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Variance as a life history outcome: Sensitivity analysis of the contributions of stochasticity and heterogeneity

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  • van Daalen, Silke
  • Caswell, Hal

Abstract

Variance in life history outcomes among individuals is a requirement for natural selection, and a determinant of the ecological dynamics of populations. Heterogeneity among individuals will cause such variance, but so will the inherently stochastic nature of their demography. The relative contributions of these variance components – stochasticity and heterogeneity – to life history outcomes are presented here in a general, demographic calculation. A general formulation of sensitivity analysis is provided for the relationship between the variance components and the demographic rates within the life cycle. We illustrate these novel methods with two examples; the variance in longevity within and between frailty groups in a laboratory population of fruit flies, and the variance in lifetime reproductive output within and between initial environment states in a perennial herb in a stochastic fire environment. In fruit flies, an increase in mortality would increase the variance due to stochasticity and reduce that due to heterogeneity. In the plant example, increasing mortality reduces, and increasing fertility increases both variance components. Sensitivity analyses such as these can provide a powerful tool in identifying patterns among life history stages and heterogeneity groups and their contributions to variance in life history outcomes.

Suggested Citation

  • van Daalen, Silke & Caswell, Hal, 2020. "Variance as a life history outcome: Sensitivity analysis of the contributions of stochasticity and heterogeneity," Ecological Modelling, Elsevier, vol. 417(C).
    • Handle: RePEc:eee:ecomod:v:417:y:2020:i:c:s0304380019303643
    DOI: 10.1016/j.ecolmodel.2019.108856
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    References listed on IDEAS

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    1. Hal Caswell, 2014. "A matrix approach to the statistics of longevity in heterogeneous frailty models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 31(19), pages 553-592.
    2. Silke van Daalen & Hal Caswell, 2015. "Lifetime reproduction and the second demographic transition: Stochasticity and individual variation," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(20), pages 561-588.
    3. 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.
    4. Hernandez-Suarez, Carlos & Rabinovich, Jorge & Hernandez, Karla, 2012. "The long-run distribution of births across environments under environmental stochasticity and its use in the calculation of unconditional life-history parameters," Theoretical Population Biology, Elsevier, vol. 82(4), pages 264-274.
    5. Magnus, J.R. & Neudecker, H., 1985. "Matrix differential calculus with applications to simple, Hadamard, and Kronecker products," Other publications TiSEM 1b2f1740-bfd1-4ea5-986c-9, Tilburg University, School of Economics and Management.
    6. Hal Caswell & Silke F. van Daalen, 2016. "A Note on the vec Operator Applied to Unbalanced Block-Structured Matrices," Journal of Applied Mathematics, Hindawi, vol. 2016, pages 1-3, November.
    7. Hal Caswell, 2011. "Beyond R0: Demographic Models for Variability of Lifetime Reproductive Output," PLOS ONE, Public Library of Science, vol. 6(6), pages 1-21, June.
    8. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
    9. James Vaupel & Kenneth Manton & Eric Stallard, 1979. "The impact of heterogeneity in individual frailty on the dynamics of mortality," Demography, Springer;Population Association of America (PAA), vol. 16(3), pages 439-454, August.
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    1. Hal Caswell & Silke van Daalen, 2021. "Healthy longevity from incidence-based models: More kinds of health than stars in the sky," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 45(13), pages 397-452.
    2. Hal Caswell, 2020. "The formal demography of kinship II: Multistate models, parity, and sibship," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 42(38), pages 1097-1146.

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