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On the solvability conditions for the diffusion equation with convection terms
Spatiotemporal dynamics of cooperation and spite behavior by conformist transmission
1. | Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 1-1-1 Higashi Mita, Tama-ku, Kawasaki, Kanagawa 214-8571, Japan |
References:
[1] |
J. Y. Wakano, K. Aoki and M. W. Feldman, Evolution of social learning: a mathematical analysis, Theoretical Population Biology, 66 (2004), 249-258.
doi: 10.1016/j.tpb.2004.06.005. |
[2] |
J. Y. Wakano and K. Aoki, Do social learning and conformist bias coevolve? Henrich and Boyd revisited, Theoretical Population Biology, 72 (2007), 504-512.
doi: 10.1016/j.tpb.2007.04.003. |
[3] |
J. Y. Wakano and K. Aoki, A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment, Theoretical Population Biology, 70 (2006), 486-497.
doi: 10.1016/j.tpb.2006.04.003. |
[4] |
K. Aoki, J. Y. Wakano and M. W. Feldman, The emergence of social learning in a temporally changing environment: A theoretical model, Current Anthropology, 46 (2005), 334-340.
doi: 10.1086/428791. |
[5] |
W. Nakahashi, The evolution of conformist transmission in social learning when the environment changes periodically, Theoretical Population Biology, 72 (2007), 52-66.
doi: 10.1016/j.tpb.2007.03.003. |
[6] |
J. Y. Wakano, A mathematical analysis on public goods games in the continuous space, Mathematical Biosciences, 201 (2006), 72-89.
doi: 10.1016/j.mbs.2005.12.015. |
[7] |
J. Y. Wakano, Evolution of cooperation in spatial public goods games with common resource dynamics, Journal of Theoretical Biology, 247 (2007), 616-622.
doi: 10.1016/j.jtbi.2007.04.008. |
[8] |
Y. Iwasa, T. Uchida and H. Yokomizo, Nonlinear behavior of the socio-economic dynamics for lake eutrophication control, Ecological Economics, 63 (2007), 219-229.
doi: 10.1016/j.ecolecon.2006.11.003. |
[9] |
J. Henrich and R. Boyd, The evolution of conformist transmission and the emergence of between-group differences, Evolution and Human Behavior, 19 (1998), 215-241.
doi: 10.1016/S1090-5138(98)00018-X. |
[10] |
T. Kameda and D. Nakanishi, Cost-benefit analysis of social/cultural learning in a nonstationary uncertain environment: an evolutionary simulation and an experiment with human subjects, Evolution and Human Behavior, 23 (2002), 373-393.
doi: 10.1016/S1090-5138(02)00101-0. |
[11] |
R. McElreath, M. Lubell, P. J. Richerson, T. M. Waring, W. Baum, E. Edsten, C. Efferson and B. Paciotti, Applying evolutionary models to the laboratory study of social learning, Evolution and Human Behavior, 26 (2005), 483-508.
doi: 10.1016/j.evolhumbehav.2005.04.003. |
[12] |
J. Henrich, Cultural group selection, coevolutionary processes and large-scale cooperation, Journal of Economic Behavior and Organization, 53 (2004), 3-35.
doi: 10.1016/S0167-2681(03)00094-5. |
[13] |
Y. Iwasa, M. Nakamaru and S. A. Levin, Allelopathy of bacteria in a lattice population: Competition between colicin-sensitive and colicin-producing strains, Evolutionary Ecology, 12 (1998), 785-802.
doi: 10.1023/A:1006590431483. |
[14] |
J. Y. Wakano, M. A. Nowak and C. Hauert, Spatial dynamics of ecological public goods, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 7910-7914.
doi: 10.1073/pnas.0812644106. |
[15] |
S. A. Levin, Dispersion and population interactions, American Naturalist, 108 (1974), 207-228.
doi: 10.1086/282900. |
[16] |
K. Kishimoto and H. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion system on convex domains, Journal of Differential Equations, 58 (1985), 15-21.
doi: 10.1016/0022-0396(85)90020-8. |
[17] |
R. Boyd and P. J. Richerson, "Culture and the Evolutionary Process," University of Chicago Press, Chicago, 1985. |
[18] |
P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling wave solutions in "Mathematical Aspects of Reacting and Diffusing Systems" (eds. S.Levin), Springer-Verlag (1979), 335-361. |
show all references
References:
[1] |
J. Y. Wakano, K. Aoki and M. W. Feldman, Evolution of social learning: a mathematical analysis, Theoretical Population Biology, 66 (2004), 249-258.
