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On principal spectrum points/principal eigenvalues of nonlocal dispersal operators and applications
Clines with directional selection and partial panmixia in an unbounded unidimensional habitat
1. | Department of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria |
2. | Department of Ecology and Evolution, University of Chicago, 1101 East 57th Street, Chicago, IL 60637 |
References:
[1] |
B. Charlesworth and D. Charlesworth, Elements of Evolutionary Genetics, Roberts, Greenwood Village, 2010. |
[2] |
J. A. Endler, Geographic Variation, Speciation, and Clines, Princeton University Press, Princeton, 1977. |
[3] |
P. C. Fife and L. A. Peletier, Nonlinear diffusion in population genetics, Arch. Rat. Mech. Anal., 64 (1977), 93-109.
doi: 10.1007/BF00280092. |
[4] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations Of Second Order, Springer, Berlin, 2001. |
[5] |
Y. Lou and T. Nagylaki, A semilinear parabolic system for migration and selection in population genetics, J. Diff. Eqs., 181 (2002), 388-418.
doi: 10.1006/jdeq.2001.4086. |
[6] |
Y. Lou, T. Nagylaki and W.-M. Ni, An introduction to migration-selection PDE models, Disc. Cont. Dyn. Syst. A, 33 (2013), 4349-4373.
doi: 10.3934/dcds.2013.33.4349. |
[7] |
Y. Lou, W.-M. Ni and L. Su, An indefinite nonlinear diffusion problem in population genetics, II: Stability and multiplicity, Disc. Cont. Dyn. Syst. A, 27 (2010), 643-655.
doi: 10.3934/dcds.2010.27.643. |
[8] |
Y. Lou, T. Nagylaki and L. Su, An integro-PDE model from population genetics, J. Diff. Eqs., 254 (2013), 2367-2392.
doi: 10.1016/j.jde.2012.12.006. |
[9] |
T. Nagylaki, Conditions for the existence of clines, Genetics, 80 (1975), 595-615. |
[10] |
T. Nagylaki, Clines with variable migration, Genetics, 83 (1976), 867-886. |
[11] |
T. Nagylaki, Clines with asymmetric migration, Genetics, 88 (1978), 813-827. |
[12] |
T. Nagylaki, The strong-migration limit in geographically structured populations, J. Math. Biol., 9 (1980), 101-114.
doi: 10.1007/BF00275916. |
[13] |
T. Nagylaki, Introduction to Theoretical Population Genetics, Biomathematics, 21, Springer, Berlin, 1992.
doi: 10.1007/978-3-642-76214-7. |
[14] |
T. Nagylaki, Polymorphism in multiallelic migration-selection models with dominance, Theor. Popul. Biol., 75 (2009), 239-259.
doi: 10.1016/j.tpb.2009.01.004. |
[15] |
T. Nagylaki, The influence of partial panmixia on neutral models of spatial variation, Theor. Popul. Biol., 79 (2011), 19-38.
doi: 10.1016/j.tpb.2010.08.006. |
[16] |
T. Nagylaki, Clines with partial panmixia, Theor. Popul. Biol., 81 (2012), 45-68.
doi: 10.1016/j.tpb.2011.09.006. |
[17] |
T. Nagylaki, Clines with partial panmixia in an unbounded unidimensional habitat, Theor. Popul. Biol., 82 (2012), 22-28.
doi: 10.1016/j.tpb.2012.02.008. |
[18] |
T. Nagylaki and Y. Lou, The dynamics of migration-selection models, in Tutorials in Mathematical Biosciences IV (ed. A. Friedman), Lecture Notes in Math., 1922, Springer, Berlin, (2008), 117-170.
doi: 10.1007/978-3-540-74331-6_4. |
[19] |
K. Nakashima, W.-M. Ni and L. Su, An indefinite nonlinear diffusion problem in population genetics, I: Existence and limiting profiles, Disc. Cont. Dyn. Syst. A, 27 (2010), 617-641.
