- Previous Article
- DCDS-B Home
- This Issue
-
Next Article
The effect of immune responses in viral infections: A mathematical model view
Evolution of mobility in predator-prey systems
1. | Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada, Canada |
2. | Biology Centre ASCR, Institute of Entomology and Department of Mathematics and Biomathematics, Faculty of Science, University of South Bohemia, Branišovská 31, 370 05 České Budějovice, Czech Republic |
References:
[1] |
P. A. Abrams, Foraging time optimization and interactions in food webs, Am Nat, 124 (1984), 80-96.
doi: 10.1086/284253. |
[2] |
P. A. Abrams, The impact of habitat selection on the heterogeneity of resources in varying environments, Ecol, 81 (2000), 2902-2913.
doi: 10.2307/177350. |
[3] |
P. A. Abrams, Habitat choice in predator-prey systems: Spatial instability due to interacting adaptive movements, Am Nat, 169 (2007), 581-594.
doi: 10.1086/512688. |
[4] |
P. A. Abrams, R. Cressman and V. Křivan, The role of behavioral dynamics in determining the patch distributions of interacting species, Am Nat, 169 (2007), 505-518.
doi: 10.1086/511963. |
[5] |
K. Argasinski, Dynamic multipopulation and density dependent evolutionary games related to replicator dynamics. A metasimplex concept, Math Biosci, 202 (2006), 88-114.
doi: 10.1016/j.mbs.2006.04.007. |
[6] |
L. Arnold, W. Horsthemke and J. W. Stucki, The influence of external real and white noise on the Lotka-Volterra model, Biom. J., 21 (1979), 451-471.
doi: 10.1002/bimj.4710210507. |
[7] |
J. S. Brown and B. P. Kotler, Hazardous duty pay and the foraging cost of predation, Ecol Lett, 7 (2004), 999-1014.
doi: 10.1111/j.1461-0248.2004.00661.x. |
[8] |
J. S. Brown, J. W. Laundré and M. Gurung, The ecology of fear: Optimal foraging, game theory, and trophic interactions, J Mammal, 80 (1999), 385-399.
doi: 10.2307/1383287. |
[9] |
E. L. Charnov, Optimal foraging: Attack strategy of a mantid, Am Nat, 110 (1976), 141-151.
doi: 10.1086/283054. |
[10] |
R. Cressman, Evolutionary Dynamics and Extensive Form Games, MIT Press, Cambridge, MA, USA, 2003. |
[11] |
R. Cressman and J. Garay, The effects of opportunistic and intentional predators on the herding behavior of prey, Ecol, 92 (2011), 432-440.
doi: 10.1890/10-0199.1. |
[12] |
R. Cressman and V. Křivan, Two-patch population models with adaptive dispersal: The effects of varying dispersal speeds, J Math Biol, 67 (2013), 329-358.
doi: 10.1007/s00285-012-0548-3. |
[13] |
M. M. Dehn, Vigilance for predators: Detection and dilution effects, Behav. Ecol. Sociobiol., 26 (1990), 337-342. |
[14] |
F. Dercole and S. Rinaldi, Analysis of Evolutionary Processes, Princeton University Press, Princeton, USA, 2008. |
[15] |
U. Dieckmann and R. Law, The dynamical theory of coevolution: A derivation from stochastic ecological processes, J. Math. Biol., 34 (1996), 579-612.
doi: 10.1007/BF02409751. |
[16] |
W. A. Foster and J. E. Treherne, Evidence for the dilution effect in the selfish herd from fish predation on a marine insect, Nature, 293 (1981), 466-467.
