-
Previous Article
The diffusive competition model with a free boundary: Invasion of a superior or inferior competitor
- DCDS-B Home
- This Issue
-
Next Article
Inside dynamics of solutions of integro-differential equations
Effects of dispersal in a non-uniform environment on population dynamics and competition: A patch model approach
1. | U.S. Geological Survey and Department of Biology, University of Miami, 1301 Memorial Drive, Coral Gables, Florida 33143, United States |
2. | Department of Biology, University of Miami, 1301 Memorial Drive, Coral Gables, Florida 33143, United States |
References:
[1] |
P. Amarasekare and R. M. Nisbet, Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species,, The American Naturalist, 158 (2001), 572.
doi: 10.1086/323586. |
[2] |
B. M. Bolker, Combining endogenous and exogenous spatial variability in analytical population models,, Theoretical Population Biology, 64 (2003), 255.
doi: 10.1016/S0040-5809(03)00090-X. |
[3] |
R. S. Cantrell, and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations,, Wiley Series in Mathematical and Computational Biology, ().
doi: 10.1002/0470871296. |
[4] |
R. S. Cantrell, C. Cosner, D. L. DeAngelis, and V. Padron, The ideal free distribution as an evolutionarily stable strategy,, Journal of Biological Dynamics, 3 (2007), 249.
doi: 10.1080/17513750701450227. |
[5] |
X. Chen, K.-Y. Lam, and Y. Lou, Dynamics of a reaction-diffusion-advection model for two competing species,, Discrete and Continuous Dynamic Systems A, 32 (2012), 3841.
doi: 10.3934/dcds.2012.32.3841. |
[6] |
P. Chesson, Coexistence of competitors in spatially and temporally varying environments: A look at the combined effects of different sorts of variability,, Theoretical Population Biology, 28 (1985), 263.
doi: 10.1016/0040-5809(85)90030-9. |
[7] |
P. Chesson, General theory of competitive coexistence in spatially-varying environments,, Theoretical Population Biology, 58 (2000), 211.
doi: 10.1006/tpbi.2000.1486. |
[8] |
R. Cressman, V. Křivan, and J. Garay, Ideal free distributions, evolutionary games, and population dynamics in multiple species environments,, The American Naturalist, 164 (2004), 473.
doi: 10.1086/423827. |
[9] |
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. |
[10] |
S. D. Fretwell, and H. R. Lucas, On territorial behavior and other factors influencing habitat distribution in birds. I,, Theoretical development. Acta Biotheoretica, 9 (1970), 16.
doi: 10.1007/BF01601953. |
[11] |
T. Hara, Effects of variation in individual growth on plant species coexistence,, Journal of Vegetarian Science, 4 (1993), 409.
doi: 10.2307/3235600. |
[12] |
R. Hambrock and Y. Lou, The evolution of conditional dispersal strategies in spatially heterogeneous habitats,, Bulletin of Mathematical Biology, 71 (2009), 1793.
doi: 10.1007/s11538-009-9425-7. |
[13] |
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. |
[14] |
X. He and W.-M. Ni, The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system. I: Heterogeneity vs. homogeneity,, Journal of Differential Equations, 254 (2013), 528.
doi: 10.1016/j.jde.2012.08.032. |
[15] |
K.-Y. Lam and Y. Lou., Evolution of conditional dispersal: Evolutionarily stable strategy in spatial models,, In press, ().
doi: 10.1007/s00285-013-0650-1. |
[16] |
K.-Y. Lam and Y. Lou., Evolutionarily stable and convergent stable strategies in reaction-diffusion models for conditional dispersal,, Submitted., ().
doi: 10.1007/s11538-013-9901-y. |
[17] |
J. Latore, P. Gould, and A. M. Mortimer, Effects of habitat heterogeneity and dispersal strategies on population persistence in annual plants,, Ecological Modelling, 123 (1999), 127.
doi: 10.1016/S0304-3800(99)00132-5. |
[18] |
Y. Lou, On the effects of migration and spatial heterogeneity on single and multiple species,, Journal of Differential Equations, 223 (2006), 400.
doi: 10.1016/j.jde.2005.05.010. |
[19] |
F. Lutscher, E. McCauley, and M. A. Lewis, Spatial patterns and coexistence mechanism in systems with unidirectional flow,, Theoretical Population Biology, 71 (2007), 267.
doi: 10.1016/j.tpb.2006.11.006. |
[20] |
D. W. Morris, Spatial scale and the cost of density-dependent habitat selection,, Evolutionary Ecology, 1 (1987), 379.
doi: 10.1007/BF02071560. |
[21] |
S. Muko and Y. Iwasa, Species coexistence by permanent spatial heterogeneity in a lottery model,, Theoretical Population Biology, 57 (2000), 273.
doi: 10.1006/tpbi.2000.1456. |
[22] |
J. Silvertown and R. Law, Do plants need niches? Some recent developments in plant community ecology,, Trends in Ecology and Evolution, 2 (1987), 24.
