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 Fundam. Prikl. Mat., 2012, Volume 17, Issue 6, Pages 41–63 (Mi fpm1449)

Projection matrices revisited: a potential-growth indicator and the merit of indication

D. O. Logofet

M. V. Lomonosov Moscow State University

Abstract: The mathematics of matrix models for age- or/and stage-structured population dynamics substantiates the use of the dominant eigenvalue $\lambda_1$ of the projection matrix $\boldsymbol L$ as a measure of the growth potential, or of adaptation, for a given species population in modern plant or animal demography. The calibration of $\boldsymbol L=\boldsymbol T+\boldsymbol F$ on the “identified-individuals-of-unknown-parents” kind of empirical data determines precisely the transition matrix $\boldsymbol T$, but admits arbitrariness in the estimation of the fertility matrix $\boldsymbol F$. We propose an adaptation principle that reduces calibration to the maximization of $\lambda_1(\boldsymbol L)$ under the fixed $\boldsymbol T$ and constraints on $\boldsymbol F$ ensuing from the data and expert knowledge. A theorem has been proved on the existence and uniqueness of the maximizing solution for projection matrices of a general pattern. A conjugated maximization problem for a “potential-growth indicator” under the same constraints has appeared to be a linear-programming problem with a ready solution, the solution testing whether the data and knowledge are compatible with the population growth observed.

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English version:
Journal of Mathematical Sciences (New York), 2013, 193:5, 671–686

UDC: 512.643.8+581.524.31

Citation: D. O. Logofet, “Projection matrices revisited: a potential-growth indicator and the merit of indication”, Fundam. Prikl. Mat., 17:6 (2012), 41–63; J. Math. Sci., 193:5 (2013), 671–686

Citation in format AMSBIB
\Bibitem{Log12} \by D.~O.~Logofet \paper Projection matrices revisited: a~potential-growth indicator and the merit of indication \jour Fundam. Prikl. Mat. \yr 2012 \vol 17 \issue 6 \pages 41--63 \mathnet{http://mi.mathnet.ru/fpm1449} \transl \jour J. Math. Sci. \yr 2013 \vol 193 \issue 5 \pages 671--686 \crossref{https://doi.org/10.1007/s10958-013-1494-3} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899436457} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Protasov V.Yu. Logofet D.O., “Rank-One Corrections of Nonnegative Matrices, with an Application to Matrix Population Models”, SIAM J. Matrix Anal. Appl., 35:2 (2014), 749–764
2. Logofet D.O., Ulanova N.G., Belova I.N., “Polyvariant Ontogeny in Woodreeds: Novel Models and New”, Zhurnal Obshchei Biol., 76:6 (2015), 438–460
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