Logofet, D.O.; Razzhevaikin, V.N. Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication. Mathematics2021, 9, 1649.
Logofet, D.O.; Razzhevaikin, V.N. Potential-Growth Indicators Revisited: Higher Generality and Wider Merit of Indication. Mathematics 2021, 9, 1649.
Abstract
The notion of 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, albeit the term has been given and the theory developed only 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 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 more ones, R1(L) and RRT(A), developed later on. All the three are different in what concerns 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.
Keywords
discrete-structured population; matrix population model; population projection matrices; calibration; net reproductive rate; reproductive uncertainty; colony excavation; Diophantine systems
Subject
Computer Science and Mathematics, Discrete Mathematics and Combinatorics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
