### Abstract

The ideal free distribution is a description of how organisms would distribute themselves in space if they were free to move so as to maximize fitness. The standard formulation of the ideal free distribution envisions the environment as consisting of finitely many discrete habitats. In this paper, a version of the ideal free distribution is derived for the case where the environment is a continuum. The continuum formulation allows computation of average fitness at the population level by taking account of both local fitness and the spatial distribution of the population. An example shows that the average fitness may have a different form than the local fitness; in particular, if local fitness is described by a logistic equation at each location, the average fitness may obey the θ-logistic equation of F. J. Ayala et al. (1973, Theor. Popul. Biol. 4, 331-356). This gives a mechanistic derivation of the θ-logistic equation.

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

Pages (from-to) | 277-284 |

Number of pages | 8 |

Journal | Theoretical Population Biology |

Volume | 61 |

Issue number | 3 |

DOIs | |

State | Published - May 2002 |

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### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Ecology, Evolution, Behavior and Systematics

### Cite this

**A Continuum Formulation of the Ideal Free Distribution and Its Implications for Population Dynamics.** / Kshatriya, Mrigesh; Cosner, George.

Research output: Contribution to journal › Article

*Theoretical Population Biology*, vol. 61, no. 3, pp. 277-284. https://doi.org/10.1006/tpbi.2002.1573

}

TY - JOUR

T1 - A Continuum Formulation of the Ideal Free Distribution and Its Implications for Population Dynamics

AU - Kshatriya, Mrigesh

AU - Cosner, George

PY - 2002/5

Y1 - 2002/5

N2 - The ideal free distribution is a description of how organisms would distribute themselves in space if they were free to move so as to maximize fitness. The standard formulation of the ideal free distribution envisions the environment as consisting of finitely many discrete habitats. In this paper, a version of the ideal free distribution is derived for the case where the environment is a continuum. The continuum formulation allows computation of average fitness at the population level by taking account of both local fitness and the spatial distribution of the population. An example shows that the average fitness may have a different form than the local fitness; in particular, if local fitness is described by a logistic equation at each location, the average fitness may obey the θ-logistic equation of F. J. Ayala et al. (1973, Theor. Popul. Biol. 4, 331-356). This gives a mechanistic derivation of the θ-logistic equation.

AB - The ideal free distribution is a description of how organisms would distribute themselves in space if they were free to move so as to maximize fitness. The standard formulation of the ideal free distribution envisions the environment as consisting of finitely many discrete habitats. In this paper, a version of the ideal free distribution is derived for the case where the environment is a continuum. The continuum formulation allows computation of average fitness at the population level by taking account of both local fitness and the spatial distribution of the population. An example shows that the average fitness may have a different form than the local fitness; in particular, if local fitness is described by a logistic equation at each location, the average fitness may obey the θ-logistic equation of F. J. Ayala et al. (1973, Theor. Popul. Biol. 4, 331-356). This gives a mechanistic derivation of the θ-logistic equation.

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U2 - 10.1006/tpbi.2002.1573

DO - 10.1006/tpbi.2002.1573

M3 - Article

VL - 61

SP - 277

EP - 284

JO - Theoretical Population Biology

JF - Theoretical Population Biology

SN - 0040-5809

IS - 3

ER -