2011/2012, VOLUME 17, NUMBER 6, PAGES 41-63

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

D. O. Logofet


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The mathematics of matrix models for age- or/and stage-structured population dynamics substantiates the use of the dominant eigenvalue l1 of the projection matrix 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 L = T + F on the "identified-individuals-of-unknown-parents" kind of empirical data determines precisely the transition matrix T, but admits arbitrariness in the estimation of the fertility matrix F. We propose an adaptation principle that reduces calibration to the maximization of l1(L) under the fixed T and constraints on 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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Last modified: November 21, 2012