Genetic variability in sensitivity to population density affects the dynamics of simple ecological models

Theoretical Population Biology

Volumn 55, Issue 1, 1999, Pages 37-52

  Doebeli, Michael ^a   De Jong, Gerdien ^b  

^a UNIVERSITY OF BASEL   (Switzerland)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Chaos; Differential selection in males and females; Polymorphism; Population dynamics; Population genetics; Stability

Indexed keywords

GENETIC VARIATION; POPULATION DYNAMICS; POPULATION MODELING;

EID: 0033080463     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1006/tpbi.1998.1385     Document Type: Article

References (37)

1. Asmussen M. A. Regular and chaotic cycling in models of ecological genetics. Theor. Popul. Biol. 16:1979;172-190.
2. Bellows T. S. Jr. The descriptive properties of some models for density dependence. J. Anim. Ecol. 50:1981;139-156.
3. Doebeli M. Dispersal and dynamics. Theor. Popul. Biol. 47:1995a;82-106.
4. Doebeli M. Phenotypic variability, sexual reproduction, and evolutionary population dynamics. J. Evol. Biol. 8:1995b;173-194.
5. Doebeli M. Quantitative genetics and population dynamics. Evolution. 50:1996;532-546.
6. Doebeli M. Genetic variation and the persistence of predator-prey interactions in the Nicholson-Bailey model. J. Theor. Biol. 188:1997;109-120.
7. Doebeli M., Koella J. C. Sex and population dynamics. Proc. Roy. Soc. London Ser. B. 257:1994;17-23.
8. Doebeli M., Koella J. C. Evolution of simple population dynamics. Proc. Roy. Soc. London Ser. B. 260:1995;119-125.
9. Doebeli M., De Jong G. A simple genetic model with non-equilibrium dynamics. J. Math. Biol. 36:1998;550-556.
10. Feldman M. W., Christiansen F. B., Liberman U. On some models of fertility selection. Genetics. 105:1983;1003-1010.
11. Ferrière R., Fox G. A. Chaos and evolution. Trends Ecol. Evol. 10:1996;480-485.
12. Hadeler K. P., Liberman U. Selection models with fertility differences. J. Math. Biol. 2:1975;19-32.
13. Hartl D. L., Clark A. G. Principles of Population Genetics. 1989;Sinauer, Sunderland.
14. Hassell M. P. Density-dependence in single-species models. J. Anim. Ecol. 44:1975;283-296.
15. Hassell M. P., Lawton J. H., May R. M. Patterns of dynamical behaviour in single-species populations. J. Anim. Ecol. 45:1976;471-486.
16. Hastings A. Complex interactions between dispersal and dynamics: Lessons from coupled logistic equations. Ecology. 74:1993;1362-1372.
17. Hastings A., Hom C. L., Ellner S., Turchin P., Godfray H. C. J. Chaos in ecology: Is mother nature a strange attractor. Ann. Rev. Ecol. Syst. 24:1993;1-33.
18. Karlin S., Lessard S. Sex Ratio Evolution. 1986;Princeton Univ. Press, Princeton.
19. Kidwell J. F., Clegg M. T., Stewart F. M., Prout T. Regions of stable equilibria for models of differential selection in the two sexes under random mating. Genetics. 85:1977;171-183.
20. May R. M. Biological populations with non-overlapping generations: stable points, stable cycles and chaos. Science. 186:1974;645-647.
21. May R. M. Simple mathematical models with very complicated dynamics. Nature. 261:1976;459-467.
22. May R. M., Oster G. F. Bifurcations and dynamic complexity in simple ecological models. Am. Nat. 110:1976;573-599.
23. Maynard Smith J., Slatkin M. The stability of predator-prey systems. Ecology. 54:1973;384-391.
24. Mueller L. D., Ayala F. J. Dynamics of single-species population growth: Stability or chaos. Ecology. 62:1981;1148-1154.
25. Philippi T. E., Carpenter M. P., Case T. J., Gilpin M. E. Drosophila. Ecology. 68:1987;154-159.
26. Pollak E. With selection for fecundity the mean fitness does not necessarily increase. Genetics. 90:1978;383-389.
27. Roughgarden J. Theory of Population Genetics and Evolutionary Ecology: An Introduction. 1979;Macmillan, New York.
28. Ruxton G. D. Low levels of immigration between chaotic populations can reduce system extinctions by inducing asynchronous regular cycles. Proc. Roy. Soc. London Ser. B. 256:1994;189-193.
29. Ruxton G. D. Population models with sexual reproduction show a reduced propensity to exhibit chaos. J. Theor. Biol. 175:1995;595-601.
30. Schoener T. Alternatives to Lotka-Volterra competition: Models of intermediate complexity. Theor. Popul. Biol. 10:1976;309-333.
31. Selgrade J. F., Ziehe M. Convergence to equilibrium in a genetic model with differential viability between the sexes. J. Math. Biol. 25:1987;477-490.
32. Smith R. H., Mead R. The dynamics of discrete-time stochastic models of population growth. J. Theor. Biol. 86:1980;607-627.
33. Stone L. Period-doubling reversals and chaos in simple ecological models. Nature. 365:1993;617-620.
34. Szucs J. M. Selection at a diallelic autosomal locus in a dioecious population. J. Math. Biol. 29:1991a;693-713.
35. Szucs J. M. Selection-mutation at a diallelic autosomal locus in a dioecious population. J. Math. Biol. 30:1991b;1-14.
36. Thomas W. R., Pomerantz M. J., Gilpin M. E. Chaos, asymmetric growth and group selection for dynamic stability. Ecology. 61:1980;1312-1320.
37. Turchin P., Taylor A. D. Complex dynamics in ecological time series. Ecology. 73:1992;289-305.