Generalized Verhulst laws for population growth.

Abstract:

:The growth or decay of population of a single species interacting with a large number of other species (or environment) according to the Volterra-Lotka model is investigated. When the environment is initially very close to its equilibrium level, the growth of a single species follows a generalized Verhulst law, containing hereditary effects. The derivation, modeled on statistical mechanical theories of Brownian motion, leads also to a "noise" source and to its relation to the heredity kernel. A special case, where the hereditary kernel is a damped exponential function of time, is solved numerically. When growth starts at a level much below equilibrium, the population first overshoots equilibrium and then approaches it. When decay starts at a level much higher than equilibrium, the population first decays precipitously to a very low level and then slowly grows toward equilibrium.

authors

Zwanzig R

doi

10.1073/pnas.70.11.3048

subject

Has Abstract

pub_date

1973-11-01 00:00:00

pages

3048-51

issue

11

eissn

0027-8424

issn

1091-6490

journal_volume

70

pub_type

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