Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication
The notion of a <i>potential-growth indicator</i> came to being in the field of matrix population models long ago, almost simultaneously with the pioneering Leslie model for age-structured population dynamics, although the term has been given and the theory developed only in recent years...
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MDPI AG
2021-07-01
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| author | Dmitrii O. Logofet Valerii N. Razzhevaikin |
| author_facet | Dmitrii O. Logofet Valerii N. Razzhevaikin |
| author_sort | Dmitrii O. Logofet |
| collection | DOAJ |
| description | The notion of a <i>potential-growth indicator</i> came to being in the field of matrix population models long ago, almost simultaneously with the pioneering Leslie model for age-structured population dynamics, although the term has been given and the theory developed only in recent years. The indicator represents an explicit function, <i>R</i>(<b><i>L</i></b>), of matrix <b><i>L</i></b> elements and indicates the position of the spectral radius of <b><i>L</i></b> relative to 1 on the real axis, thus signifying the population growth, or decline, or stabilization. Some indicators turned out to be useful in theoretical layouts and practical applications prior to calculating the spectral radius itself. The most senior (1994) and popular indicator, <i>R</i><sub>0</sub>(<b><i>L</i></b>), is known as the net reproductive rate, and we consider two others, <i>R</i><sub>1</sub>(<b><i>L</i></b>) and <i>R</i><sub>RT</sub>(<b><i>A</i></b>), developed later on. All the three are different in terms of their simplicity and the level of generality, and we illustrate them with a case study of <i>Calamagrostis epigeios</i>, a long-rhizome perennial weed actively colonizing open spaces in the temperate zone. While the <i>R</i><sub>0</sub>(<b><i>L</i></b>) and <i>R</i><sub>1</sub>(<b><i>L</i></b>) fail, respectively, because of complexity and insufficient generality, the <i>R</i><sub>RT</sub>(<b><i>L</i></b>) does succeed, justifying the merit of indication. |
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| spelling | doaj.art-67b58b22435644498a335e1f2507240a2023-11-22T04:20:04ZengMDPI AGMathematics2227-73902021-07-01914164910.3390/math9141649Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of IndicationDmitrii O. Logofet0Valerii N. Razzhevaikin1Laboratory of Mathematical Ecology, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, RussiaFederal Research Center “Computer Science and Control” of Russian Academy of Sciences, 119333 Moscow, RussiaThe notion of a <i>potential-growth indicator</i> came to being in the field of matrix population models long ago, almost simultaneously with the pioneering Leslie model for age-structured population dynamics, although the term has been given and the theory developed only in recent years. The indicator represents an explicit function, <i>R</i>(<b><i>L</i></b>), of matrix <b><i>L</i></b> elements and indicates the position of the spectral radius of <b><i>L</i></b> relative to 1 on the real axis, thus signifying the population growth, or decline, or stabilization. Some indicators turned out to be useful in theoretical layouts and practical applications prior to calculating the spectral radius itself. The most senior (1994) and popular indicator, <i>R</i><sub>0</sub>(<b><i>L</i></b>), is known as the net reproductive rate, and we consider two others, <i>R</i><sub>1</sub>(<b><i>L</i></b>) and <i>R</i><sub>RT</sub>(<b><i>A</i></b>), developed later on. All the three are different in terms of their simplicity and the level of generality, and we illustrate them with a case study of <i>Calamagrostis epigeios</i>, a long-rhizome perennial weed actively colonizing open spaces in the temperate zone. While the <i>R</i><sub>0</sub>(<b><i>L</i></b>) and <i>R</i><sub>1</sub>(<b><i>L</i></b>) fail, respectively, because of complexity and insufficient generality, the <i>R</i><sub>RT</sub>(<b><i>L</i></b>) does succeed, justifying the merit of indication.https://www.mdpi.com/2227-7390/9/14/1649discrete-structured populationmatrix population modelpopulation projection matricescalibrationnet reproductive ratereproductive uncertainty |
| spellingShingle | Dmitrii O. Logofet Valerii N. Razzhevaikin Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication Mathematics discrete-structured population matrix population model population projection matrices calibration net reproductive rate reproductive uncertainty |
| title | Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication |
| title_full | Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication |
| title_fullStr | Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication |
| title_full_unstemmed | Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication |
| title_short | Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication |
| title_sort | potential growth indicators revisited higher generality and wider merit of indication |
| topic | discrete-structured population matrix population model population projection matrices calibration net reproductive rate reproductive uncertainty |
| url | https://www.mdpi.com/2227-7390/9/14/1649 |
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