doi: 10.1016/0169-5347(87)90197-2. |
[23] |
R. E. Snyder and P. Chesson, Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity,, Ecology Letters, 6 (2003), 301.
doi: 10.1046/j.1461-0248.2003.00434.x. |
[24] |
R. E. Snyder and P. Chesson, How the spatial scales of dispersal, competition, and environmental heterogeneity interact to affect coexistence,, The American Naturalist, 164 (2004), 633.
doi: 10.1086/424969. |
[25] |
D. Tilman, Competition and biodiversity in spatially structures habitats,, Ecology, 75 (1994), 2.
doi: 10.2307/1939377. |
[26] |
D. W. Yu, H. B. Wilson and N. E. Pierce, An empirical model of species coexistence in a spatially structured environment,, Ecology, 82 (2001), 1761.
doi: 10.2307/2679816. |
show all references
References:
[1] |
P. Amarasekare and R. M. Nisbet, Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species,, The American Naturalist, 158 (2001), 572.
doi: 10.1086/323586. |
[2] |
B. M. Bolker, Combining endogenous and exogenous spatial variability in analytical population models,, Theoretical Population Biology, 64 (2003), 255.
doi: 10.1016/S0040-5809(03)00090-X. |
[3] |
R. S. Cantrell, and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations,, Wiley Series in Mathematical and Computational Biology, ().
doi: 10.1002/0470871296. |
[4] |
R. S. Cantrell, C. Cosner, D. L. DeAngelis, and V. Padron, The ideal free distribution as an evolutionarily stable strategy,, Journal of Biological Dynamics, 3 (2007), 249.
doi: 10.1080/17513750701450227. |
[5] |
X. Chen, K.-Y. Lam, and Y. Lou, Dynamics of a reaction-diffusion-advection model for two competing species,, Discrete and Continuous Dynamic Systems A, 32 (2012), 3841.
doi: 10.3934/dcds.2012.32.3841. |
[6] |
P. Chesson, Coexistence of competitors in spatially and temporally varying environments: A look at the combined effects of different sorts of variability,, Theoretical Population Biology, 28 (1985), 263.
doi: 10.1016/0040-5809(85)90030-9. |
[7] |
P. Chesson, General theory of competitive coexistence in spatially-varying environments,, Theoretical Population Biology, 58 (2000), 211.
doi: 10.1006/tpbi.2000.1486. |
[8] |
R. Cressman, V. Křivan, and J. Garay, Ideal free distributions, evolutionary games, and population dynamics in multiple species environments,, The American Naturalist, 164 (2004), 473.
doi: 10.1086/423827. |
[9] |
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. |
[10] |
S. D. Fretwell, and H. R. Lucas, On territorial behavior and other factors influencing habitat distribution in birds. I,, Theoretical development. Acta Biotheoretica, 9 (1970), 16.
doi: 10.1007/BF01601953. |
[11] |
T. Hara, Effects of variation in individual growth on plant species coexistence,, Journal of Vegetarian Science, 4 (1993), 409.
doi: 10.2307/3235600. |
[12] |
R. Hambrock and Y. Lou, The evolution of conditional dispersal strategies in spatially heterogeneous habitats,, Bulletin of Mathematical Biology, 71 (2009), 1793.
doi: 10.1007/s11538-009-9425-7. |
[13] |
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. |
[14] |
X. He and W.-M. Ni, The effects of diffusion and spatial variation in Lotka-Volterra competition-diffusion system. I: Heterogeneity vs. homogeneity,, Journal of Differential Equations, 254 (2013), 528.
doi: 10.1016/j.jde.2012.08.032. |
[15] |
K.-Y. Lam and Y. Lou., Evolution of conditional dispersal: Evolutionarily stable strategy in spatial models,, In press, ().
doi: 10.1007/s00285-013-0650-1. |
[16] |
K.-Y. Lam and Y. Lou., Evolutionarily stable and convergent stable strategies in reaction-diffusion models for conditional dispersal,, Submitted., ().
doi: 10.1007/s11538-013-9901-y. |
[17] |
J. Latore, P. Gould, and A. M. Mortimer, Effects of habitat heterogeneity and dispersal strategies on population persistence in annual plants,, Ecological Modelling, 123 (1999), 127.
doi: 10.1016/S0304-3800(99)00132-5. |
[18] |
Y. Lou, On the effects of migration and spatial heterogeneity on single and multiple species,, Journal of Differential Equations, 223 (2006), 400.
doi: 10.1016/j.jde.2005.05.010. |
[19] |
F. Lutscher, E. McCauley, and M. A. Lewis, Spatial patterns and coexistence mechanism in systems with unidirectional flow,, Theoretical Population Biology, 71 (2007), 267.
doi: 10.1016/j.tpb.2006.11.006. |
[20] |
D. W. Morris, Spatial scale and the cost of density-dependent habitat selection,, Evolutionary Ecology, 1 (1987), 379.
doi: 10.1007/BF02071560. |
[21] |
S. Muko and Y. Iwasa, Species coexistence by permanent spatial heterogeneity in a lottery model,, Theoretical Population Biology, 57 (2000), 273.
