A sex-structured delayed recruitment model

Mathematical Biosciences

Volumn 134, Issue 1, 1996, Pages 85-111

  Cruywagen, Gerhard C ^a  

^a MARINE AND COASTAL MANAGEMENT   (South Africa)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; FEMALE; MALE; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; PATIENT SELECTION; POPULATION MODEL; POPULATION RESEARCH; POPULATION STRUCTURE; SEX DIFFERENCE; STEADY STATE;

DELAYED RECRUITMENT; MODELLING; RECRUITMENT; SEX-STRUCTURED POPULATION;

EID: 0029663493     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/0025-5564(95)00122-0     Document Type: Article

References (23)

1. C. W. Clark, A delayed-recruitment model of population dynamics with an application to baleen whale populations, J. Math. Biol. 3:381-391 (1976).
2. S. A. Levin and R. M. May, A Note on difference delay equations, Theor. Popul. Biol. 9:245-274 (1976).
3. K. R. Allen, Analysis of stock-recruitment relations in Antarctic fin whales, Cons. Int. l'Explor. Mer-Rapp. Proc.-Verb. 164:132-137 (1963).
4. J. R. Beddington, On the dynamics of Sei whales under exploitation, Rep. Int. Whaling Commission Sc/29/Doc 7, pp. 169-172 (1978).
5. D. S. Butterworth and A. E. Punt, Hitter-fitter assessments of the East Greenland-Iceland fin whale stock, IWC Doc. SC/F91/F7, 1991, p. 71.
6. H. Caswell and D. E. Weeks, Two-sex models: chaos, extinction and other dynamic consequences of sex, Am. Nat. 128:707-735 (1986).
7. B. S. Goh and T. T. Agnew, Stability in a harvested population with delayed recruitment, Math Biosci. 42:187-197 (1977).
8. L. W. Botsford, Further analysis of Clark's delayed recruitment model, Bull. Math. Biol. 54:275-293 (1992).
9. M. O. Bergh, Population and harvesting theory for nonlinear sex and age-structured resources, Nat. Res. Mod. 5:91-134 (1991).
10. G. C. Cruywagen, P. Tracqui, D. E. Woodward, G. T. Bartoo, J. D. Murray, and E. C. Alvord, The modeling of diffusive tumours, Journal of Biological Systems (1996) (in press).
11. T. M. Apostel, Mathematical Analysis, 2nd ed., Addison-Wesley, Reading, MA, 1974.
12. W. M. Getz and R. G. Haight, Population Harvesting, Princeton Univ. Press, Princeton, NJ, 1989.
13. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes in Pascal, Cambridge Univ. Press, New York, 1992.
14. M. O. Bergh and W. M. Getz, Stability of discrete age-structured and aggregated delay-difference population models, J. Math. Biol. 26:551-581 (1988).
15. E. R. Lewis, Network Models in Population Biology, Springer, New York, 1977.
16. R. Schoen, The harmonic mean as the basis of a realistic two-sex marriage model, Demography 18:201-216 (1981).
17. R. Schoen, Relationships in a simple harmonic mean two-sex fertility model, J. Math Biol. 18:201-216 (1984).
18. S. Karlin and S. Lessard, Sex Ratio Evolution, Princeton Univ. Press, Princeton, NJ, 1965.
19. J. J. Bull and E. L. Charnov, Enigmatic reptilian sex ratios, Evolution 43:1561-1566 (1989).
20. R. B. Deriso, Harvesting strategies and parameter estimation for an age-structured model, Can. J. Fish Aquat. Sci. 37:268-282 (1980).
21. R. J. H. Beverton and S. J. Holt, On the Dynamics of Exploited Fish Populations; Fisheries Investment Ser. 2, Vol. 19, UK Ministry of Fisheries and Agriculture, London, 1957.
22. W. E. Ricker, Stock and recruitment, J. Fish. Res. Bd. Can. 11:559-623 (1954).
23. G. C. Cruywagen, P. Kareiva, M. A. Lewis, and J. D. Murray, Modeling the risk of spread of a genetically engineered population in a spatially heterogeneous environment, Theor. Popul. Biol. (1996) (in press).