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A comparative approach to stabilizing mechanisms between discrete- and continuous-time consumer-resource models.

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  • 1Department of Electrical and Computer Engineering, Department of Biomedical Engineering, Department of Mathematical Sciences, Center for Bioinformatics and Computational Biology, University of Delaware, Newark, DE, United States of America.

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Comparing continuous-time and discrete-time models reveals how ecological processes impact consumer-resource population dynamics. Mutual interference stabilizes, while cooperation destabilizes host-parasitoid interactions in both frameworks.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Consumer-resource interactions are fundamental to ecological systems.
  • Continuous-time (e.g., Lotka-Volterra) and discrete-time (e.g., Nicholson-Bailey) models are widely used to study population dynamics.
  • Density-dependent consumer attack rates significantly influence interaction stability.

Purpose of the Study:

  • To systematically compare the stabilizing and destabilizing effects of ecological processes on consumer-resource dynamics in discrete-time versus continuous-time models.
  • To analyze host-parasitoid interactions with density-dependent parasitoid attack rates.
  • To elucidate the distinct impacts of functional responses (Type II, Type III) and inter-parasitoid interactions on population stability.

Main Methods:

  • Developed and analyzed mathematical models for host-parasitoid interactions.
  • Incorporated density-dependent parasitoid attack rates, including Type II and Type III functional responses.
  • Investigated the effects of mutual interference and cooperation between parasitoids on population dynamics.
  • Compared stability outcomes between discrete-time and continuous-time modeling frameworks.

Main Results:

  • A Type II functional response stabilizes dynamics only when coupled with other mechanisms like mutual interference.
  • A Type III functional response is inherently stabilizing, requiring higher attack-rate acceleration in discrete-time models and benefiting from increased host reproduction.
  • Mutual interference among parasitoids promotes stability, whereas cooperation to handle hosts leads to destabilization in both modeling frameworks.

Conclusions:

  • The choice between discrete-time and continuous-time models can alter the interpretation of ecological processes' impact on population stability.
  • Understanding density-dependent attack rates and inter-consumer interactions is crucial for predicting population dynamics.
  • This comparative analysis provides a systematic framework for characterizing drivers of stability in consumer-resource models.