Modeling of the Population Density Flow for Periodically Migrating Organisms

Authored by Yu V Tyutyunov, A D Zagrebneva, F A Surkov, A I Azovsky

Date Published: 2010

DOI: 10.1134/s000143701001008x

Sponsors: Russian Foundation for Basic Research

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

The Patlak-Keller-Segel population density flow equation was derived based on the hypotheses concerning the way of movement of the benthic organisms with periodic appearance in the water mass differing from the commonly used assumptions {[}12, 14, 15]. On the basis of these hypotheses, a time-discrete and space-continuous individual-based model of the population distribution in the environment with the continuous stimulus distribution was built. Using this model, we have shown that the analyzed taxis mechanism (i.e., the decrease of the migration frequency of the individuals from the bottom to the water mass with the increase of the stimulus concentration) leads to the aggregation of the organisms in the places with a high concentration of the stimulus. The population dynamics is well approximated by the continuous model in which the obtained Patlak-Keller-Segel flow equation is used. The numerical modeling has shown that the form of the dependence of the individual migration frequency to the water mass on the stimulus concentration (hyperbolic, exponential, linear, and sigmoid) slightly influences the pattern of the individuals' distribution.

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Copepods Sediments