Periodic Oscillations in an Ideal-Free Predator-Prey Distribution

Oikos ◽  
1990 ◽  
Vol 59 (1) ◽  
pp. 85 ◽  
Author(s):  
Susanne Schwinning ◽  
Michael L. Rosenzweig
Keyword(s):  
Periodic Oscillations ◽  
Predator Prey ◽  
Prey Distribution ◽  
Ideal Free

Size-Based Structure and Production in the Pelagia of Lakes Ontario and Michigan

1994 ◽  
Vol 51 (11) ◽  
pp. 2603-2611 ◽  
Author(s):  
W. Gary Sprules ◽  
Andy P. Goyke
Keyword(s):  
Particle Size ◽  
Analytical Solutions ◽  
Secondary Production ◽  
Aquatic Ecosystems ◽  
Lake Ontario ◽  
Quadratic Trend ◽  
Periodic Oscillations ◽  
Predator Prey ◽  
Pelagic Food Webs ◽  
Biomass Spectra

Analytical solutions to allometric models of predator–prey interactions in aquatic ecosystems indicate that normalized biomass spectra should consist of a smooth quadratic trend around which periodic oscillations occur. We confirm these assertions by showing that parabolas provide good models of normalized biomass as a function of body mass within homogeneous trophic groupings of organisms (phytoplankton, zooplankton, or fish) in the pelagic food webs of Lakes Ontario and Michigan. In addition, we show that the normalized biomass spectrum for the whole pelagic community in these lakes can be modelled by a series of parabolas of constant curvature that are aligned along a smooth quadratic base, as predicted by theory. Total secondary production in Lake Ontario is predicted from these models to be 234 kcal∙m−2∙yr−1 (1 kcal = 4.19 kJ), which compares favourably with sampling estimates of about 154 kcal∙m−2∙yr−1 for the whole community except rotifers and some hypolimnetic organisms, but both are higher than particle-size conversion efficiency estimates of 75–125 kcal∙m−2∙yr−1.

scholarly journals Characterizing the Phase Transitions between Stable Equilibrium and Periodic Oscillations in Predator-prey Population Dynamics: A Theoretical Appraisal from an Extended Nicholson & Bailey Model

2020 ◽  
pp. 32-45
Author(s):  
Jean Béguinot
Keyword(s):  
Phase Transitions ◽  
Continuous Phase ◽  
Real Field ◽  
Periodic Oscillations ◽  
Predator Prey ◽  
Host Interactions ◽  
Interacting Species ◽  
Equilibrium Level ◽  
Interactive Dynamics ◽  
Multi Phase

Multi-phase patterns with more or less sharp phase transitions, first highlighted in thermodynamics, have progressively revealed having wider relevance, being encountered in various other contexts, for example fluid mechanics, and can even occur in the interactive dynamics in biological populations involving two or more species that share opposite interests, such as predator-prey or parasite-host pairs of species. In the latter, the pattern of abundances of both interacting species usually reaches an equilibrium level which can be either stable or cyclic (with large periodic oscillations in the latter case). Both alternative modes are separated by well-define boundaries and, accordingly, can relevantly be described in terms of phases and phase transitions. While this has recently been approached from very general perspectives, a more focused analysis is still lacking, regarding the nature of the phase transitions between stable and oscillatory equilibria and – still more importantly – how the nature of these phase transitions may possibly depend (or not) on the biological and contextual factors driving the parasite-host interactive dynamics. These issues are addressed hereafter, on a theoretical basis, yet intimately related to the real field context, by taking advantage of a newly derived extension of the classical Nicholson & Bailey model of parasite-host interactions. Highlighted in particular are the possibility of either first-order, second-order or continuous phase-transitions, depending on (i) the respective own dynamics of both host and parasite, (ii) the density of feeding resource for the host, (iii) the level of migration exchange in a meta-population context.

