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Beyond R0: Demographic Models for Variability of Lifetime Reproductive Output

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  • Hal Caswell

Abstract

The net reproductive rate measures the expected lifetime reproductive output of an individual, and plays an important role in demography, ecology, evolution, and epidemiology. Well-established methods exist to calculate it from age- or stage-classified demographic data. As an expectation, provides no information on variability; empirical measurements of lifetime reproduction universally show high levels of variability, and often positive skewness among individuals. This is often interpreted as evidence of heterogeneity, and thus of an opportunity for natural selection. However, variability provides evidence of heterogeneity only if it exceeds the level of variability to be expected in a cohort of identical individuals all experiencing the same vital rates. Such comparisons require a way to calculate the statistics of lifetime reproduction from demographic data. Here, a new approach is presented, using the theory of Markov chains with rewards, obtaining all the moments of the distribution of lifetime reproduction. The approach applies to age- or stage-classified models, to constant, periodic, or stochastic environments, and to any kind of reproductive schedule. As examples, I analyze data from six empirical studies, of a variety of animal and plant taxa (nematodes, polychaetes, humans, and several species of perennial plants).

Suggested Citation

  • 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.
  • Handle: RePEc:plo:pone00:0020809
    DOI: 10.1371/journal.pone.0020809
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    Cited by:

    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. 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.
    3. 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.
    4. 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).
    5. Roth, Gregory & Caswell, Hal, 2018. "Occupancy time in sets of states for demographic models," Theoretical Population Biology, Elsevier, vol. 120(C), pages 62-77.
    6. Daniel C. Schneider & Mikko Myrskylä, 2023. "Statistical inference for discrete-time multistate models: extensions to Markov Chains with rewards," MPIDR Working Papers WP-2023-042, Max Planck Institute for Demographic Research, Rostock, Germany.
    7. 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).
    8. Hal Caswell & Fanny Annemarie Kluge, 2015. "Demography and the statistics of lifetime economic transfers under individual stochasticity," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 32(19), pages 563-588.
    9. Caswell, Hal & Shyu, Esther, 2012. "Sensitivity analysis of periodic matrix population models," Theoretical Population Biology, Elsevier, vol. 82(4), pages 329-339.
    10. Vindenes, Yngvild & Sæther, Bernt-Erik & Engen, Steinar, 2012. "Effects of demographic structure on key properties of stochastic density-independent population dynamics," Theoretical Population Biology, Elsevier, vol. 82(4), pages 253-263.

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