Realistic Choice of Annual Matrices Contracts the Range of <i>λ</i><sub>S</sub> Estimates
In matrix population modeling the multi-year monitoring of a population structure results in a set of annual population projection matrices (PPMs), which gives rise to the stochastic growth rate <i>λ</i><sub>S</sub>, a quantitative measure of long-term population viability. T...
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MDPI AG
2020-12-01
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| author | Dmitrii O. Logofet Leonid L. Golubyatnikov Nina G. Ulanova |
| author_facet | Dmitrii O. Logofet Leonid L. Golubyatnikov Nina G. Ulanova |
| author_sort | Dmitrii O. Logofet |
| collection | DOAJ |
| description | In matrix population modeling the multi-year monitoring of a population structure results in a set of annual population projection matrices (PPMs), which gives rise to the stochastic growth rate <i>λ</i><sub>S</sub>, a quantitative measure of long-term population viability. This measure is usually found in the paradigm of population growth in a variable environment. The environment is represented by the set of PPMs, and <i>λ</i><sub>S</sub> ensues from a long sequence of PPMs chosen at random from the given set. because the known rules of random choice, such as the iid (independent and identically distributed) matrices, are generally artificial, the challenge is to find a more realistic rule. We achieve this with the a following a Markov chain that models, in a certain sense, the real variations in the environment. We develop a novel method to construct the ruling Markov chain from long-term weather data and to simulate, in a Monte Carlo mode, the long sequences of PPMs resulting in the estimates of <i>λ</i><sub>S</sub>. The stochastic nature of sequences causes the estimates to vary within some range, and we compare the range obtained by the “realistic choice” from 10 PPMs for a local population of a Red-Book species to those using the iid choice. As noted in the title of this paper, this realistic choice contracts the range of <i>λ</i><sub>S</sub> estimates, thus improving the estimation and confirming the Red-Book status of the species. |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T13:54:28Z |
| publishDate | 2020-12-01 |
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| series | Mathematics |
| spelling | doaj.art-a33ff5fdfd5349ad839f58d3d7cd86d12023-11-21T01:47:57ZengMDPI AGMathematics2227-73902020-12-01812225210.3390/math8122252Realistic Choice of Annual Matrices Contracts the Range of <i>λ</i><sub>S</sub> EstimatesDmitrii O. Logofet0Leonid L. Golubyatnikov1Nina G. Ulanova2Laboratory of Mathematical Ecology, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119 017 Moscow, RussiaLaboratory of Mathematical Ecology, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119 017 Moscow, RussiaBiological Department, Moscow State University, 119234 Moscow, RussiaIn matrix population modeling the multi-year monitoring of a population structure results in a set of annual population projection matrices (PPMs), which gives rise to the stochastic growth rate <i>λ</i><sub>S</sub>, a quantitative measure of long-term population viability. This measure is usually found in the paradigm of population growth in a variable environment. The environment is represented by the set of PPMs, and <i>λ</i><sub>S</sub> ensues from a long sequence of PPMs chosen at random from the given set. because the known rules of random choice, such as the iid (independent and identically distributed) matrices, are generally artificial, the challenge is to find a more realistic rule. We achieve this with the a following a Markov chain that models, in a certain sense, the real variations in the environment. We develop a novel method to construct the ruling Markov chain from long-term weather data and to simulate, in a Monte Carlo mode, the long sequences of PPMs resulting in the estimates of <i>λ</i><sub>S</sub>. The stochastic nature of sequences causes the estimates to vary within some range, and we compare the range obtained by the “realistic choice” from 10 PPMs for a local population of a Red-Book species to those using the iid choice. As noted in the title of this paper, this realistic choice contracts the range of <i>λ</i><sub>S</sub> estimates, thus improving the estimation and confirming the Red-Book status of the species.https://www.mdpi.com/2227-7390/8/12/2252discrete-structured populationmatrix population modelpopulation projection matricesstochastic growth raterandom choiceweather indices |
| spellingShingle | Dmitrii O. Logofet Leonid L. Golubyatnikov Nina G. Ulanova Realistic Choice of Annual Matrices Contracts the Range of <i>λ</i><sub>S</sub> Estimates Mathematics discrete-structured population matrix population model population projection matrices stochastic growth rate random choice weather indices |
| title | Realistic Choice of Annual Matrices Contracts the Range of <i>λ</i><sub>S</sub> Estimates |
| title_full | Realistic Choice of Annual Matrices Contracts the Range of <i>λ</i><sub>S</sub> Estimates |
| title_fullStr | Realistic Choice of Annual Matrices Contracts the Range of <i>λ</i><sub>S</sub> Estimates |
| title_full_unstemmed | Realistic Choice of Annual Matrices Contracts the Range of <i>λ</i><sub>S</sub> Estimates |
| title_short | Realistic Choice of Annual Matrices Contracts the Range of <i>λ</i><sub>S</sub> Estimates |
| title_sort | realistic choice of annual matrices contracts the range of i λ i sub s sub estimates |
| topic | discrete-structured population matrix population model population projection matrices stochastic growth rate random choice weather indices |
| url | https://www.mdpi.com/2227-7390/8/12/2252 |
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