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The dynamics of technological change under constraints: Adopters and resources
Evolutionarily stable diffusive dispersal
1. | Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton AB T6G 2G1, Canada, Canada |
2. | Department of Mathematical and Statistical Sciences, Department of Biological Sciences, University of Alberta, Edmonton AB T6G 2G1, Canada |
References:
[1] |
P. A. Abrams and L. Ruokolainen, How does adaptive consumer movement affect population dynamics in consumer-resource metacommunities with homogeneous patches?, J. Theor. Biol., 277 (2011), 99-110.
doi: 10.1016/j.jtbi.2011.02.019. |
[2] |
D. G. Aronson, The role of diffusion in mathematical biology: Skellam revisited, in Mathematics in Biology and Medicine (eds. V. Capasso, E. Grosso, S.L. Paaveri-Fontana) Springer, Berlin, (1985), 2-6.
doi: 10.1007/978-3-642-93287-8_1. |
[3] |
J. E. Brittain and T. J. Eikeland, Invertebrate drift - a review, Hydrobiologia, 166 (1988), 77-93.
doi: 10.1007/BF00017485. |
[4] |
R. S. Cantrell and C. Cosner, Spatial Ecology Via Reaction-Diffusion Equations, Wiley, The Atrium, Southern Gate, 2003.
doi: 10.1002/0470871296. |
[5] |
R. S. Cantrell, C. Cosner and Y. Lou, Approximating the ideal free distribution via reaction-diffusion-advection equations, J. Differential Equations, 245 (2008), 3687-3703.
doi: 10.1016/j.jde.2008.07.024. |
[6] |
J. Dockery, V. Hutson, K. Mischaikow and M. Pernarowski, The evolution of slow dispersal rates: A reaction diffusion model, J. Math. Biol., 37 (1998), 61-83.
doi: 10.1007/s002850050120. |
[7] |
S. D. Fretwell and H. L. Lucas, On territorial behavior and other factors influencing habitat distribution in birds I. Theoretical development, Acta Biotheoretica, 19 (1969), 16-36.
doi: 10.1007/BF01601953. |
[8] |
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge Univ. Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179. |
[9] |
V. Křivan, R. Cressman and C. Schneider, The ideal free distribution: A review and synthesis of the game-theoretic perspective, Theor. Population Biol., 73 (2008), 403-425. |
[10] |
Y. Lou, Some Challenging Mathematical Problems in Evolution of Dispersal and Population Dynamics, in Tutorials in Mathematical Biosciences IV Lecture Notes in Mathematics Vol. 1922, Springer, Berlin Heidelberg (2008), 171-205.
doi: 10.1007/978-3-540-74331-6_5. |
[11] |
D. W. Morris, Adaptation and habitat selection in the eco-evolutionary process, Proc. Roy. Soc. B, 278 (2011), 2401-2411.
doi: 10.1098/rspb.2011.0604. |
[12] |
D. W. Morris and P. Lundberg, Pillars of Evolution, Oxford Univ. Press, Oxford, 2011.
doi: 10.1093/acprof:oso/9780198568797.001.0001. |
[13] |
L. Ni, A Perron type theorem on the principal eigenvalue of nonsymmetric elliptic operators,, to appear in American Mathematical Monthly. Avalable online at URL: , (): 1210.
|
[14] |
A. Okubo and S. Levin, Diffusion and Ecological Problems, Springer, NY, 2001.
doi: 10.1007/978-1-4757-4978-6. |
[15] |
O. Ovaskainen and S. J. Cornell, Biased Movement at a Boundary and Conditional Occupancy Times for Diffusion Processes, J. Appl. Prob., 40 (2003), 557-580.
doi: 10.1239/jap/1059060888. |
[16] |
A. Potapov, Stochastic model of lake system invasion and its optimal control: neurodynamic programming as a solution method, Nat. Res. Mod., 22 (2009), 257-288.
doi: 10.1111/j.1939-7445.2008.00036.x. |
[17] |
R. Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2007. ISBN 3-900051-07-0, http://www.R-project.org. |
[18] |
H. E. Romeijn and R. L. Smith, Simulated annealing for constrained global optimization, J. Global Optimization, 5 (1994), 101-126.
