IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v417y2020ics0304380019303643.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380019303643
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2019.108856?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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. Caswell, Hal & Shyu, Esther, 2012. "Sensitivity analysis of periodic matrix population models," Theoretical Population Biology, Elsevier, vol. 82(4), pages 329-339.
    4. 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.
    5. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    6. Coste, Christophe F.D. & Pavard, Samuel, 2020. "Analysis of a multitrait population projection matrix reveals the evolutionary and demographic effects of a life history trade-off," Ecological Modelling, Elsevier, vol. 418(C).
    7. Coste, Christophe F.D. & Austerlitz, Frédéric & Pavard, Samuel, 2017. "Trait level analysis of multitrait population projection matrices," Theoretical Population Biology, Elsevier, vol. 116(C), pages 47-58.
    8. 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.
    9. 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.
    10. Paulo M. D. C. Parente & Richard J. Smith, 2021. "Quasi‐maximum likelihood and the kernel block bootstrap for nonlinear dynamic models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(4), pages 377-405, July.
    11. Bagdonavicius, Vilijandas & Nikulin, Mikhail, 2000. "On goodness-of-fit for the linear transformation and frailty models," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 177-188, April.
    12. Chen Tong & Peter Reinhard Hansen & Ilya Archakov, 2024. "Cluster GARCH," Papers 2406.06860, arXiv.org.
    13. Yahia Salhi & Pierre-Emmanuel Thérond, 2016. "Age-Specific Adjustment of Graduated Mortality," Working Papers hal-01391285, HAL.
    14. Feehan, Dennis & Wrigley-Field, Elizabeth, 2020. "How do populations aggregate?," SocArXiv 2fkw3, Center for Open Science.
    15. M. K. Lintu & Asha Kamath, 2022. "Performance of recurrent event models on defect proneness data," Annals of Operations Research, Springer, vol. 315(2), pages 2209-2218, August.
    16. Il Do Ha & Maengseok Noh & Youngjo Lee, 2010. "Bias Reduction of Likelihood Estimators in Semiparametric Frailty Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 307-320, June.
    17. Andreas Wienke & Anne M. Herskind & Kaare Christensen & Axel Skytthe & Anatoli I. Yashin, 2002. "The influence of smoking and BMI on heritability in susceptibility to coronary heart disease," MPIDR Working Papers WP-2002-003, Max Planck Institute for Demographic Research, Rostock, Germany.
    18. Svetlana V. Ukraintseva & Anatoli I. Yashin, 2005. "Economic progress as cancer risk factor. I: Puzzling facts of cancer epidemiology," MPIDR Working Papers WP-2005-021, Max Planck Institute for Demographic Research, Rostock, Germany.
    19. K. Motarjem & M. Mohammadzadeh & A. Abyar, 2020. "Geostatistical survival model with Gaussian random effect," Statistical Papers, Springer, vol. 61(1), pages 85-107, February.
    20. Schultz, T. Paul, 2010. "Population and Health Policies," Handbook of Development Economics, in: Dani Rodrik & Mark Rosenzweig (ed.), Handbook of Development Economics, edition 1, volume 5, chapter 0, pages 4785-4881, Elsevier.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecomod:v:417:y:2020:i:c:s0304380019303643. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.