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Mathematical study of the effects of travel costs on optimal dispersal in a two-patch model
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References:
[1] |
P. A. Abrams, Implications of flexible foraging for interspecific interactions: Lessons from simple models,, Functional Ecology, 24 (2010), 7.
doi: 10.1111/j.1365-2435.2009.01621.x. |
[2] |
P. A. Abrams, H. Matsuda and Y. Harada, Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits,, Evolutionary Ecology, 7 (1993), 465.
doi: 10.1007/BF01237642. |
[3] |
I. Averill, Y. Lou and D. Munther, On several conjectures from evolution of dispersal,, Journal of Biological Dynamics, 6 (2012), 117.
doi: 10.1080/17513758.2010.529169. |
[4] |
F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment,, Canadian Applied Math Quarterly, 3 (1995), 379.
|
[5] |
R. S. Cantrell, C. Cosner, D. L. DeAngelis and V. Padron, The ideal free distribution as an evolutionarily stable strategy,, Journal of Biological Dynamics, 1 (2007), 249.
doi: 10.1080/17513750701450227. |
[6] |
R. S. Cantrell, C. Cosner and Y. Lou, Approximating the ideal free distribution via reaction-diffusion-advection equations,, Journal of Differential Equations, 245 (2008), 3687.
doi: 10.1016/j.jde.2008.07.024. |
[7] |
R. S. Cantrell, C. Cosner and Y. Lou, Evolution of dispersal and the ideal free distribution,, Mathematical Biosciences and Engineering, 7 (2010), 17.
doi: 10.3934/mbe.2010.7.17. |
[8] |
R. S. Cantrell, C. Cosner and Y. Lou, Evolutionary stability of ideal free dispersal strategies in patchy environments,, Journal of Mathematical Biology, 65 (2012), 943.
doi: 10.1007/s00285-011-0486-5. |
[9] |
C. Cosner, A dynamic model for the ideal-free distribution as a partial differential equation,, Theoretical Population Biology, 67 (2005), 101.
doi: 10.1016/j.tpb.2004.09.002. |
[10] |
R. Cressman and V. Křivan, The ideal free distribution as an evolutionarily stable state in density-dependent population games,, Oikos, 119 (2010), 1231.
doi: 10.1111/j.1600-0706.2010.17845.x. |
[11] |
D. L. DeAngelis, G. S. K. Wolkowicz, Y. Lou, Y. Jiang, M. Novak, R. Svanback, M. S. Araujo, Y. Jo and E. A. Cleary, The effect of travel loss on evolutionarily stable distributions of populations in space,, American Naturalist, 178 (2011), 15.
doi: 10.1086/660280. |
[12] |
O. Diekmann, A beginner's guide to adaptive dynamics,, Banach center publications, 63 (2004), 47.
|
[13] |
J. E. Diffendorfer, Testing models of source-sink dynamics and balanced dispersal,, Oikos, 81 (1998), 417.
doi: 10.2307/3546763. |
[14] |
J. Dockery, V. Hutson, K. Mischaikow and M. Pernarowski, The evolution of slow dispersal rates: A reaction diffusion model,, Journal of Mathematical Biology, 37 (1998), 61.
doi: 10.1007/s002850050120. |
[15] |
S. M. Flaxman and Y. Lou, Tracking prey or tracking the prey's resource? Mechanisms of movement and optimal habitat selection by predators,, Journal of Theoretical Biology, 256 (2009), 187.
doi: 10.1016/j.jtbi.2008.09.024. |
[16] |
H. I. Freedman, B. Rai and P. Waltman, Mathematical models of population interactions with dispersal. II: Differential survival in a change of habitat,, Journal of Mathematical Analysis and Applications, 115 (1986), 140.
doi: 10.1016/0022-247X(86)90029-6. |
[17] |
H. I. Freedman and P. Waltman, Mathematical models of population interactions with dispersal. I: Stability of two habitats with and without a predator,, SIAM Journal of Applied Mathematics, 32 (1977), 631.
doi: 10.1137/0132052. |
[18] |
S. D. Fretwell and H. L. Lucas, On territorial behavior and other factors influencing habitat distribution in birds,, Acta Biotheoretica, 19 (1969), 37.
doi: 10.1007/BF01601954. |
[19] |
T. E. Galanthay and S. M. Flaxman, Generalized movement strategies for constrained consumers: Ignoring fitness can be adaptive,, American Naturalist, 179 (2012), 475.
