Revealing the role of predator interference in a predator–prey system with disease in prey population

Chakraborty, Subhendu; Kooi, Bob W.; Biswas, Barasha; Chattopadhyay, Joydev

doi:10.1016/j.ecocom.2014.11.005

Cited by 18 publications

(16 citation statements)

References 64 publications

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“…In addition to top‐down control, sharks are very likely to exert a wide range of functions that remain to be quantified (Roff et al., ). For example, sharks may be involved in nutrient cycling (Schmitz, Hawlena, & Trussell, ), nutrient transport between different areas and habitats (Heupel & Simpfendorfer, ; McCauley et al., ; Papastamatiou, Meyer, Kosaki, Wallsgrove, & Popp, ), scavenging (Dudley, Anderson‐Reade, Thompson, & McMullen, ; Wilson & Wolkovich, ), invasive species removal (Wallach, Izhaki, Toms, Ripple, & Shanas, ; Wallach, Ripple, & Carroll, ), diseased and weak individual removal (Chakraborty, Kooi, Biswas, & Chattopadhyay, ) as well as food web stability (Wallach, Izhaki, et al., ; Wallach, Ripple, et al., ).…”

Section: Discussionmentioning

confidence: 99%

Reef accessibility impairs the protection of sharks

Juhel

Vigliola

Mouillot

et al. 2017

Journal of Applied Ecology

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Reef sharks are declining world‐wide under ever‐increasing fishing pressure, with potential consequences on ecosystem functioning. Marine protected areas (MPAs) are currently one of the management tools used to counteract the pervasive impacts of fishing. However, MPAs in which reef sharks are abundant tend to be located in remote and underexploited areas, preventing a fair assessment of management effectiveness beyond remoteness from human activities. Here, we determine the conditions under which MPAs can effectively protect sharks along a wide gradient of reef accessibility, from the vicinity of a regional capital towards remote areas, using 385 records from baited remote underwater video systems and 2,790 underwater visual censuses performed in areas open to fishing and inside 15 MPAs across New Caledonia (South‐Western Pacific). We show that even one of the world's oldest (43 years), largest (172 km2) and most restrictive (no‐entry) MPA (Merlet reserve) on coral reefs has between 17.3% and 45.3% fewer shark species and between 37.2% and 79.8% fewer shark abundance than remote areas in a context where sharks are not historically exploited. On coral reefs situated at less than 1 hr of travel time from humans, shark populations are so low in abundance (less than 0.05 individuals per 1,000 m2) that their functional roles are severely limited. Synthesis and applications. Remote areas are the last sanctuaries for reef sharks, providing a new baseline from which to evaluate human impacts on the species. However, there is no equivalent close to human activities even in large, old and strongly restrictive marine protected areas. As such sharks deserve strong protection efforts. The large, no‐entry marine protected areas, close to humans, offer limited benefits for reef shark populations, but provide more realistic conservation targets for managers of human‐dominated reefs. The exclusion of human activities on a sufficiently large area is key to protect reef shark populations. However, this strategy remains difficult to apply in many countries critically depending on reef resources for food security or livelihood.

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Section: Discussionmentioning

confidence: 99%

Reef accessibility impairs the protection of sharks

Juhel

Vigliola

Mouillot

et al. 2017

Journal of Applied Ecology

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“…transcritical, tangent (saddle node) and Hopf bifurcations, here also the torus (Neimark-Sacker) bifurcation occurs. A new phenomenon is represented by the abrupt destruction of the quasi-periodic dynamics on a torus similar to what was found in [3,6] .…”

Section: Introductionmentioning

confidence: 87%

“…15 and 16 ), resembles the way a limit cycle is broken by a saddle point giving a homoclinic connection of this saddle to itself (see also [4] ). Here it happens in one dimension higher: the point is replaced by a limit cycle and the limit cycle by a quasi-periodic dynamics on a torus (see also [6] for more details). In [3] the destruction by a saddle-cycle, is called a homoclinic bifurcation.…”

Section: Discussionmentioning

confidence: 99%

Ecoepidemic predator–prey model with feeding satiation, prey herd behavior and abandoned infected prey

