Physiological Basis of Ratio-Dependent Predator-Prey Theory: The Metabolic Pool Model as a Paradigm

AbstractThe field population dynamics of pea aphid (Acyrthosiphon pisum) and blue alfalfa aphid (A. kondoi) in alfalfa (Medicago sativa), as influenced by weather, competitors (Egyptian alfalfa weevil = EAW, Hypera brunneipennis), predation from coccinellids (Hippodamia convergens) and harvesting practices, are examined with a stochastic multitrophic level simulation model. The model incorporates a demand-driven functional-response model to estimate prey consumption, and a metabolic pool model to determine the rates and priorities of food allocation to respiration, growth, reproduction, and egestion.The model results compare favorably with field data, and are used to examine the effects of removal of each of the above factors on the dynamics of the aphids. The model shows that the observed density of EAW did not affect the aphid dynamics, but did reduce the standing crop of alfalfa. The predator H. convergens had a significant effect on the population dynamics of the aphids and the plant. Harvesting greatly affected the aphid population dynamics, as well as the dynamics of plant growth and reserve accumulation. However, high temperatures mediated through species-specific respiration costs and possibly a fungal pathogen were responsible for the observed dominance of blue aphid populations in the cool parts of the year and pea aphid populations during warmer parts of the year.

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MULTITROPHIC MODELS OF PREDATOR–PREY ENERGETICS: I. AGE-SPECIFIC ENERGETICS MODELS—PEA APHID ACYRTHOSIPHON PISUM (HOMOPTERA: APHIDIDAE) AS AN EXAMPLE

The Canadian Entomologist ◽

10.4039/ent116923-7 ◽

1984 ◽

Vol 116 (7) ◽

pp. 923-932 ◽

Cited By ~ 52

Author(s):

A. P. Gutierrez ◽

J. U. Baumgaertner ◽

C. G. Summers

Keyword(s):

Acyrthosiphon Pisum ◽

Pea Aphid ◽

Data Sets ◽

Temperature Dependent ◽

Predator Prey ◽

Dependent Rate ◽

Current State ◽

Pea Aphids ◽

Pool Model ◽

Metabolic Pool

AbstractA simple age-specific energetics (calories or biomass) model for the growth and development, reproduction, respiration, ageing, and intrinsic survivorship as a function of temperature and per capita energy availability for pea aphid (Acyrthosiphon pisum (Harris)) is reported. The ratio of energy supply–demand is used to scale all of the rates in the model. The maximum demand for energy based upon current state values is used to drive the Frazer–Gilbert functional response model (i.e. food acquisition), which is a component of the metabolic pool model used to assimilate energy to growth, reproduction, respiration, and egestion. The extensive data sets on pea aphid energetics published by Randolph et al. (1975) were used to develop the model. As the model estimates reproduction (Mx) and survivorship (Lx) values, extensive published age-specific life-data sets on pea aphids are used to test it. The results suggest:(1) the lower thermal threshold for development is raised and the upper threshold is lowered as food resources are decreased(2) the temperature-dependent rate of development is slowed with decreasing energy resources(3) the size of individuals and reproduction become smaller as temperature approaches the upper and lower thermal thresholds.A simple model for multitrophic level interactions incorporating the acquisition and assimilation functions is presented.

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Spatiotemporal dynamics in a diffusive ratio-dependent predator–prey model near a Hopf–Turing bifurcation point

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2014.04.015 ◽

2014 ◽

Vol 67 (10) ◽

pp. 1978-1997 ◽

Cited By ~ 41

Author(s):

Yongli Song ◽

Xingfu Zou

Keyword(s):

Bifurcation Point ◽

Spatiotemporal Dynamics ◽

Predator Prey ◽

Turing Bifurcation ◽

Predator Prey Model ◽

Prey Model ◽

Ratio Dependent

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Spatial Pattern of Ratio-Dependent Predator–Prey Model with Prey Harvesting and Cross-Diffusion

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127419500366 ◽

2019 ◽

Vol 29 (03) ◽

pp. 1950036 ◽

Cited By ~ 1

Author(s):

R. Sivasamy ◽

M. Sivakumar ◽

K. Balachandran ◽

K. Sathiyanathan

Keyword(s):

Temporal Dynamics ◽

Intake Rate ◽

Diffusion Term ◽

Predator Prey ◽

Cross Diffusion ◽

Predator Prey Model ◽

Prey Model ◽

Nonlinear Harvesting ◽

Ratio Dependent ◽

The Cross

This study focuses on the spatial-temporal dynamics of predator–prey model with cross-diffusion where the intake rate of prey is per capita predator according to ratio-dependent functional response and the prey is harvested through nonlinear harvesting strategy. The permanence analysis and local stability analysis of the proposed model without cross-diffusion are analyzed. We derive the conditions for the appearance of diffusion-driven instability and global stability of the considered model. Also the parameter space for Turing region is specified by keeping the cross-diffusion coefficient as one of the crucial parameters. Numerical simulations are given to justify the proposed theoretical results and to show that the cross-diffusion term plays a significant role in the pattern formation.

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