doi: 10.1086/664625. |
[20] |
S. A. H. Geritz, É. Kisdi, G. Meszéna and J. A. J. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree,, Evolutionary Ecology, 12 (1998), 35. Google Scholar |
[21] |
B. S. Goh, Global stability in 2 species interactions,, Journal of Mathematical Biology, 3 (1976), 313.
doi: 10.1007/BF00275063. |
[22] |
H. Hakoyama and K. Iguchi, The information of food distribution realizes an ideal free distribution: Support of perceptual limitation,, Journal of Ethology, 15 (1997), 69.
doi: 10.1007/BF02769391. |
[23] |
A. Hastings, Dynamics of a single species in a spatially varying environment: The stabilizing role of high dispersal rates,, Journal of Mathematical Biology, 16 (1982), 49.
doi: 10.1007/BF00275160. |
[24] |
A. Hastings, Can spatial variation alone lead to selection for dispersal?,, Theoretical Population Biology, 24 (1983), 244.
doi: 10.1016/0040-5809(83)90027-8. |
[25] |
R. D. Holt, Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution,, Theoretical Population Biology, 28 (1985), 181.
doi: 10.1016/0040-5809(85)90027-9. |
[26] |
D. M. Hugie and T. C. Grand, Movement between patches, unequal competitors and the ideal free distribution,, Evolutionary Ecology, 12 (1998), 1. Google Scholar |
[27] |
M. Kennedy and R. D. Gray, Can ecological theory predict the distribution of foraging animals? A critical analysis of experiments on the ideal free distribution,, Oikos, 68 (1993), 158.
doi: 10.2307/3545322. |
[28] |
M. Kennedy and R. D. Gray, Habitat choice, habitat matching and the effect of travel distance,, Behaviour, 134 (1997), 905.
doi: 10.1163/156853997X00223. |
[29] |
S. Kirkland, C.-K. Li and S. J. Schreiber, On the evolution of dispersal in patchy landscapes,, SIAM Journal of Applied Mathematics, 66 (2006), 1366.
doi: 10.1137/050628933. |
[30] |
R. Korona, Travel costs and ideal free distribution of ovipositing female flour beetles, Tribolium confusum,, Animal Behaviour, 40 (1990), 186.
doi: 10.1016/S0003-3472(05)80680-3. |
[31] |
V. Křivan, Dynamic ideal free distribution: Effects of optimal patch choice on predator-prey dynamics,, American Naturalist, 149 (1997), 164. Google Scholar |
[32] |
V. Křivan, R. Cressman and C. Schneider, The ideal free distribution: A review and synthesis of the game-theoretic perspective,, Theoretical Population Biology, 73 (2008), 403. Google Scholar |
[33] |
Y. Lou, Some challenging mathematical problems in evolution of dispersal and population dynamics,, in Tutorials in Mathematical Biosciences IV (ed. A. Friedman), (1922), 171.
doi: 10.1007/978-3-540-74331-6_5. |
[34] |
Y. Lou and C.-H. Wu, Global dynamics of a tritrophic model for two patches with cost of dispersal,, SIAM Journal of Applied Mathematics, 71 (2011), 1801.
doi: 10.1137/100817954. |
[35] |
S. Matsumura, R. Arlinghaus and U. Dieckmann, Foraging on spatially distributed resources with sub-optimal movement, imperfect information, and travelling costs: Departures from the ideal free distribution,, Oikos, 119 (2010), 1469.
doi: 10.1111/j.1600-0706.2010.18196.x. |
[36] |
M. A. McPeek and R. D. Holt, The evolution of dispersal in spatially and temporally varying environments,, American Naturalist, 140 (1992), 1010.
doi: 10.1086/285453. |
[37] |
J. D. Meiss, Differential Dynamical Systems,, Society for Industrial and Applied Mathematics, (2007).
doi: 10.1137/1.9780898718232. |
[38] |
G. Meszéna, M. Gyllenberg, F. J. Jacobs and J. A. J. Metz, Link between population dynamics and dynamics of Darwinian evolution,, Physical Review Letters, 95 (2005).
doi: 10.1103/PhysRevLett.95.078105. |
[39] |
M. Milinski, An evolutionarily stable feeding strategy in sticklebacks,, Journal of comparative ethology, 51 (1979), 36.
doi: 10.1111/j.1439-0310.1979.tb00669.x. |
[40] |
M. Milinski, Ideal free theory predicts more than only matching - a critique of Kennedy and Gray's review,, Oikos, 71 (1994), 163.
doi: 10.2307/3546183. |
[41] |
D. W. Morris, Spatial scale and the cost of density-dependent habitat selection,, Evolutionary Ecology, 1 (1987), 379.
doi: 10.1007/BF02071560. |
[42] |
R. Nathan, An emerging movement ecology paradigm,, in Proceedings of the National Academy of Sciences of the U.S.A., 105 (2008), 19050.