doi: 10.1016/j.tpb.2004.06.005. |
[2] |
J. Y. Wakano and K. Aoki, Do social learning and conformist bias coevolve? Henrich and Boyd revisited, Theoretical Population Biology, 72 (2007), 504-512.
doi: 10.1016/j.tpb.2007.04.003. |
[3] |
J. Y. Wakano and K. Aoki, A mixed strategy model for the emergence and intensification of social learning in a periodically changing natural environment, Theoretical Population Biology, 70 (2006), 486-497.
doi: 10.1016/j.tpb.2006.04.003. |
[4] |
K. Aoki, J. Y. Wakano and M. W. Feldman, The emergence of social learning in a temporally changing environment: A theoretical model, Current Anthropology, 46 (2005), 334-340.
doi: 10.1086/428791. |
[5] |
W. Nakahashi, The evolution of conformist transmission in social learning when the environment changes periodically, Theoretical Population Biology, 72 (2007), 52-66.
doi: 10.1016/j.tpb.2007.03.003. |
[6] |
J. Y. Wakano, A mathematical analysis on public goods games in the continuous space, Mathematical Biosciences, 201 (2006), 72-89.
doi: 10.1016/j.mbs.2005.12.015. |
[7] |
J. Y. Wakano, Evolution of cooperation in spatial public goods games with common resource dynamics, Journal of Theoretical Biology, 247 (2007), 616-622.
doi: 10.1016/j.jtbi.2007.04.008. |
[8] |
Y. Iwasa, T. Uchida and H. Yokomizo, Nonlinear behavior of the socio-economic dynamics for lake eutrophication control, Ecological Economics, 63 (2007), 219-229.
doi: 10.1016/j.ecolecon.2006.11.003. |
[9] |
J. Henrich and R. Boyd, The evolution of conformist transmission and the emergence of between-group differences, Evolution and Human Behavior, 19 (1998), 215-241.
doi: 10.1016/S1090-5138(98)00018-X. |
[10] |
T. Kameda and D. Nakanishi, Cost-benefit analysis of social/cultural learning in a nonstationary uncertain environment: an evolutionary simulation and an experiment with human subjects, Evolution and Human Behavior, 23 (2002), 373-393.
doi: 10.1016/S1090-5138(02)00101-0. |
[11] |
R. McElreath, M. Lubell, P. J. Richerson, T. M. Waring, W. Baum, E. Edsten, C. Efferson and B. Paciotti, Applying evolutionary models to the laboratory study of social learning, Evolution and Human Behavior, 26 (2005), 483-508.
doi: 10.1016/j.evolhumbehav.2005.04.003. |
[12] |
J. Henrich, Cultural group selection, coevolutionary processes and large-scale cooperation, Journal of Economic Behavior and Organization, 53 (2004), 3-35.
doi: 10.1016/S0167-2681(03)00094-5. |
[13] |
Y. Iwasa, M. Nakamaru and S. A. Levin, Allelopathy of bacteria in a lattice population: Competition between colicin-sensitive and colicin-producing strains, Evolutionary Ecology, 12 (1998), 785-802.
doi: 10.1023/A:1006590431483. |
[14] |
J. Y. Wakano, M. A. Nowak and C. Hauert, Spatial dynamics of ecological public goods, Proceedings of the National Academy of Sciences of the United States of America, 106 (2009), 7910-7914.
doi: 10.1073/pnas.0812644106. |
[15] |
S. A. Levin, Dispersion and population interactions, American Naturalist, 108 (1974), 207-228.
doi: 10.1086/282900. |
[16] |
K. Kishimoto and H. F. Weinberger, The spatial homogeneity of stable equilibria of some reaction-diffusion system on convex domains, Journal of Differential Equations, 58 (1985), 15-21.
doi: 10.1016/0022-0396(85)90020-8. |
[17] |
R. Boyd and P. J. Richerson, "Culture and the Evolutionary Process," University of Chicago Press, Chicago, 1985. |
[18] |
P. C. Fife and J. B. McLeod, The approach of solutions of nonlinear diffusion equations to traveling wave solutions in "Mathematical Aspects of Reacting and Diffusing Systems" (eds. S.Levin), Springer-Verlag (1979), 335-361. |
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