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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Resonance in Physiologically Structured Population Models.

Kevin Gross1, André M de Roos2,3

  • 1Department of Statistics, North Carolina State University, Raleigh, NC, 27695, USA. krgross@ncsu.edu.

Bulletin of Mathematical Biology
|June 22, 2021
PubMed
Summary
This summary is machine-generated.

Environmental variation impacts population dynamics. We present a transfer function method for size-structured populations, revealing multi-decade resonances in coral reef dynamics driven by competition.

Keywords:
Benthic invertebratesEnvironmental stochasticityIntraspecific competitionMathematical modelPopulation dynamicsSpectral analysis

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Area of Science:

  • Ecology
  • Population Dynamics
  • Marine Biology

Background:

  • Understanding how environmental variation influences population dynamics is a key ecological challenge.
  • Transfer functions, using linearization theory, link environmental variation spectra to population abundance fluctuations.

Purpose of the Study:

  • To derive and compute the transfer function for continuous-time, size-structured population models.
  • To analyze the transfer function for a stony coral population model to identify dynamical patterns.

Main Methods:

  • Developed a method to derive and compute transfer functions for size-structured populations.
  • Applied the method to a size-structured model of stony corals with open recruitment.
  • Analyzed the frequency spectrum of population abundance in relation to environmental variation.

Main Results:

  • Identified a sharp, multi-decade resonance in coral population dynamics.
  • The resonance is driven by space competition between established colonies and recruits.
  • Resonant frequency is primarily determined by colony growth rate; oscillations are favored by weak density dependence.

Conclusions:

  • Transfer functions are effective for analyzing dynamics in physiologically structured population models.
  • Size-structured models can reveal significant resonant phenomena, like those observed in coral reefs.
  • These findings suggest potential dynamical behaviors in marine invertebrates in less degraded ecosystems.