doi: 10.1007/BF01100688. |
[19] |
P. Turchin, Quantitative Analysis of Movement, Sinauer Assoc., Sunderland, MA., 1998. |
show all references
References:
[1] |
P. A. Abrams and L. Ruokolainen, How does adaptive consumer movement affect population dynamics in consumer-resource metacommunities with homogeneous patches?, J. Theor. Biol., 277 (2011), 99-110.
doi: 10.1016/j.jtbi.2011.02.019. |
[2] |
D. G. Aronson, The role of diffusion in mathematical biology: Skellam revisited, in Mathematics in Biology and Medicine (eds. V. Capasso, E. Grosso, S.L. Paaveri-Fontana) Springer, Berlin, (1985), 2-6.
doi: 10.1007/978-3-642-93287-8_1. |
[3] |
J. E. Brittain and T. J. Eikeland, Invertebrate drift - a review, Hydrobiologia, 166 (1988), 77-93.
doi: 10.1007/BF00017485. |
[4] |
R. S. Cantrell and C. Cosner, Spatial Ecology Via Reaction-Diffusion Equations, Wiley, The Atrium, Southern Gate, 2003.
doi: 10.1002/0470871296. |
[5] |
R. S. Cantrell, C. Cosner and Y. Lou, Approximating the ideal free distribution via reaction-diffusion-advection equations, J. Differential Equations, 245 (2008), 3687-3703.
doi: 10.1016/j.jde.2008.07.024. |
[6] |
J. Dockery, V. Hutson, K. Mischaikow and M. Pernarowski, The evolution of slow dispersal rates: A reaction diffusion model, J. Math. Biol., 37 (1998), 61-83.
doi: 10.1007/s002850050120. |
[7] |
S. D. Fretwell and H. L. Lucas, On territorial behavior and other factors influencing habitat distribution in birds I. Theoretical development, Acta Biotheoretica, 19 (1969), 16-36.
doi: 10.1007/BF01601953. |
[8] |
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge Univ. Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179. |
[9] |
V. Křivan, R. Cressman and C. Schneider, The ideal free distribution: A review and synthesis of the game-theoretic perspective, Theor. Population Biol., 73 (2008), 403-425. |
[10] |
Y. Lou, Some Challenging Mathematical Problems in Evolution of Dispersal and Population Dynamics, in Tutorials in Mathematical Biosciences IV Lecture Notes in Mathematics Vol. 1922, Springer, Berlin Heidelberg (2008), 171-205.
doi: 10.1007/978-3-540-74331-6_5. |
[11] |
D. W. Morris, Adaptation and habitat selection in the eco-evolutionary process, Proc. Roy. Soc. B, 278 (2011), 2401-2411.
doi: 10.1098/rspb.2011.0604. |
[12] |
D. W. Morris and P. Lundberg, Pillars of Evolution, Oxford Univ. Press, Oxford, 2011.
doi: 10.1093/acprof:oso/9780198568797.001.0001. |
[13] |
L. Ni, A Perron type theorem on the principal eigenvalue of nonsymmetric elliptic operators,, to appear in American Mathematical Monthly. Avalable online at URL: , (): 1210.
|
[14] |
A. Okubo and S. Levin, Diffusion and Ecological Problems, Springer, NY, 2001.
doi: 10.1007/978-1-4757-4978-6. |
[15] |
O. Ovaskainen and S. J. Cornell, Biased Movement at a Boundary and Conditional Occupancy Times for Diffusion Processes, J. Appl. Prob., 40 (2003), 557-580.
doi: 10.1239/jap/1059060888. |
[16] |
A. Potapov, Stochastic model of lake system invasion and its optimal control: neurodynamic programming as a solution method, Nat. Res. Mod., 22 (2009), 257-288.
doi: 10.1111/j.1939-7445.2008.00036.x. |
[17] |
R. Development Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria, 2007. ISBN 3-900051-07-0, http://www.R-project.org. |
[18] |
H. E. Romeijn and R. L. Smith, Simulated annealing for constrained global optimization, J. Global Optimization, 5 (1994), 101-126.
doi: 10.1007/BF01100688. |
[19] |
P. Turchin, Quantitative Analysis of Movement, Sinauer Assoc., Sunderland, MA., 1998. |
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