Nonlinear Dynamics of Interacting Populations

Bazykin, Alexander D; Khibnik, Alexander I.; Krauskopf, Bernd

doi:10.1142/2284

Cited by 388 publications

(249 citation statements)

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“…An increase of clearance rate with P can be considered as one of criteria of the emergence Holling type III response. Note that theoretical studies predict enhancing stability of predator -prey A c c e p t e d m a n u s c r i p t 13 interactions in case the clearance rate is an increasing function of the food density (Oaten and Murdoch, 1975a;Bazykin, 1998).…”

Section: 3 Results Of Modellingmentioning

confidence: 99%

Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling

Морозов

2010

Journal of Theoretical Biology

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Food-web population models are rather sensitive to parameterization of functional response in predation terms. Theoretical studies would predict enhancing of ecosystems' stability for a functional response of sigmoid type (Holling type III). The choice of a correct type of response is especially important for modelling outcome of grazing control of algal blooms by zooplankton in nutrient-rich ecosystems. Extensive experiments on zooplankton feeding in laboratories show non-sigmoid nature of response for most herbivorous zooplankton species.As a consequence, there is a strong opinion in the literature that the implementation of Holling III type grazing in plankton models is biologically meaningless. I argue, however, that such an 'evident' claim might be wrong and sigmoid functional responses in real plankton communities would emerge more often than it was suggested earlier. Especially, this concerns plankton models without vertical resolution, which ignore heterogeneity in species vertical distribution. By having conducted extensive literature search of data on zooplankton feeding in situ, I show that vertical heterogeneity in food distribution as well as active food searching behaviour of zooplankton can modify the type of functional response. A c c e p t e d m a n u s c r i p t 2In particular, the rate of food intake by the whole zooplankton population in the column, as a function of total amount of food, often exhibits a sigmoid behaviour, instead of a nonsigmoid one postulated previously based upon laboratory experiments. This conceptual discrepancy is due to the ability of zooplankton to feed mostly in layers with high algal density. I propose a generic model explaining the observed alteration of type between the overall and the local functional responses. I show that emergence of Holling type III in plankton systems is due to mechanisms different from those well known in the ecological literature (e.g. food search learning, existence of alternative food, refuge for prey).

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Section: 3 Results Of Modellingmentioning

confidence: 99%

Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling

Морозов

2010

Journal of Theoretical Biology

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“…For an introduction to bifurcation analysis the reader is referred to (Guckenheimer and Holmes, 1985;Kuznetsov, 1998) and to (Bazykin, 1998) for the application to ecosystem models. Bifurcation analysis gives information about the long-term dynamic behaviour of nonlinear dynamic systems.…”

Section: Bifurcation Analysismentioning

confidence: 99%

Aggregation methods in food chains with nutrient recycling

Kooi

Poggiale

Auger

et al. 2002

Ecological Modelling

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This paper is devoted to the study of food chain models under batch and chemostat conditions where nutrient recycling is taken into account. The food chain is formed by a nutrient and two populations, prey and predator (producers and consumers). Species at both trophic levels digest their food source only partly. The unusable parts of the food not used for growth is ejected in the reactor as faeces together with metabolic products. The excreted material together with death material, detritus, is decomposed and this gives the recycling of the nutrient. In closed (batch-type environment) systems the elemental matter needed by producers must be provided through recycling where light energy from the environment supplies the necessary energy that fuels the life processes. In open (chemostat-type environment) systems this energy is added to the system via the chemical energy stored in the organic compounds in the inflow. An aggregation method is developed for situations in which each trophic level is characterized by differing time scales. This allows us the reduce the dimension of the model which gives good approximations after the fast transient. We will show that in the chemostat case first-order approximations are needed in order to get the same qualitative long-term dynamics for both the full and the reduced model.

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“…Using a similar SI model with the strong Allee effect, Thieme et al [16] established by mathematical theorems that the transition from population decline to population collapse is mediated by a Hopf bifurcation and a heteroclinic orbit. The SI models of Hilker et al and Thieme et al are structurally similar to predator-prey models that have an Allee effect in the prey population and a linear functional response (prey eaten per predator per unit time) [2,3,6,10,[12][13][14]17,18]. However, most of these studies on the interplay ofAllee effects and infectious diseases, especially those in the conservation biology literature, seem to be largely concerned with the role of the Allee effect at small population densities [9].…”

Section: Introductionmentioning

confidence: 99%

Fatal disease and demographic Allee effect: population persistence and extinction

Friedman

Yakubu

2012

Journal of Biological Dynamics

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If a healthy stable host population at the disease-free equilibrium is subject to the Allee effect, can a small number of infected individuals with a fatal disease cause the host population to go extinct? That is, does the Allee effect matter at high densities? To answer this question, we use a susceptible-infected epidemic model to obtain model parameters that lead to host population persistence (with or without infected individuals) and to host extinction. We prove that the presence of an Allee effect in host demographics matters even at large population densities. We show that a small perturbation to the disease-free equilibrium can eventually lead to host population extinction. In addition, we prove that additional deaths due to a fatal infectious disease effectively increase the Allee threshold of the host population demographics.

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Nonlinear Dynamics of Interacting Populations

Cited by 388 publications

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Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling

Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling

Aggregation methods in food chains with nutrient recycling

Fatal disease and demographic Allee effect: population persistence and extinction

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