Generalizing Fisher's "reproductive value": linear differential and difference equations of "dilute" biological systems.
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.
D000367:Age Factors; D008433:Mathematics; D008962:Models, Theoretical; D011158:Population Growth; D013997:Time Factors
Proc Natl Acad Sci U S A. 1943 Dec;29(11):397-401
16588633
Proc Natl Acad Sci U S A. 1943 Dec;29(11):393-7
16588632
Proc Natl Acad Sci U S A. 1920 Jun;6(6):275-88
16576496
Proc Natl Acad Sci U S A. 1974 Jul;71(7):2813-7
4527607
Ann Hum Genet. 1972 Jul;36(1):1-7
4656765