Herbivore harvesting and alternative steady states in coral reefs

Ikbal Hossein Sarkar; Joydeb Bhattacharyya; Samares Pal

Applications of Mathematics (2021)

  • Volume: 66, Issue: 2, page 233-268
  • ISSN: 0862-7940

Abstract

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Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability of steady states are derived. We have shown that under certain conditions the system is uniformly persistent in presence of all the organisms. Moreover, it is shown that the system undergoes a Hopf bifurcation when the carrying capacity of macroalgae crosses certain critical value. Computer simulations have been carried out to illustrate different analytical results.

How to cite

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Sarkar, Ikbal Hossein, Bhattacharyya, Joydeb, and Pal, Samares. "Herbivore harvesting and alternative steady states in coral reefs." Applications of Mathematics 66.2 (2021): 233-268. <http://eudml.org/doc/297362>.

@article{Sarkar2021,
abstract = {Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability of steady states are derived. We have shown that under certain conditions the system is uniformly persistent in presence of all the organisms. Moreover, it is shown that the system undergoes a Hopf bifurcation when the carrying capacity of macroalgae crosses certain critical value. Computer simulations have been carried out to illustrate different analytical results.},
author = {Sarkar, Ikbal Hossein, Bhattacharyya, Joydeb, Pal, Samares},
journal = {Applications of Mathematics},
keywords = {phase shift; coral bleaching; harvesting; Hopf bifurcation},
language = {eng},
number = {2},
pages = {233-268},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Herbivore harvesting and alternative steady states in coral reefs},
url = {http://eudml.org/doc/297362},
volume = {66},
year = {2021},
}

TY - JOUR
AU - Sarkar, Ikbal Hossein
AU - Bhattacharyya, Joydeb
AU - Pal, Samares
TI - Herbivore harvesting and alternative steady states in coral reefs
JO - Applications of Mathematics
PY - 2021
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 66
IS - 2
SP - 233
EP - 268
AB - Coral reefs can undergo relatively rapid changes in the dominant biota, a phenomenon referred to as phase shift. Degradation of coral reefs is often associated with changes in community structure towards a macroalgae-dominated reef ecosystem due to the reduction in herbivory caused by overfishing. We investigate the coral-macroalgal phase shift due to the effects of harvesting of herbivorous reef fish by means of a continuous time model in the food chain. Conditions for local asymptotic stability of steady states are derived. We have shown that under certain conditions the system is uniformly persistent in presence of all the organisms. Moreover, it is shown that the system undergoes a Hopf bifurcation when the carrying capacity of macroalgae crosses certain critical value. Computer simulations have been carried out to illustrate different analytical results.
LA - eng
KW - phase shift; coral bleaching; harvesting; Hopf bifurcation
UR - http://eudml.org/doc/297362
ER -

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