Competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predation
We propose a model oftwo-species competition in the chemostat for a single growth-limiting,nonreproducing resource that extends that of Roy [38]. The response functions are specified to be Michaelis-Menten, and there is no predation in Roy's work. Our model generalizes Roy's model to gener...
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AIMS Press
2016-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016018 |
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| author | Jean-Jacques Kengwoung-Keumo |
| author_facet | Jean-Jacques Kengwoung-Keumo |
| author_sort | Jean-Jacques Kengwoung-Keumo |
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| description | We propose a model oftwo-species competition in the chemostat for a single growth-limiting,nonreproducing resource that extends that of Roy [38]. The response functions are specified to be Michaelis-Menten, and there is no predation in Roy's work. Our model generalizes Roy's model to general uptake functions. The competition is exploitative so that species compete by decreasing the common pool ofresources. The model also allows allelopathic effects of one toxin-producingspecies, both on itself (autotoxicity) and on its nontoxic competitor(phytotoxicity). We show that a stable coexistence equilibrium exists as long as (a) there are allelopathic effects and (b) the input nutrient concentration is above a critical value. The model is reconsidered under instantaneous nutrient recycling. We further extend this work to include a zooplankton species as a fourth interacting component to study the impact of predation on the ecosystem. The zooplankton species is allowed to feed only on the two phytoplankton species which are its perfectly substitutable resources. Each of the models is analyzed for boundedness, equilibria, stability, anduniform persistence (or permanence). Each model structure fits very well with some harmful algal bloom observations where the phytoplankton assemblage can be envisioned in two compartments, toxin producing and non-toxic. The Prymnesium parvum literature, where the suppressing effects of allelochemicals are quite pronounced, is a classic example. This work advances knowledge in an area of research becoming ever more important, which is understanding the functioning of allelopathy in food webs. |
| format | Article |
| id | doaj-art-46948906ecc94b04829363a0d6d59bf6 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-46948906ecc94b04829363a0d6d59bf62025-01-24T02:36:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-04-0113478781210.3934/mbe.2016018Competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predationJean-Jacques Kengwoung-Keumo0Department of Mathematical Sciences, Cameron University, 2800 West Gore Boulevard, Lawton, OK 73505We propose a model oftwo-species competition in the chemostat for a single growth-limiting,nonreproducing resource that extends that of Roy [38]. The response functions are specified to be Michaelis-Menten, and there is no predation in Roy's work. Our model generalizes Roy's model to general uptake functions. The competition is exploitative so that species compete by decreasing the common pool ofresources. The model also allows allelopathic effects of one toxin-producingspecies, both on itself (autotoxicity) and on its nontoxic competitor(phytotoxicity). We show that a stable coexistence equilibrium exists as long as (a) there are allelopathic effects and (b) the input nutrient concentration is above a critical value. The model is reconsidered under instantaneous nutrient recycling. We further extend this work to include a zooplankton species as a fourth interacting component to study the impact of predation on the ecosystem. The zooplankton species is allowed to feed only on the two phytoplankton species which are its perfectly substitutable resources. Each of the models is analyzed for boundedness, equilibria, stability, anduniform persistence (or permanence). Each model structure fits very well with some harmful algal bloom observations where the phytoplankton assemblage can be envisioned in two compartments, toxin producing and non-toxic. The Prymnesium parvum literature, where the suppressing effects of allelochemicals are quite pronounced, is a classic example. This work advances knowledge in an area of research becoming ever more important, which is understanding the functioning of allelopathy in food webs.https://www.aimspress.com/article/doi/10.3934/mbe.2016018phytoplanktonchemostatzooplanktonpredationallelopathynutrient recycling. |
| spellingShingle | Jean-Jacques Kengwoung-Keumo Competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predation Mathematical Biosciences and Engineering phytoplankton chemostat zooplankton predation allelopathy nutrient recycling. |
| title | Competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predation |
| title_full | Competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predation |
| title_fullStr | Competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predation |
| title_full_unstemmed | Competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predation |
| title_short | Competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predation |
| title_sort | competition between a nonallelopathic phytoplankton and an allelopathic phytoplankton species under predation |
| topic | phytoplankton chemostat zooplankton predation allelopathy nutrient recycling. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016018 |
| work_keys_str_mv | AT jeanjacqueskengwoungkeumo competitionbetweenanonallelopathicphytoplanktonandanallelopathicphytoplanktonspeciesunderpredation |