Regulation of Predator-Prey Systems through Spatial Interactions: A Possible Solution to the Paradox of Enrichment

Jansen, Vincent A. A.

doi:10.2307/3545983

Cited by 148 publications

(134 citation statements)

References 20 publications

(20 reference statements)

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“…This suggests that spatial oscillating systems have stable synchronous and asynchronous modes, which exist simultaneously. This feature has been demonstrated here and in other models (Hassell et al, 1991;Adler, 1993;Jansen, 1995a).…”

Section: Discussionsupporting

confidence: 59%

“…Guided by the observations on two coupled patches with Lotka Volterra local dynamics (Jansen, 1994(Jansen, , 1995a) the other parameters were fixed at +=r=1, b=9.96. This particular value for b was chosen for numerical convenience; for other values of b qualitatively similar results can be obtained.…”

Section: Model Descriptionmentioning

confidence: 99%

“…The spatial averages in well-mixed systems can differ largely form their counterparts with limited movement, due to the asynchronous dynamics that can occur in the latter. In most cases asynchronous dynamics lead to the increased persistence of populations (Hassell et al, 1991;De Roos et al, 1991;Allen et al, 1993;Adler, 1993;Jansen, 1995a).…”

Section: Introductionmentioning

confidence: 99%

“…The work in this paper builds on work on two diffusively coupled identical patches in which the dynamics in each patch were given by the Lotka Volterra predator prey equations without self limitation (Jansen, 1994(Jansen, , 1995aCzaran, 1998;Jansen and De Roos, 2000;Jansen and Lloyd, 2000). This model has a family of closed orbits on which the dynamics are synchronized.…”

Section: Introductionmentioning

confidence: 99%

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The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Jansen¹

2001

Theoretical Population Biology

153

110

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I analyze the dynamics of predator and prey populations living in two patches. Within a patch the prey grow logistically and the predators have a Holling type II functional response. The two patches are coupled through predator migration. The system can be interpreted as a simple predator prey metapopulation or as a spatially explicit predator prey system. Asynchronous local dynamics are presumed by metapopulation theory. The main question I address is when synchronous and when asynchronous dynamics arise. Contrary to biological intuition, for very small migration rates the oscillations always synchronize. For intermediate migration rates the synchronous oscillations are unstable and I found periodic, quasi-periodic, and intermittently chaotic attractors with asynchronous dynamics. For large predator migration rates, attractors in the form of equilibria or limit cycles exist in which one of the patches contains no prey. The dynamical behavior of the system is described using bifurcation diagrams. The model shows that spatial predator prey populations can be regulated through the interplay of local dynamics and migration. ]

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Section: Discussionsupporting

confidence: 59%

Section: Model Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Jansen¹

2001

Theoretical Population Biology

153

110

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“…Third, a successful control of phytoplankton by zooplankton in model (5) (Rosenzweig, 1971;Gilpin, 1972;Jansen, 1995;Morozov et al, 2007). According to the paradox of enrichment, a gradual increase of the resource stock for prey (i.e.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Towards a correct description of zooplankton feeding in models: Taking into account food-mediated unsynchronized vertical migration

Морозов

Арашкевич

2010

Journal of Theoretical Biology

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Complex nature of foraging behaviour of zooplankton makes it difficult to describe adequately zooplankton grazing in models with vertical space. In mean-field models (based on systems of PDEs or coupled ODEs), zooplankton feeding at a given depth is normally computed as the product of the local functional response and the zooplankton density at this depth. Such simplification is often at odds with field observations which show the absence of clear relationship between intake rates of organisms and the ambient food density. The observed discrepancy is generic and is often caused by fast non-synchronous vertical migration of organisms with different nutrition status. In this paper, we suggest a simple way of incorporating unsynchronized short-term vertical migration of zooplankton into the mean-field modelling framework. We compute grazing of zooplankton in each layer depending on feeding activity of organisms in the layer. We take into account grazing impact of animals which are in the active phase of foraging cycle at the given moment of time but neglect the impact of animals which are in the non-active phase of the cycle (e.g. digesting food). Unsynchronized vertical migration determines the vertical distribution of actively feeding animals in layers depending on vertical distribution of food. In this paper, we compare two generic plankton models: (i) a model based on 'classical' grazing approach and (ii) a model incorporating food-mediated unsynchronized vertical migration of zooplankton. We show that including unsynchronized food-mediated migration would make the behaviour of a plankton model more realistic. This would imply a significant enhancement of ecosystem's stability and some additional mechanisms of regulation of algal blooms. In the system with food-mediated unsynchronized vertical migration, the control of phytoplankton by herbivorous becomes possible even for very large concentrations of nutrients in the water (formally, when the system's carrying capacity tends to infinity).

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Multi‐scale effects of habitat loss and the role of trait evolution

Bagawade,

van Benthem,

Wittmann

2024

Ecology and Evolution

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Habitat loss (HL) is a major cause of species extinctions. Although the effects of HL beyond the directly impacted area have been previously observed, they have not been modelled explicitly, especially in an eco‐evolutionary context. To start filling this gap, we study a two‐patch deterministic consumer‐resource model, with one of the patches experiencing loss of resources as a special case of HL. Our model allows foraging and mating within a patch as well as between patches. We then introduce heritable variation in consumer traits related to resource utilization and patch use to investigate eco‐evolutionary dynamics and compare results with constant and no trait variation scenarios. Our results show that HL in one patch can indeed reduce consumer densities in the neighbouring patch but can also increase consumer densities in the neighbouring patch when the resources are overexploited. Yet at the landscape scale, the effect of HL on consumer densities is consistently negative. Patch isolation increases consumer density in the patch experiencing HL but has generally negative effects on the neighbouring patch, with context‐dependent results at the landscape scale. With high cross‐patch dependence and coupled foraging and mating preferences, local HL can sometimes even lead to landscape‐level consumer extinction. Eco‐evolutionary dynamics can rescue consumers from such extinction in some cases if their death rates are sufficiently small. More generally, trait evolution had positive or negative effects on equilibrium consumer densities after HL, depending on the evolving trait and the spatial scale considered. In summary, our findings show that HL at a local scale can affect the neighbouring patch and the landscape as a whole, where heritable trait variation can, in some cases, alleviate the impact of HL. We thus suggest joint consideration of multiple spatial scales and trait variation when assessing and predicting the impacts of HL.

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Regulation of Predator-Prey Systems through Spatial Interactions: A Possible Solution to the Paradox of Enrichment

Cited by 148 publications

References 20 publications

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

The Dynamics of Two Diffusively Coupled Predator–Prey Populations

Towards a correct description of zooplankton feeding in models: Taking into account food-mediated unsynchronized vertical migration

Multi‐scale effects of habitat loss and the role of trait evolution

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