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Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates

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  • Hal Caswell

    (Universiteit van Amsterdam)

Abstract

The population growth rate, or intrinsic rate of increase, measures the potential rate of growth of a population with specified and fixed vital rates.The sensitivity of population growth rate to changes in the vital rates can be written in terms of the stable stage or age distribution and the reproductive value distribution. If the vital rate measures the rate of production of one type of individual by another, then the sensitivity of growth rate is proportional to the reproductive value of the destination type and the representation in the stable stage distribution of the source type. This formal relationship exists in three forms: one limited to age-classified populations, a second that applies to stage- or age-classified populations, and a third that uses matrix calculus. Each uses a different set of formal demographic techniques; together they provide a relationship that beautifully cuts across different types of demographic models.

Suggested Citation

  • Hal Caswell, 2010. "Reproductive value, the stable stage distribution, and the sensitivity of the population growth rate to changes in vital rates," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 23(19), pages 531-548.
    • Handle: RePEc:dem:demres:v:23:y:2010:i:19
    DOI: 10.4054/DemRes.2010.23.19
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    Citations

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    Cited by:

    1. Hartemink, Nienke & Missov, Trifon I. & Caswell, Hal, 2017. "Stochasticity, heterogeneity, and variance in longevity in human populations," Theoretical Population Biology, Elsevier, vol. 114(C), pages 107-116.
    2. Hal Caswell & Nora Sánchez Gassen, 2015. "The sensitivity analysis of population projections," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(28), pages 801-840.
    3. Karsten, Richard & Teismann, Holger & Vogels, Angela, 2013. "Reproductive value, sensitivity, and nonlinearity: Population-management heuristics derived from classical demography," Theoretical Population Biology, Elsevier, vol. 85(C), pages 20-25.
    4. Caswell, Hal & Shyu, Esther, 2012. "Sensitivity analysis of periodic matrix population models," Theoretical Population Biology, Elsevier, vol. 82(4), pages 329-339.

    More about this item

    Keywords

    population growth; senescence; matrix population models; sensitivity analysis;
    All these keywords.

    JEL classification:

    • J1 - Labor and Demographic Economics - - Demographic Economics
    • Z0 - Other Special Topics - - General

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