On the definition of the reproductive value: Response to the discussion by Bacaër and Abdurahman

Journal of Mathematical Biology

Volumn 59, Issue 5, 2009, Pages 651-657

  Ediev, Dalkhat M ^a  

^a VIENNA INSTITUTE OF DEMOGRAPHY   (Austria)

Author keywords

Demographic potential; Ergodicity; Reproductive value; Stable population

Indexed keywords

AGE; ALGORITHM; ARTICLE; BIOLOGICAL MODEL; BIRTH RATE; DEMOGRAPHY; FERTILITY; MORTALITY; POPULATION DYNAMICS; POPULATION GROWTH;

AGE FACTORS; ALGORITHMS; BIRTH RATE; DEMOGRAPHY; FERTILITY; MODELS, BIOLOGICAL; MORTALITY; POPULATION DYNAMICS; POPULATION GROWTH;

EID: 70349925718     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-008-0246-3     Document Type: Article

References (20)

1. Bacaër N, Abdurahman X (2008) Resonance of the epidemic threshold in a periodic Environment. J Math Biol. doi:10.1007/s00285-008-0183-1.
2. Fisher RA (1927) The actuarial treatment of official birth records. Eugen Rev 19: 103-108.
3. Fisher RA (1930) The genetical theory of natural selection. Dover Publications, New York.
4. Crow J (2002) Perspective: here's to Fisher, additive genetic variance, and the fundamental theorem of natural selection. Evol Int J Org Evol 56(7): 1313-1316.
5. Galindo C (2007) On Fisher's Reproductive Value and Lotka's Stable Population. Presented at annual meeting of the Population Association of America, New York. Available at: http://paa2007.princeton.edu/download.aspx?submissionId=72160.
6. Galindo C (2008) On Fisher's reproductive value and Lotka's stable population. Presented at European population conference, Barcelona.
7. Ediev DM (1996) Demographic potential. In: Non-local boundary problems and related problems of mathematical biology, informatics, and physics. Kabardino-Balkarsky Scientific Center of Rus. Acad. Sc., Nalchik, pp 109-110 (in Russian).
8. Ediev DM (1997, 1999) Demographic and economic-demographic potentials. Ph.D. thesis, Moscow Institute of Physics and Technology, Moscow (in Russian).
9. Ediev DM (2003) The concept of demographic potential and its applications. Matematicheskoje Modelirovanije 15(12): 37-74. Mathematical Modeling.
10. Ediev DM (2007a) On an extension of R.A. Fisher's result on the dynamics of the reproductive value. Theor Popul Biol 72(4): 480-484. doi:10.1016/j.tpb.2007.03.001.
11. Ediev DM (2007b) Demographic potentials: theory and applications. Max-PRESS, Moscow, 348 pp (in Russian).
12. Ediev DM (2008) Theory and applications of demographic potentials. Doktor Nauk Dissertation. Computational Center of Russian academy of Sciences, Moscow, 356 pp (in Russian).
13. Kim YI, Sykes Z (1978) An experimental study of weak ergodicity in human populations. Theor Popul Biol 10: 150-172. doi:10.1016/0040-5809(76)90013-7.
14. Samuelson PA (1977a) Generalizing Fisher's 'reproductive value': linear differential and difference equations of 'dilute' biological systems. Proc Natl Acad Sci USA 74(11): 5189-5192. doi:10.1073/pnas.74.11.5189.
15. Samuelson PA (1977b) Generalizing Fisher's "reproductive value": Nonlinear, homogeneous, biparental systems. Proc Natl Acad Sci USA 74(12): 5772-5775. doi:10.1073/pnas.74.12.5772.
16. Samuelson PA (1978) Generalizing Fisher's "reproductive value": "Incipient" and "penultimate" reproductive-value functions when environment limits growth; linear approximations for nonlinear Mendelian mating models. Proc Natl Acad Sci USA 75(12): 6327-6331. doi:10.1073/pnas.75.12.6327.
17. Kim YI (1987) Dynamics of populations with changing vital rates: generalizations of the stable population theory. Theor Popul Biol 31: 306-322. doi:10.1016/0040-5809(87)90031-1.
18. Tuljapurkar S, Caswell H (1997) Structured-population models in marine, terrestrial and freshwater systems. Springer/Chapman and Hall, New York, 656 pp.
19. Tuljapurkar S, Lee R (1997) Demographic uncertainty and the stable equivalent population. Math Comput Model 26(6): 39-56. doi:10.1016/S0895-7177(97)00168-4.
20. Vandermeer H (1968) Reproductive value in a population of arbitrary age distribution. Am Nat 102(928): 586-589. doi:10.1086/282571.