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Related Concept Videos

Population Growth00:57

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Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...
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Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
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Monitoring Intraspecies Competition in a Bacterial Cell Population by Cocultivation of Fluorescently Labelled Strains
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Noise and correlations in a spatial population model with cyclic competition.

Tobias Reichenbach1, Mauro Mobilia, Erwin Frey

  • 1Arnold Sommerfeld Center for Theoretical Physics (ASC) and Center for NanoScience (CeNS), Department of Physics, Ludwig-Maximilians-Universität München, Theresienstrasse 37, D-80333 München, Germany.

Physical Review Letters
|February 1, 2008
PubMed
Summary

Spatial noise and diffusion drive coevolution in cyclic competition models. This study reveals emergent entangled spiral patterns, offering insights into ecological dynamics and wave propagation.

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Area of Science:

  • Ecology
  • Theoretical Ecology
  • Mathematical Biology

Background:

  • Ecosystems exhibit noise and spatial dynamics.
  • Coevolution in cyclic competition is influenced by these factors.
  • Previous experiments show some effects of spatial dynamics.

Purpose of the Study:

  • To theoretically understand the influence of noise and spatial degrees of freedom on coevolution.
  • To investigate a spatial model of three species with cyclic dominance.
  • To analyze emergent patterns and dynamics in ecological systems.

Main Methods:

  • Individual-based modeling.
  • Stochastic partial differential equations.
  • Deterministic reaction-diffusion equations.
  • Spatiotemporal correlation functions.

Main Results:

  • Emergence of fascinating patterns of entangled spirals.
  • Accounting for stochastic fluctuations and spatial diffusion at different levels.
  • Analytical expressions for front velocity and wavelength of spiral waves.

Conclusions:

  • Noise and spatial diffusion are crucial for understanding coevolutionary dynamics.
  • The model provides a theoretical framework for emergent spiral patterns.
  • The findings offer insights into the propagation of ecological waves.