### Abstract

Understanding the spatial distribution of populations in heterogeneous environments is an important problem in ecology. In the case of a population of organisms that can sense the quality of their environment and move to increase their fitness, one theoretical description of the expected distribution of the population is the ideal free distribution, where individuals locate themselves to optimize fitness. A model for a dynamical process that allows a population to achieve an ideal free distribution was proposed by the Cosner (Theor Popul Biol 67:101-108, 2005). The model is based on a reaction-diffusion-advection equation with nonlinear diffusion which is similar to a porous medium equation with additional advection and population growth terms. We establish that the model is well-posed, show that solutions stabilize, determine the stationary states, discuss their stability, and describe the biological interpretation of the results.

Original language | English (US) |
---|---|

Pages (from-to) | 1343-1382 |

Number of pages | 40 |

Journal | Journal of Mathematical Biology |

Volume | 69 |

Issue number | 6-7 |

DOIs | |

State | Published - Dec 1 2014 |

### Fingerprint

### ASJC Scopus subject areas

- Medicine(all)

### Cite this

*Journal of Mathematical Biology*,

*69*(6-7), 1343-1382. https://doi.org/10.1007/s00285-013-0733-z

**Well-posedness and qualitative properties of a dynamical model for the ideal free distribution.** / Cosner, George; Winkler, Michael.

Research output: Contribution to journal › Article

*Journal of Mathematical Biology*, vol. 69, no. 6-7, pp. 1343-1382. https://doi.org/10.1007/s00285-013-0733-z

}

TY - JOUR

T1 - Well-posedness and qualitative properties of a dynamical model for the ideal free distribution

AU - Cosner, George

AU - Winkler, Michael

PY - 2014/12/1

Y1 - 2014/12/1

N2 - Understanding the spatial distribution of populations in heterogeneous environments is an important problem in ecology. In the case of a population of organisms that can sense the quality of their environment and move to increase their fitness, one theoretical description of the expected distribution of the population is the ideal free distribution, where individuals locate themselves to optimize fitness. A model for a dynamical process that allows a population to achieve an ideal free distribution was proposed by the Cosner (Theor Popul Biol 67:101-108, 2005). The model is based on a reaction-diffusion-advection equation with nonlinear diffusion which is similar to a porous medium equation with additional advection and population growth terms. We establish that the model is well-posed, show that solutions stabilize, determine the stationary states, discuss their stability, and describe the biological interpretation of the results.

AB - Understanding the spatial distribution of populations in heterogeneous environments is an important problem in ecology. In the case of a population of organisms that can sense the quality of their environment and move to increase their fitness, one theoretical description of the expected distribution of the population is the ideal free distribution, where individuals locate themselves to optimize fitness. A model for a dynamical process that allows a population to achieve an ideal free distribution was proposed by the Cosner (Theor Popul Biol 67:101-108, 2005). The model is based on a reaction-diffusion-advection equation with nonlinear diffusion which is similar to a porous medium equation with additional advection and population growth terms. We establish that the model is well-posed, show that solutions stabilize, determine the stationary states, discuss their stability, and describe the biological interpretation of the results.

UR - http://www.scopus.com/inward/record.url?scp=84932112377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84932112377&partnerID=8YFLogxK

U2 - 10.1007/s00285-013-0733-z

DO - 10.1007/s00285-013-0733-z

M3 - Article

C2 - 24170293

AN - SCOPUS:84886200942

VL - 69

SP - 1343

EP - 1382

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 6-7

ER -