A simple spatially explicit ideal-free distribution: A model and an experiment

D. W. Stephens, J. R. Stevens

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

This investigation presents a simple spatially explicit analysis of the ideal-free distribution. The traditional ideal-free distribution assumes discrete sites with definite boundaries, and predicts how many individuals should occupy each site. In contrast, the present analysis assumes that a forager's gains gradually decline with distance from a site, and asks where in space individuals ought to be. Although many interesting situations may arise, the analysis asks how individuals should position themselves as the distance between two identical sources increases. Nash equilibrium positions should follow a pitchfork pattern as the distance between sites is increased; that is, an individual should maintain a position between two sources when they are close together but should move nearer one of the sources when they are far apart. In addition, the text describes an experimental study that parallels the theoretical analysis. The experiment supports the predicted pitchfork pattern, and provides somewhat weaker support for the predicted differences in "individual" and "paired" pitchforks.

Original languageEnglish (US)
Pages (from-to)220-234
Number of pages15
JournalBehavioral Ecology and Sociobiology
Volume49
Issue number2-3
DOIs
StatePublished - Feb 17 2001

Fingerprint

ideal free distribution
Individuality
Theoretical Models
experiment
experimental study
analysis

Keywords

  • Foraging
  • Ideal-free distribution
  • Spatial models
  • Starling

ASJC Scopus subject areas

  • Ecology, Evolution, Behavior and Systematics
  • Animal Science and Zoology

Cite this

A simple spatially explicit ideal-free distribution : A model and an experiment. / Stephens, D. W.; Stevens, J. R.

In: Behavioral Ecology and Sociobiology, Vol. 49, No. 2-3, 17.02.2001, p. 220-234.

Research output: Contribution to journalArticle

@article{3e93649001144d30916483b12e7e5ba0,
title = "A simple spatially explicit ideal-free distribution: A model and an experiment",
abstract = "This investigation presents a simple spatially explicit analysis of the ideal-free distribution. The traditional ideal-free distribution assumes discrete sites with definite boundaries, and predicts how many individuals should occupy each site. In contrast, the present analysis assumes that a forager's gains gradually decline with distance from a site, and asks where in space individuals ought to be. Although many interesting situations may arise, the analysis asks how individuals should position themselves as the distance between two identical sources increases. Nash equilibrium positions should follow a pitchfork pattern as the distance between sites is increased; that is, an individual should maintain a position between two sources when they are close together but should move nearer one of the sources when they are far apart. In addition, the text describes an experimental study that parallels the theoretical analysis. The experiment supports the predicted pitchfork pattern, and provides somewhat weaker support for the predicted differences in {"}individual{"} and {"}paired{"} pitchforks.",
keywords = "Foraging, Ideal-free distribution, Spatial models, Starling",
author = "Stephens, {D. W.} and Stevens, {J. R.}",
year = "2001",
month = "2",
day = "17",
doi = "10.1007/s002650000276",
language = "English (US)",
volume = "49",
pages = "220--234",
journal = "Behavioral Ecology and Sociobiology",
issn = "0340-5443",
publisher = "Springer Verlag",
number = "2-3",

}

TY - JOUR

T1 - A simple spatially explicit ideal-free distribution

T2 - A model and an experiment

AU - Stephens, D. W.

AU - Stevens, J. R.

PY - 2001/2/17

Y1 - 2001/2/17

N2 - This investigation presents a simple spatially explicit analysis of the ideal-free distribution. The traditional ideal-free distribution assumes discrete sites with definite boundaries, and predicts how many individuals should occupy each site. In contrast, the present analysis assumes that a forager's gains gradually decline with distance from a site, and asks where in space individuals ought to be. Although many interesting situations may arise, the analysis asks how individuals should position themselves as the distance between two identical sources increases. Nash equilibrium positions should follow a pitchfork pattern as the distance between sites is increased; that is, an individual should maintain a position between two sources when they are close together but should move nearer one of the sources when they are far apart. In addition, the text describes an experimental study that parallels the theoretical analysis. The experiment supports the predicted pitchfork pattern, and provides somewhat weaker support for the predicted differences in "individual" and "paired" pitchforks.

AB - This investigation presents a simple spatially explicit analysis of the ideal-free distribution. The traditional ideal-free distribution assumes discrete sites with definite boundaries, and predicts how many individuals should occupy each site. In contrast, the present analysis assumes that a forager's gains gradually decline with distance from a site, and asks where in space individuals ought to be. Although many interesting situations may arise, the analysis asks how individuals should position themselves as the distance between two identical sources increases. Nash equilibrium positions should follow a pitchfork pattern as the distance between sites is increased; that is, an individual should maintain a position between two sources when they are close together but should move nearer one of the sources when they are far apart. In addition, the text describes an experimental study that parallels the theoretical analysis. The experiment supports the predicted pitchfork pattern, and provides somewhat weaker support for the predicted differences in "individual" and "paired" pitchforks.

KW - Foraging

KW - Ideal-free distribution

KW - Spatial models

KW - Starling

UR - http://www.scopus.com/inward/record.url?scp=0035151074&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035151074&partnerID=8YFLogxK

U2 - 10.1007/s002650000276

DO - 10.1007/s002650000276

M3 - Article

AN - SCOPUS:0035151074

VL - 49

SP - 220

EP - 234

JO - Behavioral Ecology and Sociobiology

JF - Behavioral Ecology and Sociobiology

SN - 0340-5443

IS - 2-3

ER -