Transition of interaction outcomes in a facilitation-competition system of two species
A facilitation-competition system of two species is considered, where one species has a facilitation effect on the other but there is spatial competition between them. Our aim is to show mechanism by which the facilitation promotes coexistence of the species. A lattice gas model describing the facil...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2017-09-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017076 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590059003445248 |
|---|---|
| author | Yuanshi Wang Hong Wu |
| author_facet | Yuanshi Wang Hong Wu |
| author_sort | Yuanshi Wang |
| collection | DOAJ |
| description | A facilitation-competition system of two species is considered, where one species has a facilitation effect on the other but there is spatial competition between them. Our aim is to show mechanism by which the facilitation promotes coexistence of the species. A lattice gas model describing the facilitation-competition system is analyzed, in which nonexistence of periodic solution is shown and previous results are extended. Global dynamics of the model demonstrate essential features of the facilitation-competition system. When a species cannot survive alone, a strong facilitation from the other would lead to its survival. However, if the facilitation is extremely strong, both species go extinct. When a species can survive alone and its mortality rate is not larger than that of the other species, it would drive the other one into extinction. When a species can survive alone and its mortality rate is larger than that of the other species, it would be driven into extinction if the facilitation from the other is weak, while it would coexist with the other if the facilitation is strong. Moreover, an extremely strong facilitation from the other would lead to extinction of species. Bifurcation diagram of the system exhibits that interaction outcome between the species can transition between competition, amensalism, neutralism and parasitism in a smooth fashion. A novel result of this paper is the rigorous and thorough analysis, which displays transparency of dynamics in the system. Numerical simulations validate the results. |
| format | Article |
| id | doaj-art-7cd3d57258bd498ebcf685cfd1a1e188 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-7cd3d57258bd498ebcf685cfd1a1e1882025-01-24T02:40:31ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-09-01145&61463147510.3934/mbe.2017076Transition of interaction outcomes in a facilitation-competition system of two speciesYuanshi Wang0Hong Wu1School of Mathematics, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Mathematics, Sun Yat-sen University, Guangzhou 510275, ChinaA facilitation-competition system of two species is considered, where one species has a facilitation effect on the other but there is spatial competition between them. Our aim is to show mechanism by which the facilitation promotes coexistence of the species. A lattice gas model describing the facilitation-competition system is analyzed, in which nonexistence of periodic solution is shown and previous results are extended. Global dynamics of the model demonstrate essential features of the facilitation-competition system. When a species cannot survive alone, a strong facilitation from the other would lead to its survival. However, if the facilitation is extremely strong, both species go extinct. When a species can survive alone and its mortality rate is not larger than that of the other species, it would drive the other one into extinction. When a species can survive alone and its mortality rate is larger than that of the other species, it would be driven into extinction if the facilitation from the other is weak, while it would coexist with the other if the facilitation is strong. Moreover, an extremely strong facilitation from the other would lead to extinction of species. Bifurcation diagram of the system exhibits that interaction outcome between the species can transition between competition, amensalism, neutralism and parasitism in a smooth fashion. A novel result of this paper is the rigorous and thorough analysis, which displays transparency of dynamics in the system. Numerical simulations validate the results.https://www.aimspress.com/article/doi/10.3934/mbe.2017076persistencecoexistenceextinctionstabilitybifurcation |
| spellingShingle | Yuanshi Wang Hong Wu Transition of interaction outcomes in a facilitation-competition system of two species Mathematical Biosciences and Engineering persistence coexistence extinction stability bifurcation |
| title | Transition of interaction outcomes in a facilitation-competition system of two species |
| title_full | Transition of interaction outcomes in a facilitation-competition system of two species |
| title_fullStr | Transition of interaction outcomes in a facilitation-competition system of two species |
| title_full_unstemmed | Transition of interaction outcomes in a facilitation-competition system of two species |
| title_short | Transition of interaction outcomes in a facilitation-competition system of two species |
| title_sort | transition of interaction outcomes in a facilitation competition system of two species |
| topic | persistence coexistence extinction stability bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017076 |
| work_keys_str_mv | AT yuanshiwang transitionofinteractionoutcomesinafacilitationcompetitionsystemoftwospecies AT hongwu transitionofinteractionoutcomesinafacilitationcompetitionsystemoftwospecies |