doi: 10.1073/pnas.0808918105. |
[43] |
V. Padron and M. C. Trevisan, Environmentally induced dispersal under heterogenous logistic growth,, Mathematical Biosciences, 199 (2006), 160.
doi: 10.1016/j.mbs.2005.11.004. |
[44] |
G. A. Parker, Searching for mates,, in Behavioural Ecology: An Evolutionary Approach (eds. J. R. Krebs and N. B. Davies), (1978), 214. Google Scholar |
[45] |
K. Parvinen, Evolution of migration in a metapopulation,, Bulletin of Mathematical Biology, 61 (1999), 531. Google Scholar |
[46] |
H. R. Pulliam, Sources, sinks, and population regulation,, American Naturalist, 132 (1988), 652.
doi: 10.1086/284880. |
[47] |
E. Ranta, P. Lundberg and V. Kaitala, Resource matching with limited knowledge,, Oikos, 86 (1999), 383.
doi: 10.2307/3546456. |
[48] |
M. L. Rosenzweig, A theory of habitat selection,, Ecology, 62 (1981), 327.
doi: 10.2307/1936707. |
[49] |
S. J. Schreiber, Interactive effects of temporal correlations, spatial heterogeneity and dispersal on population persistence,, Proceedings of the Royal Society B, 277 (2010), 1907.
doi: 10.1098/rspb.2009.2006. |
[50] |
H. G. Spencer, M. Kennedy and R. D. Gray, Perceptual constraints on optimal foraging: The effect of variation among foragers,, Evolutionary Ecology, 10 (1996), 331.
doi: 10.1007/BF01237721. |
[51] |
T. Tregenza, Building on the ideal free distribution,, Advances in Ecological Research, 26 (1995), 253.
doi: 10.1016/S0065-2504(08)60067-7. |
[52] |
M. van Baalen and M. W. Sabelis, Coevolution of patch selection strategies of predator and prey and the consequences for ecological stability,, American Naturalist, 142 (1993), 646. Google Scholar |
[53] |
J. H. Vandermeer, The community matrix and the number of species in a community,, American Naturalist, 104 (1970), 73. Google Scholar |
show all references
References:
[1] |
P. A. Abrams, Implications of flexible foraging for interspecific interactions: Lessons from simple models,, Functional Ecology, 24 (2010), 7.
doi: 10.1111/j.1365-2435.2009.01621.x. |
[2] |
P. A. Abrams, H. Matsuda and Y. Harada, Evolutionarily unstable fitness maxima and stable fitness minima of continuous traits,, Evolutionary Ecology, 7 (1993), 465.
doi: 10.1007/BF01237642. |
[3] |
I. Averill, Y. Lou and D. Munther, On several conjectures from evolution of dispersal,, Journal of Biological Dynamics, 6 (2012), 117.
doi: 10.1080/17513758.2010.529169. |
[4] |
F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment,, Canadian Applied Math Quarterly, 3 (1995), 379.
|
[5] |
R. S. Cantrell, C. Cosner, D. L. DeAngelis and V. Padron, The ideal free distribution as an evolutionarily stable strategy,, Journal of Biological Dynamics, 1 (2007), 249.
doi: 10.1080/17513750701450227. |
[6] |
R. S. Cantrell, C. Cosner and Y. Lou, Approximating the ideal free distribution via reaction-diffusion-advection equations,, Journal of Differential Equations, 245 (2008), 3687.
doi: 10.1016/j.jde.2008.07.024. |
[7] |
R. S. Cantrell, C. Cosner and Y. Lou, Evolution of dispersal and the ideal free distribution,, Mathematical Biosciences and Engineering, 7 (2010), 17.
doi: 10.3934/mbe.2010.7.17. |
[8] |
R. S. Cantrell, C. Cosner and Y. Lou, Evolutionary stability of ideal free dispersal strategies in patchy environments,, Journal of Mathematical Biology, 65 (2012), 943.
doi: 10.1007/s00285-011-0486-5. |
[9] |
C. Cosner, A dynamic model for the ideal-free distribution as a partial differential equation,, Theoretical Population Biology, 67 (2005), 101.
doi: 10.1016/j.tpb.2004.09.002. |
[10] |
R. Cressman and V. Křivan, The ideal free distribution as an evolutionarily stable state in density-dependent population games,, Oikos, 119 (2010), 1231.
