Abstract
How to go beyond Fisher's 1930 linear eigenvector definition of reproductive value has been established for dilute systems whose dynamic relations are first-degree-homogeneous functions so that intensive ratios are scale-free. Here such an extension is applied to standard mendelian models. It is shown that, aside from singular cases like that of the Hardy-Weinberg razor's-edge labile equilibrium, such general systems are irreducibly nonlinear and admit of reproductive value functions that are calculable only in an infinite number of steps.
Full text
PDF
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Keyfitz N. On the momentum of population growth. Demography. 1971 Feb;8(1):71–80. [PubMed] [Google Scholar]
- Samuelson P. A. Generalizing Fisher's "reproductive value": Nonlinear, homogeneous, biparental systems. Proc Natl Acad Sci U S A. 1977 Dec;74(12):5772–5775. doi: 10.1073/pnas.74.12.5772. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Samuelson P. A. Generalizing Fisher's "reproductive value": linear differential and difference equations of "dilute" biological systems. Proc Natl Acad Sci U S A. 1977 Nov;74(11):5189–5192. doi: 10.1073/pnas.74.11.5189. [DOI] [PMC free article] [PubMed] [Google Scholar]
- Samuelson P. A. Time symmetry and asymmetry in population and deterministic dynamic systems. Theor Popul Biol. 1976 Feb;9(1):82–122. doi: 10.1016/0040-5809(76)90037-x. [DOI] [PubMed] [Google Scholar]
- Yellin J., Samuelson P. A. Comparison of linear and nonlinear models for human population dynamics. Theor Popul Biol. 1977 Feb;11(1):105–126. doi: 10.1016/0040-5809(77)90010-7. [DOI] [PubMed] [Google Scholar]