Kooi

Venturino

2016

Mathematical Biosciences

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MSC: Keywords:Herd behavior Disease transmission Ecoepidemics System collapse Local and global bifurcations a b s t r a c tIn this paper we analyse a predator-prey model where the prey population shows group defense and the prey individuals are affected by a transmissible disease. The resulting model is of the RosenzweigMacArthur predator-prey type with an SI (susceptible-infected) disease in the prey. Modeling prey group defense leads to a square root dependence in the Holling type II functional for the predator-prey interaction term. The system dynamics is investigated using simulations, classical existence and asymptotic stability analysis and numerical bifurcation analysis. A number of bifurcations, such as transcritical and Hopf bifurcations which occur commonly in predator-prey systems will be found. Because of the square root interaction term there is non-uniqueness of the solution and a singularity where the prey population goes extinct in a finite time. This results in a collapse initiated by extinction of the healthy or susceptible prey and thereafter the other population(s). When also a positive attractor exists this leads to bistability similar to what is found in predator-prey models with a strong Allee effect. For the two-dimensional disease-free (i.e. the purely demographic) system the region in the parameter space where bistability occurs is marked by a global bifurcation. At this bifurcation a heteroclinic connection exists between saddle prey-only equilibrium points where a stable limit cycle together with its basin of attraction, are destructed. In a companion paper (Gimmelli et al., 2015) the same model was formulated and analysed in which the disease was not in the prey but in the predator. There we also observed this phenomenon. Here we extend its analysis using a phase portrait analysis. For the three-dimensional ecoepidemic predator-prey system where the prey is affected by the disease, also tangent bifurcations including a cusp bifurcation and a torus bifurcation of limit cycles occur. This leads to new complex dynamics. Continuation by varying one parameter of the emerging quasi-periodic dynamics from a torus bifurcation can lead to its destruction by a collision with a saddle-cycle. Under other conditions the quasi-periodic dynamics changes gradually in a trajectory that lands on a boundary point where the prey go extinct in finite time after which a total collapse of the three-dimensional system occurs.

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“…(ii) Backward bifurcation is a type of bifurcation where a stable endemic equilibrium coexists with a stable disease-free equilibrium when R 0 < 1 [7,19,22]. Considering (10) the following points hold for equation (9), there is Thus, for equilibrium point E 4 there is no endemic equilibrium when R 0 < 1 and so it does not have a backward bifurcation about R 0 = 1. (iii) A Hopf bifurcation occurs when a pair of eigenvalues crosses the imaginary axis.…”

Section: Bifurcation Analysesmentioning

confidence: 99%

“…In the presence of a consumer and diseased resource, the overall system can show different complex dynamical behaviours, such as bistability, quasi-periodicity and chaos [10,32]. Here we use the classic Rosenzweig-MacArthur model approach for consumerresource dynamics which incorporates reasonable biology in the form of logistic resource growth and a saturating functional response of resource consumption, and can produce steady-state or cyclical dynamics [28].…”

Section: Introductionmentioning

confidence: 99%

Consumer-resource coexistence as a means of reducing infectious disease

Duffy

Collins

2019

Journal of Biological Dynamics

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Maintaining sustainable ecosystems are important for all the inhabitants of earth. Also, an important component of sustainable ecosystems is the maintenance of healthy coexistence of consumers and their resources which can include diseases in the species involved. We formulate a model, where the resources are plants, to explore how consumer-resource coexistence could of itself limit the spread of infectious diseases. The important mathematical features of the model are discussed using the basic reproduction number and the consumption number. The results show an association between species coexistence and a decrease in ecosystem resource disease. The possible importance of these results are discussed.

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Revealing the role of predator interference in a predator–prey system with disease in prey population

Cited by 18 publications

References 64 publications

Reef accessibility impairs the protection of sharks

Reef accessibility impairs the protection of sharks

Ecoepidemic predator–prey model with feeding satiation, prey herd behavior and abandoned infected prey

Consumer-resource coexistence as a means of reducing infectious disease

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