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Proceedings of the National Academy of Sciences of the United States of America logoLink to Proceedings of the National Academy of Sciences of the United States of America
. 1969 Apr;62(4):1056–1060. doi: 10.1073/pnas.62.4.1056

ON POPULATION GROWTH IN A RANDOMLY VARYING ENVIRONMENT

R C Lewontin 1,2, D Cohen 1,2,*
PMCID: PMC223613  PMID: 5256406

Abstract

If a population is growing in a randomly varying environment, such that the finite rate of increase per generation is a random variable with no serial autocorrelation, the logarithm of population size at any time t is normally distributed. Even though the expectation of population size may grow infinitely large with time, the probability of extinction may approach unity, owing to the difference between the geometric and arithmetic mean growth rates.

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