Speed and shape of population fronts with density-dependent diffusion
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909393177542656 |
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| author | Stokes, Beth M. Rogers, Tim James, Richard |
| author_facet | Stokes, Beth M. Rogers, Tim James, Richard |
| contents | We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of diffusion at low density. For sufficiently large low-density diffusion, the wave propagates at a speed predicted by a simple linear analysis. For small or zero low-density diffusion, the linear analysis is not sufficient, but a variational approach yields exact or approximate expressions for the speed and shape of population fronts. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_07915 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Speed and shape of population fronts with density-dependent diffusion Stokes, Beth M. Rogers, Tim James, Richard Populations and Evolution Dynamical Systems We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of diffusion at low density. For sufficiently large low-density diffusion, the wave propagates at a speed predicted by a simple linear analysis. For small or zero low-density diffusion, the linear analysis is not sufficient, but a variational approach yields exact or approximate expressions for the speed and shape of population fronts. |
| title | Speed and shape of population fronts with density-dependent diffusion |
| topic | Populations and Evolution Dynamical Systems |
| url | https://arxiv.org/abs/2407.07915 |