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.
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Pearl R., Reed L. J. On the Rate of Growth of the Population of the United States since 1790 and Its Mathematical Representation. Proc Natl Acad Sci U S A. 1920 Jun;6(6):275–288. doi: 10.1073/pnas.6.6.275. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Price G. R., Smith C. A. Fisher's Malthusian parameter and reproductive value. Ann Hum Genet. 1972 Jul;36(1):1–7. doi: 10.1111/j.1469-1809.1972.tb00577.x. [DOI] [PubMed] [Google Scholar]
- Samuelson P. A. A Simple Method of Interpolation. Proc Natl Acad Sci U S A. 1943 Dec;29(11):397–401. doi: 10.1073/pnas.29.11.397. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Samuelson P. A. Efficient Computation of the Latent Vectors of a Matrix. Proc Natl Acad Sci U S A. 1943 Dec;29(11):393–397. doi: 10.1073/pnas.29.11.393. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Yellin J., Samuelson P. A. A dynamical model for human population. Proc Natl Acad Sci U S A. 1974 Jul;71(7):2813–2817. doi: 10.1073/pnas.71.7.2813. [DOI] [PMC free article] [PubMed] [Google Scholar]