Modeling frequency-dependent selection with an application to cichlid fish
Negative frequency-dependent selection is a wellknown microevolutionary process that has been documented in a population ofPerissodus microlepis, a species of cichlid fish endemic to Lake Tanganyika(Africa). Adult P. microlepis are lepidophages, feeding on the scales of otherliving fish. As an adapt...
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AIMS Press
2008-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.889 |
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| author | Sheree L. Arpin J. M. Cushing |
| author_facet | Sheree L. Arpin J. M. Cushing |
| author_sort | Sheree L. Arpin |
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| description | Negative frequency-dependent selection is a wellknown microevolutionary process that has been documented in a population ofPerissodus microlepis, a species of cichlid fish endemic to Lake Tanganyika(Africa). Adult P. microlepis are lepidophages, feeding on the scales of otherliving fish. As an adaptation for this feeding behavior P. microlepis exhibitlateral asymmetry with respect to jaw morphology: the mouth either opens tothe right or left side of the body. Field data illustrate a temporalphenotypic oscillation in the mouth-handedness, and this oscillation ismaintained by frequency-dependent selection. Since both genetic and populationdynamics occur on the same time scale in this case, we develop a (discretetime) model for P. microlepis populations that accounts for both dynamicprocesses. We establish conditions on model parameters under which the modelpredicts extinction and conditions under which there exists a unique positive(survival) equilibrium. We show that at the positive equilibrium there is a1:1 phenotypic ratio. Using a local stability and bifurcation analysis, wegive further conditions under which the positive equilibrium is stable andconditions under which it is unstable. Destabilization results in abifurcation to a periodic oscillation and occurs when frequency-dependentselection is sufficiently strong. This bifurcation is offered as anexplanation of the phenotypic frequency oscillations observed in P.microlepis. An analysis of the bifurcating periodic cycle results in someinteresting and unexpected predictions. |
| format | Article |
| id | doaj-art-a520536939c642afa50e3a5b23c0c1a9 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-09-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a520536939c642afa50e3a5b23c0c1a92025-01-24T01:58:42ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-09-015488990310.3934/mbe.2008.5.889Modeling frequency-dependent selection with an application to cichlid fishSheree L. Arpin0J. M. Cushing1Interdisciplinary Program in Applied Mathematics, 617 N Santa Rita, University of Arizona, Tucson AZ 85721Interdisciplinary Program in Applied Mathematics, 617 N Santa Rita, University of Arizona, Tucson AZ 85721Negative frequency-dependent selection is a wellknown microevolutionary process that has been documented in a population ofPerissodus microlepis, a species of cichlid fish endemic to Lake Tanganyika(Africa). Adult P. microlepis are lepidophages, feeding on the scales of otherliving fish. As an adaptation for this feeding behavior P. microlepis exhibitlateral asymmetry with respect to jaw morphology: the mouth either opens tothe right or left side of the body. Field data illustrate a temporalphenotypic oscillation in the mouth-handedness, and this oscillation ismaintained by frequency-dependent selection. Since both genetic and populationdynamics occur on the same time scale in this case, we develop a (discretetime) model for P. microlepis populations that accounts for both dynamicprocesses. We establish conditions on model parameters under which the modelpredicts extinction and conditions under which there exists a unique positive(survival) equilibrium. We show that at the positive equilibrium there is a1:1 phenotypic ratio. Using a local stability and bifurcation analysis, wegive further conditions under which the positive equilibrium is stable andconditions under which it is unstable. Destabilization results in abifurcation to a periodic oscillation and occurs when frequency-dependentselection is sufficiently strong. This bifurcation is offered as anexplanation of the phenotypic frequency oscillations observed in P.microlepis. An analysis of the bifurcating periodic cycle results in someinteresting and unexpected predictions.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.889phenotypicoscillation period doubling bifurcationmicroevolutionfrequency-dependent selectionpopulation dynamicspopulation genetics |
| spellingShingle | Sheree L. Arpin J. M. Cushing Modeling frequency-dependent selection with an application to cichlid fish Mathematical Biosciences and Engineering phenotypicoscillation period doubling bifurcation microevolution frequency-dependent selection population dynamics population genetics |
| title | Modeling frequency-dependent selection with an application to cichlid fish |
| title_full | Modeling frequency-dependent selection with an application to cichlid fish |
| title_fullStr | Modeling frequency-dependent selection with an application to cichlid fish |
| title_full_unstemmed | Modeling frequency-dependent selection with an application to cichlid fish |
| title_short | Modeling frequency-dependent selection with an application to cichlid fish |
| title_sort | modeling frequency dependent selection with an application to cichlid fish |
| topic | phenotypicoscillation period doubling bifurcation microevolution frequency-dependent selection population dynamics population genetics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.889 |
| work_keys_str_mv | AT shereelarpin modelingfrequencydependentselectionwithanapplicationtocichlidfish AT jmcushing modelingfrequencydependentselectionwithanapplicationtocichlidfish |