doi: 10.3934/dcds.2010.27.617. |
[20] |
D. H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J., 21 (1972), 979-1000. |
show all references
References:
[1] |
B. Charlesworth and D. Charlesworth, Elements of Evolutionary Genetics, Roberts, Greenwood Village, 2010. |
[2] |
J. A. Endler, Geographic Variation, Speciation, and Clines, Princeton University Press, Princeton, 1977. |
[3] |
P. C. Fife and L. A. Peletier, Nonlinear diffusion in population genetics, Arch. Rat. Mech. Anal., 64 (1977), 93-109.
doi: 10.1007/BF00280092. |
[4] |
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations Of Second Order, Springer, Berlin, 2001. |
[5] |
Y. Lou and T. Nagylaki, A semilinear parabolic system for migration and selection in population genetics, J. Diff. Eqs., 181 (2002), 388-418.
doi: 10.1006/jdeq.2001.4086. |
[6] |
Y. Lou, T. Nagylaki and W.-M. Ni, An introduction to migration-selection PDE models, Disc. Cont. Dyn. Syst. A, 33 (2013), 4349-4373.
doi: 10.3934/dcds.2013.33.4349. |
[7] |
Y. Lou, W.-M. Ni and L. Su, An indefinite nonlinear diffusion problem in population genetics, II: Stability and multiplicity, Disc. Cont. Dyn. Syst. A, 27 (2010), 643-655.
doi: 10.3934/dcds.2010.27.643. |
[8] |
Y. Lou, T. Nagylaki and L. Su, An integro-PDE model from population genetics, J. Diff. Eqs., 254 (2013), 2367-2392.
doi: 10.1016/j.jde.2012.12.006. |
[9] |
T. Nagylaki, Conditions for the existence of clines, Genetics, 80 (1975), 595-615. |
[10] |
T. Nagylaki, Clines with variable migration, Genetics, 83 (1976), 867-886. |
[11] |
T. Nagylaki, Clines with asymmetric migration, Genetics, 88 (1978), 813-827. |
[12] |
T. Nagylaki, The strong-migration limit in geographically structured populations, J. Math. Biol., 9 (1980), 101-114.
doi: 10.1007/BF00275916. |
[13] |
T. Nagylaki, Introduction to Theoretical Population Genetics, Biomathematics, 21, Springer, Berlin, 1992.
doi: 10.1007/978-3-642-76214-7. |
[14] |
T. Nagylaki, Polymorphism in multiallelic migration-selection models with dominance, Theor. Popul. Biol., 75 (2009), 239-259.
doi: 10.1016/j.tpb.2009.01.004. |
[15] |
T. Nagylaki, The influence of partial panmixia on neutral models of spatial variation, Theor. Popul. Biol., 79 (2011), 19-38.
doi: 10.1016/j.tpb.2010.08.006. |
[16] |
T. Nagylaki, Clines with partial panmixia, Theor. Popul. Biol., 81 (2012), 45-68.
doi: 10.1016/j.tpb.2011.09.006. |
[17] |
T. Nagylaki, Clines with partial panmixia in an unbounded unidimensional habitat, Theor. Popul. Biol., 82 (2012), 22-28.
doi: 10.1016/j.tpb.2012.02.008. |
[18] |
T. Nagylaki and Y. Lou, The dynamics of migration-selection models, in Tutorials in Mathematical Biosciences IV (ed. A. Friedman), Lecture Notes in Math., 1922, Springer, Berlin, (2008), 117-170.
doi: 10.1007/978-3-540-74331-6_4. |
[19] |
K. Nakashima, W.-M. Ni and L. Su, An indefinite nonlinear diffusion problem in population genetics, I: Existence and limiting profiles, Disc. Cont. Dyn. Syst. A, 27 (2010), 617-641.
doi: 10.3934/dcds.2010.27.617. |
[20] |
D. H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J., 21 (1972), 979-1000. |
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