Extinction and uniform persistence in a microbial food web with mycoloop: limiting behavior of a population model with parasitic fungi

Alexis Erich S. Almocera; Sze-Bi Hsu; Polly W. Sy; Alexis Erich S. Almocera; Sze-Bi Hsu; Polly W. Sy

doi:10.3934/mbe.2019024

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 1: 516-537. doi: 10.3934/mbe.2019024

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Extinction and uniform persistence in a microbial food web with mycoloop: limiting behavior of a population model with parasitic fungi

1.
Division of Physical Sciences and Mathematics, College of Arts and Sciences, University of the Philippines Visayas, Miag-ao
2.
Department of Mathematics, National Tsing-Hua University, Hsinchu 300, Tawain
3.
Institute of Mathematics, University of the Philippines, C.P. Garcia St., U.P. Campus, Diliman, 1101 Quezon City, Philippines

Received: 04 November 2018 Accepted: 05 November 2018 Published: 24 December 2018

It is recently known that parasites provide a better picture of an ecosystem, gaining attention in theoretical ecology. Parasitic fungi belong to a food chain between zooplankton and inedible phytoplankton, called mycoloop. We consider a chemostat model that incorporates a single mycoloop, and analyze the limiting behavior of solutions, adding to previous work on steady-state analysis. By way of persistence theory, we establish that a given species survives depending on the food web configuration and the nutrient level. Moreover, we conclude that the model predicts coexistence under bounded nutrient levels.
- uniform persistence,
- local and global stability,
- chemostat,
- mycoloop,
- phytoplankton,
- zooplankton,
- parasitic fungi
Citation: Alexis Erich S. Almocera, Sze-Bi Hsu, Polly W. Sy. Extinction and uniform persistence in a microbial food web with mycoloop: limiting behavior of a population model with parasitic fungi[J]. Mathematical Biosciences and Engineering, 2019, 16(1): 516-537. doi: 10.3934/mbe.2019024

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Abstract

It is recently known that parasites provide a better picture of an ecosystem, gaining attention in theoretical ecology. Parasitic fungi belong to a food chain between zooplankton and inedible phytoplankton, called mycoloop. We consider a chemostat model that incorporates a single mycoloop, and analyze the limiting behavior of solutions, adding to previous work on steady-state analysis. By way of persistence theory, we establish that a given species survives depending on the food web configuration and the nutrient level. Moreover, we conclude that the model predicts coexistence under bounded nutrient levels.

References

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