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

This article is cited in 2 scientific papers (total in 2 papers)

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
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    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  crossref  mathscinet  zmath  isi  elib
    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  mathscinet  isi
  • Фундаментальная и прикладная математика
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