Qualitative theory of the spread of a new gene into a resident population

Ecological Modelling

Volumn 163, Issue 1-2, 2003, Pages 33-44

  Soboleva, T K ^a   Shorten, P R ^a   Pleasants, A B ^a   Rae, A L ^b  

^a RUAKURA RESEARCH CENTRE   (New Zealand)

^b MASSEY UNIVERSITY   (New Zealand)

Author keywords

Allee effect; Fisher; GMO; Invasion; Thresholds

Indexed keywords

ECOLOGICAL IMPACT; GENE FLOW; GENETICALLY MODIFIED ORGANISM; RISK ASSESSMENT;

MARTES PENNANTI;

EID: 0037406002     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3800(02)00357-5     Document Type: Article

References (45)

1. Allee, W.C., 1938. The Social Life of Animals. W.W. Norton and Co., New York.
2. Allen, J.C., Brewster, C., Slone, D., 2001. Spatially explicit ecological models: a spatial convolution approach. Chaos Solitons Fractals 12, 333-347.
3. Ammerman, A.J., Cavalli-Sforza, L.L., 1984. The Neolithic Transition and the Genetics of Populations in Europe. Princeton University Press, Princeton.
4. Aoki, K., 1987. Gene-culture waves of advance. J. Math. Biol. 25, 453-464.
5. Aronson, D.G., Weinberger, H.F., 1975. Non-linear diffusion in population genetics, combustion, and nerve propagation. In: Goldstein, J.A. (Ed.), Partial Differential Equations and Related Topics, vol. 446. Lecture Notes Mathematics, Springer-Verlag, New York, pp. 5-49.
6. Aronson, D.G., Weinberger, H.F., 1978. Multi-dimensional non-linear diffusion arising in population genetics. Adv. Math. 30, 33-76.
7. Brauer, F., Soudack, A.C., 1979. Response of predator prey nutrient enrichment and proportional harvesting. Int. J. Control 27, 65-75.
8. Courchamp, F., 1999. Inverse density-dependence and the Allee effect. Trends Ecol. Evol. 14, 405-410.
9. Crow, J.F., Kimura, M., 1970. An Introduction to Population Kinetics Theory. Harper & Row, New York.
10. Davis, S.A., Fulford, G.R., 1999. Modeling the integration of a transgene by stocking. Theor. Popul. Biol. 55, 53-60.
11. Davis, S.A., Catchpole, E.A., Fulford, G.R., 2000. Periodic triggering of an inducible gene for control of a wild population. Theor. Popul. Biol. 58, 95-106.
12. Davis, S., Bax, N., Grewe, P., 2001. Engineered underdominance allows efficient and economical introgression of traits into pest populations. J. Theor. Biol. 212, 83-98.
13. Dennis, B., 1989. Allee effects: population growth, critical density and the chance of extinction. Nat. Res. Model. 3, 481-538.
14. Dennis, B., 2002. Allee effects in stochastic populations. Oikos 96, 389-401.
15. Etienne, R., Wertheim, B., Hemerik, L., Schneider, P., Powell, J., 2002. The interaction between dispersal, the Allee effect and scramble competition affects population dynamics. Ecol. Model. 148, 153-168.
16. Fagan, W.F., Lewis, M.A., Neubert, M.G., van den Driessche, P., 2002. Invasion theory and biological control. Ecol. Lett. 5, 148-157.
17. Fife, P.C., 1970. Mathematical Aspects of Reacting and Diffusing Systems. Springer, Berlin.
18. Fisher, R.A., 1937. The wave of advance of advantageous genes. Ann. Eugenics 7, 355-369.
19. Fort, J., Méndez, V., 1999. Time-delayed theory of the neolithic transition in Europe. Phys. Rev. Lett. 82, 867-870.
20. Gandhi, A., Levin, S., Orszag, S., 1999. Nucleation and relaxation from metastability in spatial ecological models. J. Theor. Biol. 200, 121-146.
21. Glansdorff, P., Prigogine, I., 1971. Thermodynamics Theory of Structure, Stability and Fluctuations. Wiley, New York.
