FLEMING-VIOT PROCESSES IN POPULATION-GENETICS

被引：136

作者：

ETHIER, SN ^{[1
]}

KURTZ, TG ^{[1
]}

机构：

[1] UNIV WISCONSIN, DEPT MATH, MADISON, WI 53706 USA

来源：

SIAM JOURNAL ON CONTROL AND OPTIMIZATION | 1993年 / 31卷 / 02期

关键词：

MEASURE-VALUED MARKOV CHAIN; MEASURE-VALUED DIFFUSION PROCESS; MARTINGALE PROBLEM; CONVERGENCE IN DISTRIBUTION; ERGODICITY; INFINITE PARTICLE SYSTEM; REVERSIBILITY; INFINITELY-MANY-NEUTRAL-ALLELES MODEL;

D O I：

10.1137/0331019

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Fleming and Viot [Indiana Univ. Math. J., 28 (1979), pp. 817-843] introduced a class of probability-measure-valued diffusion processes that has attracted the interest of both pure and applied probabilists. This paper surveys the subject of Fleming-Viot processes as it relates to population genetics. Topics include: 1. Introduction. 2. Some measure-valued Markov chains. 2.1. A diploid model. 2.2. The Wright-Fisher model. 2.3. A Moran model. 3. The Fleming-Viot process: characterization. 4. Convergence. 5. Ergodicity. 6. An infinite particle system. 7. Bounded mutation operators. 8. Reversibility. 9. Examples. 9.1. Continuous-state stepwise-mutation model. 9.2. Infinitely-many-neutral-alleles model. 9.3. Infinitely-many-neutral-alleles model with ages. 9.4. Two-locus model with recombination. 9.5. n-locus model with gene conversion. 9.6. Infinitely-many-sites model without recombination. 9.7. Infinitely-many-neutral-alleles model with allelic genealogies.

引用

页码：345 / 386

页数：42

共 81 条

[1]

CROW JF, 1989, GENETICS, V121, P631

[2]

DAWSON D. A., 1978, CANAD J STAT, V6, P143, DOI [10.2307/3315044, DOI 10.2307/3315044]

[3] WANDERING RANDOM MEASURES IN THE FLEMING-VIOT MODEL [J].

DAWSON, DA ;

HOCHBERG, KJ .

ANNALS OF PROBABILITY, 1982, 10 (03) :554-580

[4]

DONNELLY P, 1986, ADV APPL PROBAB, V18, P1023

[5] CONSISTENT ORDERED SAMPLING DISTRIBUTIONS - CHARACTERIZATION AND CONVERGENCE [J].

DONNELLY, P ;

JOYCE, P .

ADVANCES IN APPLIED PROBABILITY, 1991, 23 (02) :229-258

[6] THE AGES OF ALLELES AND A COALESCENT [J].

DONNELLY, P ;

TAVARE, S .

ADVANCES IN APPLIED PROBABILITY, 1986, 18 (01) :1-19

[7] PARTITION STRUCTURES, POLYA URNS, THE EWENS SAMPLING FORMULA, AND THE AGES OF ALLELES [J].

DONNELLY, P .

THEORETICAL POPULATION BIOLOGY, 1986, 30 (02) :271-288

[8] CONTINUITY AND WEAK-CONVERGENCE OF RANKED AND SIZE-BIASED PERMUTATIONS ON THE INFINITE SIMPLEX [J].

DONNELLY, P ;

JOYCE, P .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1989, 31 (01) :89-103

[9] THE POPULATION GENEALOGY OF THE INFINITELY - MANY NEUTRAL ALLELES MODEL [J].

DONNELLY, P ;

TAVARE, S .

JOURNAL OF MATHEMATICAL BIOLOGY, 1987, 25 (04) :381-391

[10]

DONNELLY P, 1993, UNPUB PARTICLE REPRE

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