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A fundamental form for the differential equation of colonial and organism growth

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Abstract

When total cell number is used as the basic parameter of growth, rational equations which describe colonial and organism growth under varying circumstances have been derived from a single differential form. These equations result from making specific, but reasonable assumptions about two additive factors, ϕ and θ which determine community growth. The first factor (ϕ) is assumed to arise from conditions within the growing cell itself, while the second factor (θ) arises from interactions between the growing cells of the community. If it is further assumed that the cells of a community are homogeneous with respect to density and volume, it has been shown that the mathematical expressions commonly used to describe growth data may be rationally derived from the general form.

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Authors and Affiliations

  1. Division of Physiology, Medical School, University of California, Berkeley

    Nathan W. Shock & Manuel F. Morales

  2. The Institute of Child Welfare, University of California, Berkeley

    Nathan W. Shock & Manuel F. Morales

Authors
  1. Nathan W. Shock
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  2. Manuel F. Morales
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Additional information

Clerical assistance in the preparation of these materials was furnished by the personnel of Work Projects Administration, Official Project No. 65-1-08-62, Unit A-8.

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Shock, N.W., Morales, M.F. A fundamental form for the differential equation of colonial and organism growth. Bulletin of Mathematical Biophysics 4, 63–71 (1942). https://doi.org/10.1007/BF02477310

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  • DOI: https://doi.org/10.1007/BF02477310

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