Implications of a partial-differential-equation cohort model

D. L. DeAngelis, J. S. Mattice

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

The growth in size of organisms in a population cohort and the change through time of the number of organisms in the cohort can be modeled in a unified way by means of a partial differential equation. This equation can be solved analytically for reasonable assumptions concerning growth and mortality rates. A cohort will have an initial distribution in sizes both because all offspring are not produced at exactly the same time and because there is some variation in the sizes of organisms at the time of reproduction. Assuming typical organism growth patterns, we show from the solution of the partial differential equation that the size distribution will at first broaden and then eventually become narrow again as the cohort grows in average size. This conclusion is in agreement with growth data on some marine and freshwater organisms. Genetic variations that cause the growth rate to be distributed normally among organisms in the cohort population are also shown to lead to predictable changes in the size distribution through time.

Original languageEnglish
Pages (from-to)271-285
Number of pages15
JournalMathematical Biosciences
Volume47
Issue number3-4
DOIs
StatePublished - Jan 1 1979

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Partial differential equations
Partial differential equation
organisms
Growth
Genetic Variation
Mortality Rate
Aquatic Organisms
Model
Fresh Water
Population
Reproduction
genetic variation
organism
mortality
Mortality

ASJC Scopus subject areas

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

Cite this

Implications of a partial-differential-equation cohort model. / DeAngelis, D. L.; Mattice, J. S.

In: Mathematical Biosciences, Vol. 47, No. 3-4, 01.01.1979, p. 271-285.

Research output: Contribution to journalArticle

DeAngelis, D. L. ; Mattice, J. S. / Implications of a partial-differential-equation cohort model. In: Mathematical Biosciences. 1979 ; Vol. 47, No. 3-4. pp. 271-285.
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