The implications of model formulation when transitioning from spatial to landscape ecology
In this article we compare and contrast the predictions of some spatially explicit and implicit models in the context of a thought problem at the interface of spatial and landscape ecology. The situation we envision is a one-dimensional spatial universe of infinite extent in which there are two disj...
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| Language: | English |
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AIMS Press
2011-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.27 |
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| author | Robert Stephen Cantrell Chris Cosner William F. Fagan |
| author_facet | Robert Stephen Cantrell Chris Cosner William F. Fagan |
| author_sort | Robert Stephen Cantrell |
| collection | DOAJ |
| description | In this article we compare and contrast the predictions of some spatially explicit and implicit models in the context of a thought problem at the interface of spatial and landscape ecology. The situation we envision is a one-dimensional spatial universe of infinite extent in which there are two disjoint focal patches of a habitat type that is favorable to some specified species. We assume that neither patch is large enough by itself to sustain the species in question indefinitely, but that a single patch of size equal to the combined sizes of the two focal patches provides enough contiguous favorable habitat to sustain the given species indefinitely. When the two patches are separated by a patch of unfavorable matrix habitat, the natural expectation is that the species should persist indefinitely if the two patches are close enough to each other but should go extinct over time when the patches are far enough apart. Our focus here is to examine how different mathematical regimes may be employed to model this situation, with an eye toward exploring the trade-off between the mathematical tractability of the model on one hand and the suitability of its predictions on the other. In particular, we are interested in seeing how precisely the predictions of mathematically rich spatially explicit regimes (reaction-diffusion models, integro-difference models) can be matched by those of ostensibly mathematically simpler spatially implicit patch approximations (discrete-diffusion models, average dispersal success matrix models). |
| format | Article |
| id | doaj-art-8d5e27da59f24d4aa5e510c31c06b34c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2011-11-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8d5e27da59f24d4aa5e510c31c06b34c2025-01-24T02:05:22ZengAIMS PressMathematical Biosciences and Engineering1551-00182011-11-0191276010.3934/mbe.2012.9.27The implications of model formulation when transitioning from spatial to landscape ecologyRobert Stephen Cantrell0Chris Cosner1William F. Fagan2Department of Mathematics, The University of Miami, Coral Gables, FL 33124Department of Mathematics, The University of Miami, Coral Gables, FL 33124Department of Mathematics, The University of Miami, Coral Gables, FL 33124In this article we compare and contrast the predictions of some spatially explicit and implicit models in the context of a thought problem at the interface of spatial and landscape ecology. The situation we envision is a one-dimensional spatial universe of infinite extent in which there are two disjoint focal patches of a habitat type that is favorable to some specified species. We assume that neither patch is large enough by itself to sustain the species in question indefinitely, but that a single patch of size equal to the combined sizes of the two focal patches provides enough contiguous favorable habitat to sustain the given species indefinitely. When the two patches are separated by a patch of unfavorable matrix habitat, the natural expectation is that the species should persist indefinitely if the two patches are close enough to each other but should go extinct over time when the patches are far enough apart. Our focus here is to examine how different mathematical regimes may be employed to model this situation, with an eye toward exploring the trade-off between the mathematical tractability of the model on one hand and the suitability of its predictions on the other. In particular, we are interested in seeing how precisely the predictions of mathematically rich spatially explicit regimes (reaction-diffusion models, integro-difference models) can be matched by those of ostensibly mathematically simpler spatially implicit patch approximations (discrete-diffusion models, average dispersal success matrix models).https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.27spatially explicit modelsspatial and landscape ecologyspatially distributed population dynamical patch models.habitat fragmentation |
| spellingShingle | Robert Stephen Cantrell Chris Cosner William F. Fagan The implications of model formulation when transitioning from spatial to landscape ecology Mathematical Biosciences and Engineering spatially explicit models spatial and landscape ecology spatially distributed population dynamical patch models. habitat fragmentation |
| title | The implications of model formulation when transitioning from spatial to landscape ecology |
| title_full | The implications of model formulation when transitioning from spatial to landscape ecology |
| title_fullStr | The implications of model formulation when transitioning from spatial to landscape ecology |
| title_full_unstemmed | The implications of model formulation when transitioning from spatial to landscape ecology |
| title_short | The implications of model formulation when transitioning from spatial to landscape ecology |
| title_sort | implications of model formulation when transitioning from spatial to landscape ecology |
| topic | spatially explicit models spatial and landscape ecology spatially distributed population dynamical patch models. habitat fragmentation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.27 |
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