Evolutionary distributions in adaptive space
An evolutionary distribution (ED), denoted by z(x,t), is a distribution of density of phenotypes over a set of adaptive traits x. Here x is an n-dimensional vector that represents the adaptive space. Evolutionary interactions among phenotypes occur within an ED and between EDs. A generic approach to...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/JAM.2005.403 |
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| _version_ | 1832564619781079040 |
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| author | Yosef Cohen |
| author_facet | Yosef Cohen |
| author_sort | Yosef Cohen |
| collection | DOAJ |
| description | An evolutionary distribution (ED), denoted by z(x,t), is a distribution of density of phenotypes over a set of adaptive
traits x. Here x is an n-dimensional
vector that represents the adaptive space. Evolutionary
interactions among phenotypes occur within an ED and between EDs.
A generic approach to modeling systems of ED is developed. With
it, two cases are analyzed. (1) A predator prey inter-ED
interactions either with no intra-ED interactions or with
cannibalism and competition (both intra-ED interactions). A
predator prey system with no intra-ED interactions is stable.
Cannibalism destabilizes it and competition strengthens its
stability. (2) Mixed interactions (where phenotypes of one ED both
benefit and are harmed by phenotypes of another ED) produce
complete separation of phenotypes on one ED from the other along
the adaptive trait. Foundational definitions of ED, adaptive
space, and so on are also given. We argue that in evolutionary
context, predator prey models with predator saturation make less
sense than in ecological models. Also, with ED, the dynamics of
population genetics may be reduced to an algebraic problem.
Finally, extensions to the theory are proposed. |
| format | Article |
| id | doaj-art-85b4cee21fdc4be791dd4c0a139a32f6 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-85b4cee21fdc4be791dd4c0a139a32f62025-02-03T01:10:41ZengWileyJournal of Applied Mathematics1110-757X1687-00422005-01-012005440342410.1155/JAM.2005.403Evolutionary distributions in adaptive spaceYosef Cohen0Department of Fisheries and Wildlife, University of Minnesota, St. Paul 55108, MN, USAAn evolutionary distribution (ED), denoted by z(x,t), is a distribution of density of phenotypes over a set of adaptive traits x. Here x is an n-dimensional vector that represents the adaptive space. Evolutionary interactions among phenotypes occur within an ED and between EDs. A generic approach to modeling systems of ED is developed. With it, two cases are analyzed. (1) A predator prey inter-ED interactions either with no intra-ED interactions or with cannibalism and competition (both intra-ED interactions). A predator prey system with no intra-ED interactions is stable. Cannibalism destabilizes it and competition strengthens its stability. (2) Mixed interactions (where phenotypes of one ED both benefit and are harmed by phenotypes of another ED) produce complete separation of phenotypes on one ED from the other along the adaptive trait. Foundational definitions of ED, adaptive space, and so on are also given. We argue that in evolutionary context, predator prey models with predator saturation make less sense than in ecological models. Also, with ED, the dynamics of population genetics may be reduced to an algebraic problem. Finally, extensions to the theory are proposed.http://dx.doi.org/10.1155/JAM.2005.403 |
| spellingShingle | Yosef Cohen Evolutionary distributions in adaptive space Journal of Applied Mathematics |
| title | Evolutionary distributions in adaptive space |
| title_full | Evolutionary distributions in adaptive space |
| title_fullStr | Evolutionary distributions in adaptive space |
| title_full_unstemmed | Evolutionary distributions in adaptive space |
| title_short | Evolutionary distributions in adaptive space |
| title_sort | evolutionary distributions in adaptive space |
| url | http://dx.doi.org/10.1155/JAM.2005.403 |
| work_keys_str_mv | AT yosefcohen evolutionarydistributionsinadaptivespace |