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Updated: Aug 13, 2026

Basic Methods for the Study of Reproductive Ecology of Fish in Aquaria
Published on: July 20, 2017
Generalizing Fisher's "reproductive value": linear differential and difference equations of "dilute" biological
Abstract:
R. A. Fisher's 1930 "reproductive value" is defined as the contribution made by a population's initial age elements to its asymptotically dominating exponential growth mode. For the Leslie discrete-time model, it is the characteristic row vector of the Leslie matrix, and for the integral-equation model of Lotka the similar eigenfunction. It generalizes neatly to a 2-sex model of linear differential equations, and to general n-variable linear systems. However, when resource limitations end the "dilute" stage of linearity, reproductive value loses positive definability. The present linear analysis prepares the way for generalizing reproductive value to nonlinear systems involving first-degree-homogeneous relationships.
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