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Population dynamics in variable environments. IV. Weak ergodicity in the Lotka equation

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Abstract

The Hilbert projective metric is applied to the continuous-time Lotka equation in demography to establish weak ergodicity: populations with the same time-varying fecundity and mortality schedules ultimately have the same age composition. The analysis displays clearly the dynamic content of Lotka's equation and identifies a contraction operator which forces convergence of birth sequences over time. The relationship between primitivity in the discrete (Leslie) and continuous (Lotka) demographic models is made clear.

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  1. Physics and Environmental Science, Portland State University, 97207, Portland, OR, USA

    Shripad D. Tuljapurkar

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  1. Shripad D. Tuljapurkar
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Tuljapurkar, S.D. Population dynamics in variable environments. IV. Weak ergodicity in the Lotka equation. J. Math. Biology 14, 221–230 (1982). https://doi.org/10.1007/BF01832846

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  • DOI: https://doi.org/10.1007/BF01832846

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