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Maximizing the total population with logistic growth in a patchy environment.

Kentaro Nagahara1, Yuan Lou2, Eiji Yanagida3

  • 1Department of Mathematics, Tokyo Institute of Technology, Meguro-ku, Tokyo, 152-8551, Japan. nagahara@hst.titech.ac.jp.

Journal of Mathematical Biology
|January 21, 2021
PubMed
Summary
This summary is machine-generated.

This study optimizes resource distribution in a patchy environment to maximize species population. We found that the optimal resource allocation can be determined for small or large diffusion rates.

Keywords:
Difference equationDispersalPatchy environmentTotal population

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Area of Science:

  • Population Biology
  • Mathematical Ecology
  • Nonlinear Optimization

Background:

  • Logistic growth models describe population dynamics within a single species.
  • Environmental patchiness and dispersal influence population equilibrium.
  • Resource allocation is a key factor in population sustainability.

Purpose of the Study:

  • To maximize total population size in a patchy environment with limited resources.
  • To analyze the impact of dispersal and spatial heterogeneity on population equilibrium.
  • To characterize the global maximizer for population resource redistribution.

Main Methods:

  • Nonlinear optimization techniques applied to population biology.
  • Calculation of the first variation for the two-patch case.
  • Asymptotic expansion using Taylor series for three or more patches.
  • Utilizing a recurrence relation to determine coefficients of the global maximizer.

Main Results:

  • The global maximizer for total population is characterized for any number of patches under specific diffusion rate conditions (small or large).
  • The first variation method was used to analyze resource distribution effects in a two-patch system.
  • Asymptotic expansion and recurrence relations provided insights into optimal resource allocation for multiple patches.

Conclusions:

  • Optimal resource distribution strategies can be identified for logistic growth in patchy environments.
  • Dispersal rates significantly influence the equilibrium population and resource allocation effectiveness.
  • The study provides a mathematical framework for understanding population dynamics and resource management in heterogeneous habitats.