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
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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Journal of Mathematical Sciences (New York), 2013, 193:5, 671–686
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
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\paper Projection matrices revisited: a~potential-growth indicator and the merit of indication
\jour Fundam. Prikl. Mat.
\jour J. Math. Sci.
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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
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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