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Perturbation analysis of nonlinear matrix population models


  • Hal Caswell

    (Universiteit van Amsterdam)


Perturbation analysis examines the response of a model to changes in its parameters. It is commonly applied to population growth rates calculated from linear models, but there has been no general approach to the analysis of nonlinear models. Nonlinearities in demographic models may arise due to density-dependence, frequency-dependence (in 2-sex models), feedback through the environment or the economy, and recruitment subsidy due to immigration, or from the scaling inherent in calculations of proportional population structure. This paper uses matrix calculus to derive the sensitivity and elasticity of equilibria, cycles, ratios (e.g. dependency ratios), age averages and variances, temporal averages and variances, life expectancies, and population growth rates, for both age-classified and stage-classified models. Examples are presented, applying the results to both human and non-human populations.

Suggested Citation

  • Hal Caswell, 2008. "Perturbation analysis of nonlinear matrix population models," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 18(3), pages 59-116, March.
  • Handle: RePEc:dem:demres:v:18:y:2008:i:3

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    Cited by:

    1. repec:eee:thpobi:v:92:y:2014:i:c:p:97-106 is not listed on IDEAS
    2. Oli, Madan K. & Loughry, W.J. & Caswell, Hal & Perez-Heydrich, Carolina & McDonough, Colleen M. & Truman, Richard W., 2017. "Dynamics of leprosy in nine-banded armadillos: Net reproductive number and effects on host population dynamics," Ecological Modelling, Elsevier, vol. 350(C), pages 100-108.
    3. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    4. repec:eee:thpobi:v:82:y:2012:i:4:p:340-347 is not listed on IDEAS
    5. Michal Engelman & Hal Caswell & Emily Agree, 2014. "Why do lifespan variability trends for the young and old diverge? A perturbation analysis," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(48), pages 1367-1396, May.
    6. repec:eee:thpobi:v:85:y:2013:i:c:p:20-25 is not listed on IDEAS
    7. repec:eee:thpobi:v:73:y:2008:i:4:p:473-482 is not listed on IDEAS
    8. repec:eee:thpobi:v:97:y:2014:i:c:p:49-56 is not listed on IDEAS
    9. repec:eee:thpobi:v:82:y:2012:i:4:p:329-339 is not listed on IDEAS
    10. repec:eee:thpobi:v:116:y:2017:i:c:p:47-58 is not listed on IDEAS

    More about this item


    barnacles; density dependence; dependency ratios; elasticity; homeostasis; immigration; matrix calculus; matrix population models; population cycles; sensitivity analysis; Tribolium; two-sex models;

    JEL classification:

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


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