doi: 10.1111/j.1600-0706.2010.17845.x. |
[11] |
D. L. DeAngelis, G. S. K. Wolkowicz, Y. Lou, Y. Jiang, M. Novak, R. Svanback, M. S. Araujo, Y. Jo and E. A. Cleary, The effect of travel loss on evolutionarily stable distributions of populations in space,, American Naturalist, 178 (2011), 15.
doi: 10.1086/660280. |
[12] |
O. Diekmann, A beginner's guide to adaptive dynamics,, Banach center publications, 63 (2004), 47.
|
[13] |
J. E. Diffendorfer, Testing models of source-sink dynamics and balanced dispersal,, Oikos, 81 (1998), 417.
doi: 10.2307/3546763. |
[14] |
J. Dockery, V. Hutson, K. Mischaikow and M. Pernarowski, The evolution of slow dispersal rates: A reaction diffusion model,, Journal of Mathematical Biology, 37 (1998), 61.
doi: 10.1007/s002850050120. |
[15] |
S. M. Flaxman and Y. Lou, Tracking prey or tracking the prey's resource? Mechanisms of movement and optimal habitat selection by predators,, Journal of Theoretical Biology, 256 (2009), 187.
doi: 10.1016/j.jtbi.2008.09.024. |
[16] |
H. I. Freedman, B. Rai and P. Waltman, Mathematical models of population interactions with dispersal. II: Differential survival in a change of habitat,, Journal of Mathematical Analysis and Applications, 115 (1986), 140.
doi: 10.1016/0022-247X(86)90029-6. |
[17] |
H. I. Freedman and P. Waltman, Mathematical models of population interactions with dispersal. I: Stability of two habitats with and without a predator,, SIAM Journal of Applied Mathematics, 32 (1977), 631.
doi: 10.1137/0132052. |
[18] |
S. D. Fretwell and H. L. Lucas, On territorial behavior and other factors influencing habitat distribution in birds,, Acta Biotheoretica, 19 (1969), 37.
doi: 10.1007/BF01601954. |
[19] |
T. E. Galanthay and S. M. Flaxman, Generalized movement strategies for constrained consumers: Ignoring fitness can be adaptive,, American Naturalist, 179 (2012), 475.
doi: 10.1086/664625. |
[20] |
S. A. H. Geritz, É. Kisdi, G. Meszéna and J. A. J. Metz, Evolutionarily singular strategies and the adaptive growth and branching of the evolutionary tree,, Evolutionary Ecology, 12 (1998), 35. Google Scholar |
[21] |
B. S. Goh, Global stability in 2 species interactions,, Journal of Mathematical Biology, 3 (1976), 313.
doi: 10.1007/BF00275063. |
[22] |
H. Hakoyama and K. Iguchi, The information of food distribution realizes an ideal free distribution: Support of perceptual limitation,, Journal of Ethology, 15 (1997), 69.
doi: 10.1007/BF02769391. |
[23] |
A. Hastings, Dynamics of a single species in a spatially varying environment: The stabilizing role of high dispersal rates,, Journal of Mathematical Biology, 16 (1982), 49.
doi: 10.1007/BF00275160. |
[24] |
A. Hastings, Can spatial variation alone lead to selection for dispersal?,, Theoretical Population Biology, 24 (1983), 244.
doi: 10.1016/0040-5809(83)90027-8. |
[25] |
R. D. Holt, Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution,, Theoretical Population Biology, 28 (1985), 181.
doi: 10.1016/0040-5809(85)90027-9. |
[26] |
D. M. Hugie and T. C. Grand, Movement between patches, unequal competitors and the ideal free distribution,, Evolutionary Ecology, 12 (1998), 1. Google Scholar |
[27] |
M. Kennedy and R. D. Gray, Can ecological theory predict the distribution of foraging animals? A critical analysis of experiments on the ideal free distribution,, Oikos, 68 (1993), 158.
doi: 10.2307/3545322. |
[28] |
M. Kennedy and R. D. Gray, Habitat choice, habitat matching and the effect of travel distance,, Behaviour, 134 (1997), 905.
doi: 10.1163/156853997X00223. |
[29] |
S. Kirkland, C.-K. Li and S. J. Schreiber, On the evolution of dispersal in patchy landscapes,, SIAM Journal of Applied Mathematics, 66 (2006), 1366.
doi: 10.1137/050628933. |
[30] |
R. Korona, Travel costs and ideal free distribution of ovipositing female flour beetles, Tribolium confusum,, Animal Behaviour, 40 (1990), 186.