doi: 10.1006/tpbi.2000.1456. |
[22] |
J. Silvertown and R. Law, Do plants need niches? Some recent developments in plant community ecology,, Trends in Ecology and Evolution, 2 (1987), 24.
doi: 10.1016/0169-5347(87)90197-2. |
[23] |
R. E. Snyder and P. Chesson, Local dispersal can facilitate coexistence in the presence of permanent spatial heterogeneity,, Ecology Letters, 6 (2003), 301.
doi: 10.1046/j.1461-0248.2003.00434.x. |
[24] |
R. E. Snyder and P. Chesson, How the spatial scales of dispersal, competition, and environmental heterogeneity interact to affect coexistence,, The American Naturalist, 164 (2004), 633.
doi: 10.1086/424969. |
[25] |
D. Tilman, Competition and biodiversity in spatially structures habitats,, Ecology, 75 (1994), 2.
doi: 10.2307/1939377. |
[26] |
D. W. Yu, H. B. Wilson and N. E. Pierce, An empirical model of species coexistence in a spatially structured environment,, Ecology, 82 (2001), 1761.
doi: 10.2307/2679816. |
[1] |
S. Sadeghi, H. Jafari, S. Nemati. Solving fractional Advection-diffusion equation using Genocchi operational matrix based on Atangana-Baleanu derivative. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020435 |
[2] |
Ágota P. Horváth. Discrete diffusion semigroups associated with Jacobi-Dunkl and exceptional Jacobi polynomials. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021002 |
[3] |
Ting Liu, Guo-Bao Zhang. Global stability of traveling waves for a spatially discrete diffusion system with time delay. Electronic Research Archive, , () : -. doi: 10.3934/era.2021003 |
[4] |
Yu Jin, Xiang-Qiang Zhao. The spatial dynamics of a Zebra mussel model in river environments. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020362 |
[5] |
Weiwei Liu, Jinliang Wang, Yuming Chen. Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020316 |
[6] |
Yoshihisa Morita, Kunimochi Sakamoto. Turing type instability in a diffusion model with mass transport on the boundary. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3813-3836. doi: 10.3934/dcds.2020160 |
[7] |
Zhihua Liu, Yayun Wu, Xiangming Zhang. Existence of periodic wave trains for an age-structured model with diffusion. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021009 |
[8] |
Hui Zhao, Zhengrong Liu, Yiren Chen. Global dynamics of a chemotaxis model with signal-dependent diffusion and sensitivity. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2021011 |
[9] |
Mohammad Ghani, Jingyu Li, Kaijun Zhang. Asymptotic stability of traveling fronts to a chemotaxis model with nonlinear diffusion. Discrete & Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021017 |
[10] |
Leilei Wei, Yinnian He. A fully discrete local discontinuous Galerkin method with the generalized numerical flux to solve the tempered fractional reaction-diffusion equation. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020319 |
[11] |
Mahir Demir, Suzanne Lenhart. A spatial food chain model for the Black Sea Anchovy, and its optimal fishery. Discrete & Continuous Dynamical Systems - B, 2021, 26 (1) : 155-171. doi: 10.3934/dcdsb.2020373 |
[12] |
H. M. Srivastava, H. I. Abdel-Gawad, Khaled Mohammed Saad. Oscillatory states and patterns formation in a two-cell cubic autocatalytic reaction-diffusion model subjected to the Dirichlet conditions. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020433 |
[13] |
Hai-Feng Huo, Shi-Ke Hu, Hong Xiang. Traveling wave solution for a diffusion SEIR epidemic model with self-protection and treatment. Electronic Research Archive, , () : -. doi: 10.3934/era.2020118 |
[14] |
Qing Li, Yaping Wu. Existence and instability of some nontrivial steady states for the SKT competition model with large cross diffusion. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3657-3682. doi: 10.3934/dcds.2020051 |
[15] |
Yukio Kan-On. On the limiting system in the Shigesada, Kawasaki and Teramoto model with large cross-diffusion rates. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3561-3570. doi: 10.3934/dcds.2020161 |
[16] |
Guillaume Cantin, M. A. Aziz-Alaoui. Dimension estimate of attractors for complex networks of reaction-diffusion systems applied to an ecological model. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2020283 |
[17] |
Michel Chipot, Mingmin Zhang. On some model problem for the propagation of interacting species in a special environment. Discrete & Continuous Dynamical Systems - A, 2020 doi: 10.3934/dcds.2020401 |
[18] |
Kimie Nakashima. Indefinite nonlinear diffusion problem in population genetics. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3837-3855. doi: 10.3934/dcds.2020169 |
[19] |
Zaihui Gan, Fanghua Lin, Jiajun Tong. On the viscous Camassa-Holm equations with fractional diffusion. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3427-3450. doi: 10.3934/dcds.2020029 |
[20] |
Hai-Liang Li, Tong Yang, Mingying Zhong. Diffusion limit of the Vlasov-Poisson-Boltzmann system. Kinetic & Related Models, , () : -. doi: 10.3934/krm.2021003 |
2019 Impact Factor: 1.27
Tools
Metrics
Other articles
by authors
[Back to Top]