### 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 language | English |
---|---|

Pages (from-to) | 271-285 |

Number of pages | 15 |

Journal | Mathematical Biosciences |

Volume | 47 |

Issue number | 3-4 |

DOIs | |

State | Published - Jan 1 1979 |

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### ASJC Scopus subject areas

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

### Cite this

*Mathematical Biosciences*,

*47*(3-4), 271-285. https://doi.org/10.1016/0025-5564(79)90042-7

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

Research output: Contribution to journal › Article

*Mathematical Biosciences*, vol. 47, no. 3-4, pp. 271-285. https://doi.org/10.1016/0025-5564(79)90042-7

}

TY - JOUR

T1 - Implications of a partial-differential-equation cohort model

AU - DeAngelis, D. L.

AU - Mattice, J. S.

PY - 1979/1/1

Y1 - 1979/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0018636901&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0018636901&partnerID=8YFLogxK

U2 - 10.1016/0025-5564(79)90042-7

DO - 10.1016/0025-5564(79)90042-7

M3 - Article

AN - SCOPUS:0018636901

VL - 47

SP - 271

EP - 285

JO - Mathematical Biosciences

JF - Mathematical Biosciences

SN - 0025-5564

IS - 3-4

ER -