doi: 10.1016/S0003-3472(05)80680-3. |
[31] |
V. Křivan, Dynamic ideal free distribution: Effects of optimal patch choice on predator-prey dynamics,, American Naturalist, 149 (1997), 164. Google Scholar |
[32] |
V. Křivan, R. Cressman and C. Schneider, The ideal free distribution: A review and synthesis of the game-theoretic perspective,, Theoretical Population Biology, 73 (2008), 403. Google Scholar |
[33] |
Y. Lou, Some challenging mathematical problems in evolution of dispersal and population dynamics,, in Tutorials in Mathematical Biosciences IV (ed. A. Friedman), (1922), 171.
doi: 10.1007/978-3-540-74331-6_5. |
[34] |
Y. Lou and C.-H. Wu, Global dynamics of a tritrophic model for two patches with cost of dispersal,, SIAM Journal of Applied Mathematics, 71 (2011), 1801.
doi: 10.1137/100817954. |
[35] |
S. Matsumura, R. Arlinghaus and U. Dieckmann, Foraging on spatially distributed resources with sub-optimal movement, imperfect information, and travelling costs: Departures from the ideal free distribution,, Oikos, 119 (2010), 1469.
doi: 10.1111/j.1600-0706.2010.18196.x. |
[36] |
M. A. McPeek and R. D. Holt, The evolution of dispersal in spatially and temporally varying environments,, American Naturalist, 140 (1992), 1010.
doi: 10.1086/285453. |
[37] |
J. D. Meiss, Differential Dynamical Systems,, Society for Industrial and Applied Mathematics, (2007).
doi: 10.1137/1.9780898718232. |
[38] |
G. Meszéna, M. Gyllenberg, F. J. Jacobs and J. A. J. Metz, Link between population dynamics and dynamics of Darwinian evolution,, Physical Review Letters, 95 (2005).
doi: 10.1103/PhysRevLett.95.078105. |
[39] |
M. Milinski, An evolutionarily stable feeding strategy in sticklebacks,, Journal of comparative ethology, 51 (1979), 36.
doi: 10.1111/j.1439-0310.1979.tb00669.x. |
[40] |
M. Milinski, Ideal free theory predicts more than only matching - a critique of Kennedy and Gray's review,, Oikos, 71 (1994), 163.
doi: 10.2307/3546183. |
[41] |
D. W. Morris, Spatial scale and the cost of density-dependent habitat selection,, Evolutionary Ecology, 1 (1987), 379.
doi: 10.1007/BF02071560. |
[42] |
R. Nathan, An emerging movement ecology paradigm,, in Proceedings of the National Academy of Sciences of the U.S.A., 105 (2008), 19050.
doi: 10.1073/pnas.0808918105. |
[43] |
V. Padron and M. C. Trevisan, Environmentally induced dispersal under heterogenous logistic growth,, Mathematical Biosciences, 199 (2006), 160.
doi: 10.1016/j.mbs.2005.11.004. |
[44] |
G. A. Parker, Searching for mates,, in Behavioural Ecology: An Evolutionary Approach (eds. J. R. Krebs and N. B. Davies), (1978), 214. Google Scholar |
[45] |
K. Parvinen, Evolution of migration in a metapopulation,, Bulletin of Mathematical Biology, 61 (1999), 531. Google Scholar |
[46] |
H. R. Pulliam, Sources, sinks, and population regulation,, American Naturalist, 132 (1988), 652.
doi: 10.1086/284880. |
[47] |
E. Ranta, P. Lundberg and V. Kaitala, Resource matching with limited knowledge,, Oikos, 86 (1999), 383.
doi: 10.2307/3546456. |
[48] |
M. L. Rosenzweig, A theory of habitat selection,, Ecology, 62 (1981), 327.
doi: 10.2307/1936707. |
[49] |
S. J. Schreiber, Interactive effects of temporal correlations, spatial heterogeneity and dispersal on population persistence,, Proceedings of the Royal Society B, 277 (2010), 1907.
doi: 10.1098/rspb.2009.2006. |
[50] |
H. G. Spencer, M. Kennedy and R. D. Gray, Perceptual constraints on optimal foraging: The effect of variation among foragers,, Evolutionary Ecology, 10 (1996), 331.
doi: 10.1007/BF01237721. |
[51] |
T. Tregenza, Building on the ideal free distribution,, Advances in Ecological Research, 26 (1995), 253.
doi: 10.1016/S0065-2504(08)60067-7. |
[52] |
M. van Baalen and M. W. Sabelis, Coevolution of patch selection strategies of predator and prey and the consequences for ecological stability,, American Naturalist, 142 (1993), 646. Google Scholar |
[53] |
J. H. Vandermeer, The community matrix and the number of species in a community,, American Naturalist, 104 (1970), 73. Google Scholar |
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