigated. The approach is sufficiently general to subsume classical models with a finite number of alleles, as well as models with a continuum of possible alleles as used in quantitative genetics. The dynamics of the corresponding probability distributions is governed by an integro-differential equation in the Banach space of Borel measures on a locally compact space. Existence and uniqueness of the solutions of the initial value problem is proved using basic semigroup theory. A complete characterization of the structure of stationary distributions is presented. Then, existence and uniqueness of stationary distributions is proved under mild conditions by applying operator theoretic generalizations of Perron–Frobenius theory. For an extension of Kingman's original house-of-cards model, a classification of possible stationary distributions is obtained.

Bibliography

BÃ¼rger, R., & Bomze, I. M. (1996). Stationary distributions under mutation-selection balance: structure and properties. Advances in Applied Probability, 28(1), 227â251.

Authors 2

Reinhard Bürger (first)
Immanuel M. Bomze (additional)

References 29 Referenced 39

10.1017/S0305004100052956
10.1007/BF00276557
10.1007/BF00275642
10.1016/0040-5809(84)90017-0
10.1007/978-3-642-65970-6
10.1017/S0021900200105534
10.1512/iumj.1979.28.28058
{'key': 'S0001867800027348_ref7', 'first-page': '495', 'volume-title': 'Proc. XI Int. Congress on Genetics.', 'author': 'Crow', 'year': '1964'} / Proc. XI Int. Congress on Genetics. by Crow (1964)
10.1017/S0001867800018139
10.1007/978-1-4612-5561-1
10.1073/pnas.54.3.731
{'key': 'S0001867800027348_ref17', 'first-page': '123', 'volume-title': 'Proc. 2nd Int. Conf on Quantitative Genetics.', 'author': 'Karlin', 'year': '1988'} / Proc. 2nd Int. Conf on Quantitative Genetics. by Karlin (1988)
{'key': 'S0001867800027348_ref23', 'volume-title': 'Human Population Genetics: The Pittsburgh Symposium.', 'author': 'Nagylaki', 'year': '1984'} / Human Population Genetics: The Pittsburgh Symposium. by Nagylaki (1984)
10.1017/S0001867800038568
{'key': 'S0001867800027348_ref1', 'volume-title': 'Positive Operators.', 'author': 'Aliprantis', 'year': '1985'} / Positive Operators. by Aliprantis (1985)
10.1007/BF01215194
10.1007/BF00168008
10.1016/0040-5809(90)90035-T
10.1017/S0016672300016037
10.1007/BF01301675
10.1016/0022-247X(84)90173-2
{'key': 'S0001867800027348_ref8', 'volume-title': 'An Introduction to Population Genetics Theory.', 'author': 'Crow', 'year': '1970'} / An Introduction to Population Genetics Theory. by Crow (1970)
10.1007/BF00160372
10.1137/0331019
{'key': 'S0001867800027348_ref6', 'first-page': '77', 'volume-title': 'Semigroup Theory and Evolution Equations.', 'author': 'Bürger', 'year': '1991'} / Semigroup Theory and Evolution Equations. by Bürger (1991)
10.1007/978-3-322-92139-0
10.1137/0136014
{'key': 'S0001867800027348_ref22', 'volume-title': 'One-Parameter Semigroups of Positive Operators. (Lecture Notes in Mathematics)', 'author': 'Nagel', 'year': '1986'} / One-Parameter Semigroups of Positive Operators. (Lecture Notes in Mathematics) by Nagel (1986)
{'key': 'S0001867800027348_ref29', 'volume-title': 'Riesz spaces: II.', 'author': 'Zaanen', 'year': '1983'} / Riesz spaces: II. by Zaanen (1983)

Dates

Type	When
Created	19 years, 4 months ago (April 23, 2006, 4:48 p.m.)
Deposited	6 years, 3 months ago (May 13, 2019, 11:06 a.m.)
Indexed	3 weeks ago (Aug. 6, 2025, 9:39 a.m.)
Issued	29 years, 5 months ago (March 1, 1996)
Published	29 years, 5 months ago (March 1, 1996)
Published Online	9 years, 1 month ago (July 1, 2016)
Published Print	29 years, 5 months ago (March 1, 1996)

Funders 0

None

BibTeX

@article{B_rger_1996, title={Stationary distributions under mutation-selection balance: structure and properties}, volume={28}, ISSN={1475-6064}, url={http://dx.doi.org/10.2307/1427919}, DOI={10.2307/1427919}, number={1}, journal={Advances in Applied Probability}, publisher={Cambridge University Press (CUP)}, author={Bürger, Reinhard and Bomze, Immanuel M.}, year={1996}, month=mar, pages={227–251} }

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