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“Realistic Choice of Annual Matrices Contracts the Range of λ S Estimates” under Reproductive Uncertainty Too

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  • Dmitrii O. Logofet

    (Laboratory of Mathematical Ecology, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, Russia)

  • Leonid L. Golubyatnikov

    (Laboratory of Mathematical Ecology, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, Russia)

  • Elena S. Kazantseva

    (Biological Department, Moscow State University, 119234 Moscow, Russia)

  • Nina G. Ulanova

    (Biological Department, Moscow State University, 119234 Moscow, Russia)

Abstract

Our study is devoted to a subject popular in the field of matrix population models, namely, estimating the stochastic growth rate , λ S , a quantitative measure of long-term population viability, for a discrete-stage-structured population monitored during many years. “ Reproductive uncertainty ” refers to a feature inherent in the data and life cycle graph (LCG) when the LCG has more than one reproductive stage, but when the progeny cannot be associated to a parent stage in a unique way. Reproductive uncertainty complicates the procedure of λ S estimation following the defining of λ S from the limit of a sequence consisting of population projection matrices (PPMs) chosen randomly from a given set of annual PPMs. To construct a Markov chain that governs the choice of PPMs for a local population of Eritrichium caucasicum , an short-lived perennial alpine plant species, we have found a local weather index that is correlated with the variations in the annual PPMs, and we considered its long time series as a realization of the Markov chain that was to be constructed. Reproductive uncertainty has required a proper modification of how to restore the transition matrix from a long realization of the chain, and the restored matrix has been governing random choice in several series of Monte Carlo simulations of long-enough sequences. The resulting ranges of λ S estimates turn out to be more narrow than those obtained by the popular i.i.d. methods of random choice (independent and identically distributed matrices); hence, we receive a more accurate and reliable forecast of population viability.

Suggested Citation

  • Dmitrii O. Logofet & Leonid L. Golubyatnikov & Elena S. Kazantseva & Nina G. Ulanova, 2021. "“Realistic Choice of Annual Matrices Contracts the Range of λ S Estimates” under Reproductive Uncertainty Too," Mathematics, MDPI, vol. 9(23), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:3007-:d:686347
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    References listed on IDEAS

    as
    1. Logofet, Dmitrii O., 2017. "Aggregation may or may not eliminate reproductive uncertainty," Ecological Modelling, Elsevier, vol. 363(C), pages 187-191.
    2. Logofet, Dmitrii O., 2013. "Projection matrices in variable environments: λ1 in theory and practice," Ecological Modelling, Elsevier, vol. 251(C), pages 307-311.
    3. Logofet, Dmitrii O. & Kazantseva, Elena S. & Onipchenko, Vladimir G., 2020. "Seed bank as a persistent problem in matrix population models: From uncertainty to certain bounds," Ecological Modelling, Elsevier, vol. 438(C).
    4. Dmitrii O. Logofet & Leonid L. Golubyatnikov & Nina G. Ulanova, 2020. "Realistic Choice of Annual Matrices Contracts the Range of λ S Estimates," Mathematics, MDPI, vol. 8(12), pages 1-15, December.
    5. Logofet, Dmitrii O., 2008. "Convexity in projection matrices: Projection to a calibration problem," Ecological Modelling, Elsevier, vol. 216(2), pages 217-228.
    6. Sanz, Luis, 2019. "Conditions for growth and extinction in matrix models with environmental stochasticity," Ecological Modelling, Elsevier, vol. 411(C).
    7. Logofet, Dmitrii O., 2019. "Does averaging overestimate or underestimate population growth? It depends," Ecological Modelling, Elsevier, vol. 411(C).
    8. Steinsaltz, David & Tuljapurkar, Shripad & Horvitz, Carol, 2011. "Derivatives of the stochastic growth rate," Theoretical Population Biology, Elsevier, vol. 80(1), pages 1-15.
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