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Extensions to the model of an infinite number of selectively neutral alleles in a finite population
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| Zeitschriftentitel: | Genetical Research |
|---|---|
| Personen und Körperschaften: | |
| In: | Genetical Research, 25, 1975, 2, S. 145-153 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Hindawi Limited
|
| Schlagwörter: |
| author_facet |
Avery, P. J. Avery, P. J. |
|---|---|
| author |
Avery, P. J. |
| spellingShingle |
Avery, P. J. Genetical Research Extensions to the model of an infinite number of selectively neutral alleles in a finite population Genetics General Medicine |
| author_sort |
avery, p. j. |
| spelling |
Avery, P. J. 0016-6723 1469-5073 Hindawi Limited Genetics General Medicine http://dx.doi.org/10.1017/s0016672300015548 <jats:title>SUMMARY</jats:title><jats:p>The model, suggested by Ohta & Kimura, of an infinite number of selectively neutral alleles, in which alleles can only mutate to neighbouring alleles, has been extended to include a migratory pattern. The stepping-stone and island models of migration have been considered. In the latter case, it has been found that as the number of colonies becomes large, the expected number of alleles,<jats:italic>n<jats:sub>e</jats:sub></jats:italic>, becomes approximately equal to</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0016672300015548eqnU1" /></jats:disp-formula></jats:p><jats:p>where<jats:italic>m</jats:italic>is the migration rate,<jats:italic>v</jats:italic>is the mutation rate and<jats:italic>N<jats:sub>e</jats:sub></jats:italic>is the effective size of each population. This solution tends to that of Ohta & Kimura as<jats:italic>m</jats:italic>→ 0 but one can see that for any appreciable value of<jats:italic>N<jats:sub>e</jats:sub>m</jats:italic>, a large increase in<jats:italic>n<jats:sub>e</jats:sub></jats:italic>is obtained. In order to check the validity of iterative results, models with a finite number of alleles have been considered, and their solutions have been found to converge quickly to those of the infinite case. The results exemplify the great power of migratory structure and neutral alleles to maintain a large amount of heterozygosity. Double step mutation and the finite time solution have also been considered.</jats:p> Extensions to the model of an infinite number of selectively neutral alleles in a finite population Genetical Research |
| doi_str_mv |
10.1017/s0016672300015548 |
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Online Free |
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Biologie |
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ElectronicArticle |
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ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9zMDAxNjY3MjMwMDAxNTU0OA |
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DE-Pl11 DE-Rs1 DE-105 DE-14 DE-Ch1 DE-L229 DE-D275 DE-Bn3 DE-Brt1 DE-D161 DE-Zwi2 DE-Gla1 DE-Zi4 DE-15 |
| imprint |
Hindawi Limited, 1975 |
| imprint_str_mv |
Hindawi Limited, 1975 |
| issn |
0016-6723 1469-5073 |
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0016-6723 1469-5073 |
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English |
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Hindawi Limited (CrossRef) |
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avery1975extensionstothemodelofaninfinitenumberofselectivelyneutralallelesinafinitepopulation |
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1975 |
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Hindawi Limited |
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ai |
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ai |
| series |
Genetical Research |
| source_id |
49 |
| title |
Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_unstemmed |
Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_full |
Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_fullStr |
Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_full_unstemmed |
Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_short |
Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_sort |
extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| topic |
Genetics General Medicine |
| url |
http://dx.doi.org/10.1017/s0016672300015548 |
| publishDate |
1975 |
| physical |
145-153 |
| description |
<jats:title>SUMMARY</jats:title><jats:p>The model, suggested by Ohta & Kimura, of an infinite number of selectively neutral alleles, in which alleles can only mutate to neighbouring alleles, has been extended to include a migratory pattern. The stepping-stone and island models of migration have been considered. In the latter case, it has been found that as the number of colonies becomes large, the expected number of alleles,<jats:italic>n<jats:sub>e</jats:sub></jats:italic>, becomes approximately equal to</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0016672300015548eqnU1" /></jats:disp-formula></jats:p><jats:p>where<jats:italic>m</jats:italic>is the migration rate,<jats:italic>v</jats:italic>is the mutation rate and<jats:italic>N<jats:sub>e</jats:sub></jats:italic>is the effective size of each population. This solution tends to that of Ohta & Kimura as<jats:italic>m</jats:italic>→ 0 but one can see that for any appreciable value of<jats:italic>N<jats:sub>e</jats:sub>m</jats:italic>, a large increase in<jats:italic>n<jats:sub>e</jats:sub></jats:italic>is obtained. In order to check the validity of iterative results, models with a finite number of alleles have been considered, and their solutions have been found to converge quickly to those of the infinite case. The results exemplify the great power of migratory structure and neutral alleles to maintain a large amount of heterozygosity. Double step mutation and the finite time solution have also been considered.</jats:p> |
