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Density-dependent dispersal and population aggregation patterns.

Vicenç Méndez1, Daniel Campos, Ignacio Pagonabarraga

  • 1Grup de Física Estadística, Departament de Física, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain. vicenc.mendez@uab.es

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Summary
This summary is machine-generated.

We derived new equations for reaction-dispersal-aggregation from random walks. The ratio of reaction to jump rates controls spatial pattern formation, with dispersal proving more stabilizing than diffusion.

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Area of Science:

  • Mathematical Biology
  • Theoretical Ecology
  • Statistical Physics

Background:

  • Reaction-diffusion-aggregation models are crucial for understanding pattern formation in biological systems.
  • Existing models often simplify movement mechanisms, potentially overlooking key dynamics.

Purpose of the Study:

  • To derive novel reaction-dispersal-aggregation equations from a more fundamental stochastic process (Markovian reaction-random walks).
  • To investigate the role of density-dependent movement in pattern formation.
  • To compare the stability properties of dispersal versus diffusion in aggregation processes.

Main Methods:

  • Derivation of reaction-dispersal-aggregation equations from Markovian random walks with density-dependent jump rates or dispersal kernels.
  • Analysis of the diffusion limit to recover known reaction-diffusion-aggregation and reaction-diffusion-advection-aggregation equations.
  • Qualitative analysis of emerging spatial patterns and comparison of stability conditions.

Main Results:

  • The ratio between reaction and jump rates is identified as a key factor controlling the onset of spatial patterns.
  • Dispersal processes were found to be more stabilizing against spatial instabilities compared to diffusion processes.
  • A general threshold value for dispersal stability was obtained.

Conclusions:

  • The study provides a new theoretical framework for reaction-dispersal-aggregation systems based on stochastic foundations.
  • Dispersal dynamics offer a more stabilizing influence on pattern formation than diffusion in aggregation contexts.
  • The findings have implications for understanding pattern emergence in various biological systems.