Individual Variability in Dispersal and Invasion Speed
We model the growth, dispersal and mutation of two phenotypes of a species using reaction−diffusion equations, focusing on the biologically realistic case of small mutation rates. Having verified that the addition of a small linear mutation term to a Lotka−Volterra system limits...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/7/9/795 |
| _version_ | 1818979927031021568 |
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| author | Aled Morris Luca Börger Elaine Crooks |
| author_facet | Aled Morris Luca Börger Elaine Crooks |
| author_sort | Aled Morris |
| collection | DOAJ |
| description | We model the growth, dispersal and mutation of two phenotypes of a species using reaction−diffusion equations, focusing on the biologically realistic case of small mutation rates. Having verified that the addition of a small linear mutation term to a Lotka−Volterra system limits it to only two steady states in the case of weak competition, an unstable extinction state and a stable coexistence state, we exploit the fact that the spreading speed of the system is known to be linearly determinate to show that the spreading speed is a nonincreasing function of the mutation rate, so that greater mixing between phenotypes leads to slower propagation. We also find the ratio at which the phenotypes occur at the leading edge in the limit of vanishing mutation. |
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| format | Article |
| id | doaj.art-10acb8782cca446f9febda666cc61221 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-12-20T17:07:18Z |
| publishDate | 2019-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-10acb8782cca446f9febda666cc612212022-12-21T19:32:14ZengMDPI AGMathematics2227-73902019-09-017979510.3390/math7090795math7090795Individual Variability in Dispersal and Invasion SpeedAled Morris0Luca Börger1Elaine Crooks2Centre for Biomathematics, College of Science, Swansea University, Swansea SA2 8PP, UKCentre for Biomathematics, College of Science, Swansea University, Swansea SA2 8PP, UKCentre for Biomathematics, College of Science, Swansea University, Swansea SA2 8PP, UKWe model the growth, dispersal and mutation of two phenotypes of a species using reaction−diffusion equations, focusing on the biologically realistic case of small mutation rates. Having verified that the addition of a small linear mutation term to a Lotka−Volterra system limits it to only two steady states in the case of weak competition, an unstable extinction state and a stable coexistence state, we exploit the fact that the spreading speed of the system is known to be linearly determinate to show that the spreading speed is a nonincreasing function of the mutation rate, so that greater mixing between phenotypes leads to slower propagation. We also find the ratio at which the phenotypes occur at the leading edge in the limit of vanishing mutation.https://www.mdpi.com/2227-7390/7/9/795invasive specieslinear determinacypopulation growthmutationspreading speedstravelling waves |
| spellingShingle | Aled Morris Luca Börger Elaine Crooks Individual Variability in Dispersal and Invasion Speed Mathematics invasive species linear determinacy population growth mutation spreading speeds travelling waves |
| title | Individual Variability in Dispersal and Invasion Speed |
| title_full | Individual Variability in Dispersal and Invasion Speed |
| title_fullStr | Individual Variability in Dispersal and Invasion Speed |
| title_full_unstemmed | Individual Variability in Dispersal and Invasion Speed |
| title_short | Individual Variability in Dispersal and Invasion Speed |
| title_sort | individual variability in dispersal and invasion speed |
| topic | invasive species linear determinacy population growth mutation spreading speeds travelling waves |
| url | https://www.mdpi.com/2227-7390/7/9/795 |
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