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| author | Avery, P. J. |
| author_facet | Avery, P. J., Avery, P. J. |
| author_sort | avery, p. j. |
| container_issue | 2 |
| container_start_page | 145 |
| container_title | Genetical Research |
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| description | <jats:title>SUMMARY</jats:title><jats:p>The model, suggested by Ohta & Kimura, of an infinite number of selectively neutral alleles, in which alleles can only mutate to neighbouring alleles, has been extended to include a migratory pattern. The stepping-stone and island models of migration have been considered. In the latter case, it has been found that as the number of colonies becomes large, the expected number of alleles,<jats:italic>n<jats:sub>e</jats:sub></jats:italic>, becomes approximately equal to</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0016672300015548eqnU1" /></jats:disp-formula></jats:p><jats:p>where<jats:italic>m</jats:italic>is the migration rate,<jats:italic>v</jats:italic>is the mutation rate and<jats:italic>N<jats:sub>e</jats:sub></jats:italic>is the effective size of each population. This solution tends to that of Ohta & Kimura as<jats:italic>m</jats:italic>→ 0 but one can see that for any appreciable value of<jats:italic>N<jats:sub>e</jats:sub>m</jats:italic>, a large increase in<jats:italic>n<jats:sub>e</jats:sub></jats:italic>is obtained. In order to check the validity of iterative results, models with a finite number of alleles have been considered, and their solutions have been found to converge quickly to those of the infinite case. The results exemplify the great power of migratory structure and neutral alleles to maintain a large amount of heterozygosity. Double step mutation and the finite time solution have also been considered.</jats:p> |
| doi_str_mv | 10.1017/s0016672300015548 |
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| finc_class_facet | Biologie |
| format | ElectronicArticle |
| format_de105 | Article, E-Article |
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| format_dech1 | Article, E-Article |
| format_ded117 | Article, E-Article |
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| format_del189 | Article, E-Article |
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| format_dezwi2 | Article, E-Article |
| format_finc | Article, E-Article |
| format_nrw | Article, E-Article |
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| id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTAxNy9zMDAxNjY3MjMwMDAxNTU0OA |
| imprint | Hindawi Limited, 1975 |
| imprint_str_mv | Hindawi Limited, 1975 |
| institution | DE-Pl11, DE-Rs1, DE-105, DE-14, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-D161, DE-Zwi2, DE-Gla1, DE-Zi4, DE-15 |
| issn | 0016-6723, 1469-5073 |
| issn_str_mv | 0016-6723, 1469-5073 |
| language | English |
| last_indexed | 2024-03-01T14:17:48.385Z |
| match_str | avery1975extensionstothemodelofaninfinitenumberofselectivelyneutralallelesinafinitepopulation |
| mega_collection | Hindawi Limited (CrossRef) |
| physical | 145-153 |
| publishDate | 1975 |
| publishDateSort | 1975 |
| publisher | Hindawi Limited |
| record_format | ai |
| recordtype | ai |
| series | Genetical Research |
| source_id | 49 |
| spelling | Avery, P. J. 0016-6723 1469-5073 Hindawi Limited Genetics General Medicine http://dx.doi.org/10.1017/s0016672300015548 <jats:title>SUMMARY</jats:title><jats:p>The model, suggested by Ohta & Kimura, of an infinite number of selectively neutral alleles, in which alleles can only mutate to neighbouring alleles, has been extended to include a migratory pattern. The stepping-stone and island models of migration have been considered. In the latter case, it has been found that as the number of colonies becomes large, the expected number of alleles,<jats:italic>n<jats:sub>e</jats:sub></jats:italic>, becomes approximately equal to</jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="gif" mimetype="image" position="float" xlink:type="simple" xlink:href="S0016672300015548eqnU1" /></jats:disp-formula></jats:p><jats:p>where<jats:italic>m</jats:italic>is the migration rate,<jats:italic>v</jats:italic>is the mutation rate and<jats:italic>N<jats:sub>e</jats:sub></jats:italic>is the effective size of each population. This solution tends to that of Ohta & Kimura as<jats:italic>m</jats:italic>→ 0 but one can see that for any appreciable value of<jats:italic>N<jats:sub>e</jats:sub>m</jats:italic>, a large increase in<jats:italic>n<jats:sub>e</jats:sub></jats:italic>is obtained. In order to check the validity of iterative results, models with a finite number of alleles have been considered, and their solutions have been found to converge quickly to those of the infinite case. The results exemplify the great power of migratory structure and neutral alleles to maintain a large amount of heterozygosity. Double step mutation and the finite time solution have also been considered.</jats:p> Extensions to the model of an infinite number of selectively neutral alleles in a finite population Genetical Research |
| spellingShingle | Avery, P. J., Genetical Research, Extensions to the model of an infinite number of selectively neutral alleles in a finite population, Genetics, General Medicine |
| title | Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_full | Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_fullStr | Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_full_unstemmed | Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_short | Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_sort | extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| title_unstemmed | Extensions to the model of an infinite number of selectively neutral alleles in a finite population |
| topic | Genetics, General Medicine |
| url | http://dx.doi.org/10.1017/s0016672300015548 |