Hysteresis in coral reefs under macroalgal toxicity and overfishing

Bhattacharyya, Joydeb; Pal, Samares

doi:10.1007/s10867-014-9371-y

Cited by 17 publications

(10 citation statements)

References 35 publications

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“…, 0 is the equilibrium of the system (5) where w 1 is a positive root of the algebraic equation μw 3 …”

Section: Stability Analysis At Ementioning

confidence: 99%

“…The proliferation of venomous, fast reproducing and aggressive Pterois volitans drives down the populations of reef herbivores drastically [2]. The loss of herbivores results in the proliferation of algae that can smother corals and prevent the growth of corals in seabed [3]. Herbivorous Parrotfish in coral reefs play an important role in maintaining tropical reef ecosystems by consuming algae to control its growth and promote coral recruitment [4,5].…”

Section: Introductionmentioning

confidence: 99%

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Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

Bhattacharyya

Pal

2016

Differ Equ Dyn Syst

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A four dimensional stage-structured ratio-dependent predator-prey model with constant prey refuge is proposed and analyzed to study the effect of predation and cannibalism of the organisms at the highest trophic level with harvesting. Our analysis leads to different thresholds in terms of the model parameters acting as conditions under which the organisms associated with the system cannot thrive even in absence of predation. Local stability of the system is obtained in absence of one or more of the predators and in presence of all the predators. Moreover, it is shown that the system undergoes Hopf bifurcation when the carrying capacity of macro-algae crosses certain critical value. Computer simulations have been carried out to illustrate various analytical results.

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“…, 0 is the equilibrium of the system (5) where w 1 is a positive root of the algebraic equation μw 3 …”

Section: Stability Analysis At Ementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

Bhattacharyya

Pal

2016

Differ Equ Dyn Syst

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“…Our model originates from the models used in [8,23] and is a direct extension of the models studied in [4,5] by assuming that the disease spreads among corals according to a Susceptible→Infected (SI) type compartmental eco-epidemiological model [2]. For free-moving terrestrial organisms, transmission rates are mainly dependent on the contact among susceptible and infectious hosts, whereas in the marine environment disease agents move more widely and rapidly within the water column [16].…”

Section: Introduction Macroalgal Proliferation and Coral Diseases Hamentioning

confidence: 99%

“…An eco-epidemiological model is considered to study the dynamics of coral reef benthic system in presence of a microbial infection, WPD-II on corals. We have modified our previous models [4,5] by introducing macroalgal toxicity on corals and by considering the dynamics of pathogens. Our model assumes the transmission of WPD-II through free living pathogens shed by infected corals at a rate proportional to the product of susceptible coral cover and pathogen concentration in the environment.…”

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confidence: 99%

Macroalgal allelopathy in the emergence of coral diseases

Bhattacharyya¹,

Pal²

2017

Discrete &Amp; Continuous Dynamical Systems - B

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Microbial disease in corals associated with the proliferation of benthic macroalgae are the major contributors to the decline of coral reefs over the past few decades. Several benthic macroalgae species produce allelopathic chemical compounds that negatively affect corals. The emergence of microbial diseases in corals occurs simultaneously with the elevated abundance of benthic macroalgae. The release of allelochemicals by toxic-macroalgae enhances microbial activity on coral surfaces via the release of dissolved compounds. Proliferation of benthic macroalgae in coral reefs results in increased physical contacts between corals and macroalgae, triggering the susceptibility of coral disease. The abundance of macroalgae changes the community structure towards macroalgae dominated reef ecosystem. We investigate coral-macroalgal phase shift in presence of macroalgal allelopathy and microbial infection on corals by means of an eco-epidemiological model under the assumption that the transmission of infection is mediated by the pathogens shed by infectious corals and under the influence of macroalgae in the environment. We perform equilibrium and stability analysis on our non-linear ODE model and found that the system is capable of exhibiting the existence of two stable configurations of the community under the same environmental conditions by allowing saddlenode bifurcations that involves in creation and destruction of fixed points and associated hysteresis effect. It is shown that the system undergoes a sudden change of transition when the transmission rate of the infection crosses some certain critical thresholds. Computer simulations have been carried out to illustrate different analytical results.

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“…and Montastraea spp.) on the seabed (Bhattacharyya & Pal, 2015). With venomous spines, P. volitans are the top-notch predators in the Atlantic and Caribbean regions.…”

Section: Introductionmentioning

confidence: 99%

Potential Effects of Invasive Pterois Volitans in Coral Reefs

Maji

Bhattacharyya

Pal

2016

LiB

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The invasion of predatory lionfish (Pterois volitans) represents a major threat to the western Atlantic coral reef ecosystems. The proliferation of venomous, fast reproducing and aggressive P. volitans in coral reefs causes severe declines in the abundance and diversity of reef herbivores. There is also widespread cannibalism amongst P. volitans populations. A mathematical model is proposed to study the effects of predation on the biomass of herbivorous reef fishes by considering two life stages and intraguild predation of P. volitans population with harvesting of adult P. volitans. The system undergoes a supercritical Hopf bifurcation when the invasiveness of P. volitans crosses a certain critical value. It is observed that cannibalism of P. volitans induces stability in the system even with high invasiveness of adult P. volitans. The dynamic instability of the system due to higher invasiveness of P. volitans can be controlled by increasing the rate of harvesting of P. volitans. It is also proven that P. volitans goes extinct when the harvest rate is greater than some critical threshold value. These results indicate that the dynamical behaviour of the model is very sensitive to the harvesting of P. volitans, which in turn is useful in the conservation of reef herbivores.

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Hysteresis in coral reefs under macroalgal toxicity and overfishing

Cited by 17 publications

References 35 publications

Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

Stage-Structured Cannibalism in a Ratio-Dependent System with Constant Prey Refuge and Harvesting of Matured Predator

Macroalgal allelopathy in the emergence of coral diseases

Potential Effects of Invasive Pterois Volitans in Coral Reefs

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