22. Hadeler, K.P., Roth, F., 1975. Traveling fronts in non-linear diffusion equations. J. Math. Biol. 2, 251-263.
23. Haken, H., 1978. Synergetics. An Introduction. Springer, Berlin.
24. Hoppensteadt, F., 1975. Mathematical Theories of Populations: Demographics, Genetics and Epidemics. SIAM, Philadelphia.
25. Kareiva, P., Parker, I.M., Pascual, M., 1996. Can we use experiments and models in predicting the invasiveness of genetically engineered organisms? Ecology 77, 1670-1675.
26. Kolmogorov, A., Petrovskii, I., Piskunov, N., 1937. Étude de l'équation de la diffusion avec croissance de la quantité de maitière et son application á un probléme biologique. Bull. Univ. Moskou. Sot. Internat. Ser. A 1, 1-25.
27. Kuzovlev, Y.E., Soboleva, T.K., Philippov, A.E., 1993a. Formation of "filamentary" structures during nucleation. JETP Lett. 58, 357-362.
28. Kuzovlev, Y.E., Soboleva, T.K., Philippov, A.E., 1993b. Structure and evolution of the nucleus of a new phase in first-order phase transitions. Sov. Phys. JETP 76, 858-867.
29. Landau, L.D., Lifshitz, E.M., 1976. Statistical Physics. Nauka, Moskow.
30. Lande, R., 1998. Demographic stochasticity and Allee effect on a scale with isotropic noise. Oikos 83, 353-358.
31. Landis, W.G., Lenart, L.A., Spromberg, J.A., 2000. Dynamics of horizontal gene transfer and the ecological risk assessment of genetically engineered organisms. Hum. Ecol. Risk Assess. 6, 875-899.
32. Legovic, T., 1987. A recent increase in jellyfish populations: a predator prey model and its implications. Ecol. Model. 38, 243-254.
33. Lewis, M.A., Kareiva, P., 1993. Allee dynamics and the spread of invading organisms. Theor. Popul. Biol. 43, 141-158.
34. Lifshitz, E.M., Pitaevskii, L.P., 1979. Physical Kinetics. Nauka, Moskow.
35. Loskutov, A.Y., Mikhailov, A.S., 1990. Introduction to Cybernetics. Nauka, Moskow.
36. Petrovskii, S., Shigesada, N., 2001. Some exact solutions of a generalized Fisher equation related to the problem of biological invasion. Math. Biosci. 172, 73-94.
37. Piálek, J., Barton, N.H., 1997. The spread of an advantageous allele across a barrier: the effects of random drift and selection against heterozygotes. Genetics 145, 493-504.
38. Sharov, A.A., Liebhold, A.M., 1998. Model of slowing the spread of gypsy moth (Lepidoptera: Lymantriidae) with a barrier zone. Ecol. Appl. 8, 1170-1179.
39. Shea, K., Possingham, H., 2000. Optimal release strategies for biological control agents: an application of stochastic dynamic programming to population management. J. Appl. Ecol. 37, 77-86.
40. Sherratt, J., Marchant, B., 1996. Algebraic decay and variable speeds in wavefront solutions of a scalar reaction-diffusion equation. IMA J. Appl. Math. 56, 289-302.
41. Skellam, J.G., 1973. The formulation and interpretation of mathematical models of diffusionary processes in population biology. In: Bartlett, M., Hioms, R. (Eds.), The Mathematical Theory of the Dynamics of Biological Populations. Academic Press, New York, pp. 63-85.
42. Stephens, P., Sutherland, W., 1999. Consequences of the Allee effect for behavior, ecology and conservation. Trends Ecol. Evol. 14, 401-405.
43. Sznajd-Weron, K., Pekalski, A., 1998a. Changes in a continuous character caused by gene flow. A Monte Carlo study. Physica A 259, 457-465.
44. Sznajd-Weron, K., Pekalski, A., 1998b. Evolution under stabilizing selection through gene flow. Physica A 252, 336-344.
45. Wang, M.H., Kot, M., 2001. Speeds of invasion in a model with strong or weak Allee effects. Math. Biosci. 171, 83-97.