Abstract
A population is considered which grows according to the logistic equation while spreading out at random. An approximate method is used to obtain transient and steady-state values for various simple boundary conditions such as that of a population started in an infinite one- or two-dimensional region with or without reflecting or absorbing barriers. An approximate steady-state solution is given for the one-dimensional case of two neighboring regions having different growth rates, mobilities, and degrees of attractiveness.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature
Jahnke, E. and F. Emde. 1945.Tables of Functions. Fourth Edition. New York: Dover Publications, Inc.
Landahl, H. D. 1953. “An Approximation Method for the Solution of Diffusion and Related Problems”.Bull. Math. Biophyics,15, 49–61.
— 1953. “On the Spread of Information with Time and Distance”.Ibid.,,15, 367–81.
Skellam, J. G. 1951. “Random Dispersal in Theoretical Populations”.Biometrika,38, 196–218.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Landahl, H.D. Population growth under the influence of random dispersal. Bulletin of Mathematical Biophysics 19, 171–186 (1957). https://doi.org/10.1007/BF02477760
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02477760