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Article

Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication

1
Laboratory of Mathematical Ecology, A.M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences, 119017 Moscow, Russia
2
Federal Research Center “Computer Science and Control” of Russian Academy of Sciences, 119333 Moscow, Russia
*
Author to whom correspondence should be addressed.
Academic Editor: Giancarlo Consolo
Mathematics 2021, 9(14), 1649; https://doi.org/10.3390/math9141649
Received: 31 May 2021 / Revised: 27 June 2021 / Accepted: 29 June 2021 / Published: 13 July 2021
(This article belongs to the Special Issue Advances in the Mathematics of Ecological Modelling)
The notion of a potential-growth indicator 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, R(L), of matrix L elements and indicates the position of the spectral radius of L 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, R0(L), is known as the net reproductive rate, and we consider two others, R1(L) and RRT(A), 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 Calamagrostis epigeios, a long-rhizome perennial weed actively colonizing open spaces in the temperate zone. While the R0(L) and R1(L) fail, respectively, because of complexity and insufficient generality, the RRT(L) does succeed, justifying the merit of indication. View Full-Text
Keywords: discrete-structured population; matrix population model; population projection matrices; calibration; net reproductive rate; reproductive uncertainty; colony excavation; Diophantine systems discrete-structured population; matrix population model; population projection matrices; calibration; net reproductive rate; reproductive uncertainty; colony excavation; Diophantine systems
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MDPI and ACS Style

Logofet, D.O.; Razzhevaikin, V.N. Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication. Mathematics 2021, 9, 1649. https://doi.org/10.3390/math9141649

AMA Style

Logofet DO, Razzhevaikin VN. Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication. Mathematics. 2021; 9(14):1649. https://doi.org/10.3390/math9141649

Chicago/Turabian Style

Logofet, Dmitrii O., and Valerii N. Razzhevaikin. 2021. "Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication" Mathematics 9, no. 14: 1649. https://doi.org/10.3390/math9141649

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