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.
In: Theoretical Population Biology, Vol. 61, No. 3, 05.2002, p. 277-284.Research output: Contribution to journal › Article
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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 -