Equilibrium, observability and controllability in selection-mutation models
In this paper we shortly discuss the problem of the equilibrium in the well-known Fisher type selection-model, also providing a formula for particular three-allele models. The considered continuous-time dynamics is a known extension of the classical model of natural selection given by Fisher. We als...
| Main Authors: | , , |
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| Format: | info:eu-repo/semantics/article |
| Language: | English |
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2017
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| Subjects: | |
| Online Access: | http://hdl.handle.net/10835/4903 https://doi.org/10.1016/j.biosystems.2005.02.006 |
| _version_ | 1789406387519881216 |
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| author | López, Inmaculada Gámez Cámara, Manuel Angel Varga, Zoltán |
| author_facet | López, Inmaculada Gámez Cámara, Manuel Angel Varga, Zoltán |
| author_sort | López, Inmaculada |
| collection | DSpace |
| description | In this paper we shortly discuss the problem of the equilibrium in the well-known Fisher type selection-model, also providing a formula for particular three-allele models. The considered continuous-time dynamics is a known extension of the classical model of natural selection given by Fisher. We also extend the existing investigation of the observability of Fisher’s model to the case when another evolutionary factor, mutation is also present. Moreover, we prove a result of technical character, which makes it possible to apply the methodology of nonlinear systems with invariant
manifold, to models of artificial selection. For an illustration, a class of three-allele systems is presented in which the controllability into equilibrium is guaranteed without any condition on the biological parameters. |
| format | info:eu-repo/semantics/article |
| id | oai:repositorio.ual.es:10835-4903 |
| institution | Universidad de Cuenca |
| language | English |
| publishDate | 2017 |
| record_format | dspace |
| spelling | oai:repositorio.ual.es:10835-49032023-04-12T19:37:11Z Equilibrium, observability and controllability in selection-mutation models López, Inmaculada Gámez Cámara, Manuel Angel Varga, Zoltán Selection-mutation dynamics Observability of nonlinear systems Controllability of nonlinear systems In this paper we shortly discuss the problem of the equilibrium in the well-known Fisher type selection-model, also providing a formula for particular three-allele models. The considered continuous-time dynamics is a known extension of the classical model of natural selection given by Fisher. We also extend the existing investigation of the observability of Fisher’s model to the case when another evolutionary factor, mutation is also present. Moreover, we prove a result of technical character, which makes it possible to apply the methodology of nonlinear systems with invariant manifold, to models of artificial selection. For an illustration, a class of three-allele systems is presented in which the controllability into equilibrium is guaranteed without any condition on the biological parameters. 2017-07-12T08:28:31Z 2017-07-12T08:28:31Z 2005 info:eu-repo/semantics/article http://hdl.handle.net/10835/4903 https://doi.org/10.1016/j.biosystems.2005.02.006 en Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess |
| spellingShingle | Selection-mutation dynamics Observability of nonlinear systems Controllability of nonlinear systems López, Inmaculada Gámez Cámara, Manuel Angel Varga, Zoltán Equilibrium, observability and controllability in selection-mutation models |
| title | Equilibrium, observability and controllability in selection-mutation models |
| title_full | Equilibrium, observability and controllability in selection-mutation models |
| title_fullStr | Equilibrium, observability and controllability in selection-mutation models |
| title_full_unstemmed | Equilibrium, observability and controllability in selection-mutation models |
| title_short | Equilibrium, observability and controllability in selection-mutation models |
| title_sort | equilibrium, observability and controllability in selection-mutation models |
| topic | Selection-mutation dynamics Observability of nonlinear systems Controllability of nonlinear systems |
| url | http://hdl.handle.net/10835/4903 https://doi.org/10.1016/j.biosystems.2005.02.006 |
| work_keys_str_mv | AT lopezinmaculada equilibriumobservabilityandcontrollabilityinselectionmutationmodels AT gamezcamaramanuelangel equilibriumobservabilityandcontrollabilityinselectionmutationmodels AT vargazoltan equilibriumobservabilityandcontrollabilityinselectionmutationmodels |