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Proc Natl Acad Sci U S A. 1977 Dec;74(12):5772-5.

Generalizing Fisher's "reproductive value": Nonlinear, homogeneous, biparental systems.

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Department of Economics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139.


Biparental demographic models violate linearity. However, in their early "dilute" stages before limited environment resources bring need for competitive selection, first-degree-homogeneous relations obtain. For them, a reproductive-value function of the initial coordinates is defined to recapitulate their contribution to the asymptotically dominating mode of exponential growth: now the generalized Fisher reproductive value of one sex is altered by relative numbers of the other sex. The new reproductive-value function is also derived for general systems of homogeneous-first-degree differential and difference equations, and is shown to grow from the start at the asymptotic growth rate.

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