Predator Migration Decisions, the Ideal Free Distribution, and Predator‐Prey Dynamics

1999 ◽  
Vol 153 (3) ◽  
pp. 267-281 ◽  
Author(s):  
Carlos Bernstein ◽  
Pierre Auger ◽  
Jean Christophe Poggiale
Keyword(s):  
Ideal Free Distribution ◽  
Predator Prey ◽  
Free Distribution ◽  
Migration Decisions ◽  
Ideal Free ◽  
The Ideal

Experimental studies on acarine predator–prey interactions: effects of temporal changes in the environment on searching behaviour, predation rates, and fecundity (Acarina: Phytoseiidae)

1982 ◽  
Vol 60 (12) ◽  
pp. 2992-3000 ◽  
Author(s):  
Eldon S. Eveleigh ◽  
D. A. Chant
Keyword(s):  
Experimental Studies ◽  
Phytoseiulus Persimilis ◽  
Temporal Changes ◽  
Patchy Environment ◽  
Changing Environment ◽  
Searching Behaviour ◽  
Predator Prey ◽  
Prey Distribution ◽  
Predation Rates

We examined the effects of temporal changes in the environment on the searching behaviour, predation rates, and fecundity of Phytoseiulus persimilis and Amblyseius degenerans in the laboratory. Phytoseiulus persimilis demonstrated an ability to respond quickly to changes in prey distribution in a patchy environment and maintained its searching efficiency despite these changes. In contrast, A. degenerans was rather insensitive to temporal changes in prey distribution and when it found a profitable patch its visits to other patches were restricted. Thus, this species was unable to maintain its searching efficiency in the changing environment. Phytoseiulus persimilis distributed its progeny in relation to the distribution of prey in the changing environment and avoided oviposition in patches without prey, whereas A. degenerans showed no such discrimination. The fecundity of both species was not adversely affected by changes in prey distribution although their fecundity was lower than when all of the prey were in a single patch and their dispersal was restricted.

Coexistence of Periodic Oscillations Induced by Predator Cannibalism in a Delayed Diffusive Predator–Prey Model

2019 ◽  
Vol 29 (07) ◽  
pp. 1950089
Author(s):  
Daifeng Duan ◽  
Ben Niu ◽  
Junjie Wei
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Hopf Bifurcations ◽  
Center Manifold Reduction ◽  
Periodic Oscillations ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey System ◽  
Predator Cannibalism ◽  
Manifold Reduction

This paper is concerned with the effect of predator cannibalism in a delayed diffusive predator–prey system. We aim for the case where the corresponding linear system has two pairs of purely imaginary eigenvalues at a critical point, leading to Hopf–Hopf bifurcation. An approach of center manifold reduction is applied to derive the normal form for such nonresonant Hopf–Hopf bifurcations. We find that the system exhibits very rich dynamics, including the coexistence of periodic and quasi-periodic oscillations. Numerically, we show that Hopf–Hopf bifurcation is induced if the strength of the predator cannibalism term belongs to an appropriate interval.

Experimental studies on acarine predator–prey interactions: the response of predators to prey distribution in an homogeneous area (Acarina: Phytoseiidae)

1982 ◽  
Vol 60 (4) ◽  
pp. 639-647 ◽  
Author(s):  
Eldon S. Eveleigh ◽  
D. A. Chant
Keyword(s):  
Functional Response ◽  
Prey Density ◽  
Experimental Studies ◽  
Phytoseiulus Persimilis ◽  
Phytoseiid Mites ◽  
Predator Prey ◽  
Prey Distribution ◽  
Uniform Distributions ◽  
Homogeneous Area ◽  
Prey Depletion

A laboratory study was conducted to determine the effects of prey distribution in an homogeneous area on the searching success and functional response of two species of phytoseiid mites, Phytoseiulus persimilis and Amblyseius degenerans. The results indicated that the spatial distribution of the prey affected the searching success and functional response of P. persimilis but not of A. degenerans. More prey were killed by the former predator when prey were clustered, followed by random and uniform distributions. In contrast to A. degenerans, the degree of prey aggregation at a given prey density also affected the number of prey killed by P. persimilis. With both predators, prey depletion affected the comparative success of the predators at certain prey distributions. It is concluded that P. persimilis is adapted to search for prey which aggregate, whereas A. degenerans is not. The results are discussed in terms of their potential importance in predation and biological control studies.

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