Travelling wave solutions for the spread of farmers into a region occupied by hunter-gatherers

Theoretical Population Biology

Volumn 50, Issue 1, 1996, Pages 1-17

  Aoki, Kenichi ^a   Shida, Mitsuo ^a   Shigesada, Nanako ^b  

^a UNIVERSITY OF TOKYO   (Japan)

^b NARA WOMEN'S UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030220123     PISSN: 00405809     EISSN: None     Source Type: Journal    
DOI: 10.1006/tpbi.1996.0020     Document Type: Article

References (21)

1. AMMERMAN, A. J., AND CAVALLI-SFORZA, L. L. 1971. Measuring the rate of spread of early farming in Europe, Man 6, 674-688.
2. AMMERMAN, A. J., AND CAVALLI-SFORZA, L. L. 1973. A population model for the diffusion of early farming in Europe, in "The Explanation of Culture Change" (C. Renfrew, Ed.), pp. 343-357, Duckworth, London.
3. AMMERMAN, A. J., AND CAVALLI-SFORZA, L. L. 1984. "The Neolithic Transition and the Genetics of Populations in Europe," Princeton Univ. Press, Princeton, NJ.
4. AOKI, K. 1994. Maximum likelihood fit of a gradual admixture model to clines of gene frequencies in the main islands of Japan, Anthropol. Sci. 102, 285-294.
5. AOKIS K., AND OMOTO, K. 1980. An analysis of the ABO gene frequency cline in Japan: A migration model, J. Anthrop. Soc. Nippon 88, 109-122.
6. ARONSON, D. G., AND WEINBERGER, H. F. 1975. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in "Partial Differential Equations and Related Topics" (J. Goldstein, Ed.), Lecture Notes in Mathematics, Vol. 446, pp. 5-49, Springer, New York/Heidelberg/Berlin.
7. ARONSON, D. G., AND WEINBERGER, H. F. 1978. Multi-dimensional nonlinear diffusion arising in population genetics, Adv. Math. 30, 33-76.
8. BRAIDWOOD, R. J., AND REED, C. A. 1957. The achievement and early consequences of food production: A consideration of the archaeological and natural-historical evidence, Cold Spring Harbor Symp. Quant. Biol. 22, 19-31.
9. BRITTON, N. F. 1986. "Reaction-Diffusion Equations and Their Applications to Biology," Academic Press, London.
10. DUNBAR, S. R. 1983. Travelling wave solutions of diffusive Lotka-Volterra equations, J. Math. Biol. 17, 1-32.
11. FIFE, P. C. 1979. "Mathematical Aspects of Reacting and Diffusing Systems," Lecture Notes in Biomathematics, Vol. 28, Springer, Berlin/Heidelberg/New York.
12. FISHER, R. A. 1937. The wave of advance of advantageous genes, Ann. Eugen. 7, 355-369.
13. HASSAN, F. A. 1981. "Demographic Archaeology," Academic Press, New York.
14. KOLMOGOROFF, A., PETROVSKY, I., AND PISCOUNOFF, N. 1937. Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application a un problème biologique, Bull. Univ. d'État à Moscou Ser. Internat. Sect. A 1, 1-25.
15. MURRAY, J. D. 1989. "Mathematical Biology," Springer-Verlag, Berlin.
16. OKUBO, A., MAINI, P. K., WILLIAMSON, M. H., AND MURRAY, J. D. 1989. On the spatial spread of the grey squirrel in Britain, Proc. Roy. Soc. Lond. B 238, 113-125.
17. RENDINE, S., PIAZZA, A., AND CAVALLI-SFORZA, L. L. 1986. Simulation and separation by principal components of multiple demic expansions in Europe, Am. Nat. 128, 681-706.
18. SGARAMELLA-ZONTA, L., AND CAVALLI-SFORZA, L. L. 1973. A method for the detection of a demic cline, in "Genetic Structure of Population" (N. E. Morton, Ed.), Population Genetics Monograph, Vol. 3, pp. 128-135, Univ. Press of Hawaii, Honolulu.
19. SHIGESADA, N. 1992. "Mathematical Modelling for Biological Invasions," Univ. of Tokyo Press, Tokyo. [In Japanese]
20. SMITH, G. D. 1978. "Numerical Solution of Partial Differential Equations," 2nd ed., Clarendon Press, Oxford.
21. YACHI, S., KAWASAKI, K., SHIGESADA, N., AND TERAMOTO, E. 1989. Spatial patterns of propagating waves of fox rabies, Forma 4, 3-12.