Modeling Refuge Effect of Submerged Macrophytes in Lake System

Dongyu Lv, Meng Fan, Yun Kang, Krystal Blanco

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

This paper considers a significant problem in biological control of algae issue in ecological environment. A four-dimensional dynamic model is carefully formulated to characterize the interactions among phytoplankton, submerged macrophyte, zooplankton, and general fish class in a lake ecosystem. The predation relationship is modeled by Beddington–DeAngelis functional responses derived from the classical Holling time budget arguments. Qualitative analyses of the global dynamics show that the system can generate very rich dynamics with potentially 10 different equilibria and several bistable scenarios. We perform analysis on the existence and local stability of equilibria and explore the refuge effect of macrophyte on the zooplankton with numerical simulations on aquatic ecosystems. We also discuss effective methods of biological control used to restrain the increase of phytoplankton. Our study shows the proposed model could have rich and complex dynamics including but not limited to bistable and chaotic phenomenon. Numerical simulation results demonstrate that both the refuge constant and the density of the macrophytes are two key factors where refuge effects take place. In addition, the intraspecific competition between the macrophyte and the phytoplankton can also affect the macrophyte’s refuge effect. Our analytical and simulation results suggest that macrophytes provide structure and shelter against predation for zooplankton such that it could restore the zooplankton population, and that planting macrophyte properly might achieve the purpose of controlling algae growth.

Original languageEnglish (US)
Pages (from-to)1-33
Number of pages33
JournalBulletin of Mathematical Biology
DOIs
StateAccepted/In press - Apr 7 2016

Fingerprint

Zooplankton
Phytoplankton
Lakes
macrophyte
macrophytes
algae
refuge
zooplankton
Algae
Biological Control
lakes
phytoplankton
lake
Ecosystem
Modeling
biological control
modeling
Aquatic ecosystems
predation
alga

Keywords

  • Algae bloom
  • Beddington–DeAngelis functional response
  • Bistable phenomenon
  • Refuge effect

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Immunology
  • Mathematics(all)
  • Computational Theory and Mathematics
  • Neuroscience(all)
  • Pharmacology

Cite this

Modeling Refuge Effect of Submerged Macrophytes in Lake System. / Lv, Dongyu; Fan, Meng; Kang, Yun; Blanco, Krystal.

In: Bulletin of Mathematical Biology, 07.04.2016, p. 1-33.

Research output: Contribution to journalArticle

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