doi: 10.1038/293466a0. |
[17] |
D. Fudenberg and D. K. Levine, The Theory of Learning in Games, MIT Press, Cambridge, MA, USA, 1998. |
[18] |
G. F. Gause, The Struggle for Existence, Williams and Wilkins, Baltimore, 1934.
doi: 10.1097/00010694-193602000-00018. |
[19] |
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, Evol. Ecol., 12 (1998), 35-57. |
[20] |
J. Hofbauer and E. Hopkins, Learning in perturbed asymmetric games, Games Econ Behav, 52 (2005), 133-152.
doi: 10.1016/j.geb.2004.06.006. |
[21] |
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, Cambridge University Press, Cambridge, 1988. |
[22] |
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179. |
[23] |
C. S. Holling, Some characteristics of simple types of predation and parasitism, Can. Entomol., 91 (1959), 385-398.
doi: 10.4039/Ent91385-7. |
[24] |
R. Huey and E. R. Pianka, Ecological consequences of foraging mode, Ecol, 62 (1981), 991-999.
doi: 10.2307/1936998. |
[25] |
V. Křivan, Optimal foraging and predator-prey dynamics, Theor Popul Biol, 49 (1996), 265-290. |
[26] |
V. Křivan, The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs, Am Nat, 170 (2007), 771-782. |
[27] |
V. Křivan and E. Sirot, Habitat selection by two competing species in a two-habitat environment, Am Nat, 160 (2002), 214-234. |
[28] |
J. H. Lü, G. R. Chen and S. C. Zhang, Dynamical analysis of a new chaotic attractor, Int. J. Bifur. Chaos Appl. Sci. Eng., 12 (2002), 1001-1015. |
[29] |
R. H. MacArthur and E. R. Pianka, On optimal use of a patchy environment, Am Nat, 100 (1966), 603-609.
doi: 10.1086/282454. |
[30] |
M. Parker and A. Kamenev, Mean extinction time in predator-prey model, J Stat Phys, 141 (2010), 201-216.
doi: 10.1007/s10955-010-0049-y. |
[31] |
M. L. Rosenzweig and R. H. MacArthur, Graphical representation and stability conditions of predator-prey interactions, Am Nat, 97 (1963), 209-223.
doi: 10.1086/282272. |
[32] |
L. Samuelson and J. Zhang, Evolutionary stability in asymmetric games, J. Econ. Theory, 57 (1992), 363-391.
doi: 10.1016/0022-0531(92)90041-F. |
[33] |
I. Scharf, E. Nulman, O. Ovadia and A. Bouskila, Efficiency evaluation of two competing foraging modes under different conditions, Am Nat, 168 (2006), 350-357.
doi: 10.1086/506921. |
[34] |
O. J. Schmitz, Behavior of predators and prey and links with population level processes. In Ecology of Predator-Prey Interactions (eds. P. Barbosa and I. Castellanos ), 256-278, Oxford University Press, 2005. |
[35] |
O. J. Schmitz, V. Křivan and O. Ovadia, Trophic cascades: The primacy of trait-mediated indirect interactions, Ecol Lett, 7 (2004), 153-163.
doi: 10.1111/j.1461-0248.2003.00560.x. |
[36] |
T. W. Schoener, Theory of feeding strategies, Annu Rev Ecol Syst, 2 (1971), 369-404.
doi: 10.1146/annurev.es.02.110171.002101. |
[37] |
J. G. Skellam, The mathematical foundations underlying the use of line transects in animal ecology, Biometrics, 14 (1958), 385-400.
doi: 10.2307/2527881. |
[38] |
D. W. Stephens and J. R. Krebs, Foraging Theory, Princeton University Press, Princeton, New Jersey, USA, 1986. |
[39] |
T. L. Vincent and J. S. Brown, Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics, Cambridge University Press, Cambridge, UK, 2005.
doi: 10.1017/CBO9780511542633. |
[40] |
E. E. Werner and B. R. Anholt, Ecological consequences of the trade-off between growth and mortality rates mediated by foraging activity, Am Nat, 142 (1993), 242-272.
doi: 10.1086/285537. |
[41] |
W. B. Yapp, The theory of line transects, Bird Study, 3 (1956), 93-104.
doi: 10.1080/00063655609475840. |
show all references
References:
[1] |
P. A. Abrams, Foraging time optimization and interactions in food webs, Am Nat, 124 (1984), 80-96.
doi: 10.1086/284253. |
[2] |
P. A. Abrams, The impact of habitat selection on the heterogeneity of resources in varying environments, Ecol, 81 (2000), 2902-2913.
doi: 10.2307/177350. |
[3] |
P. A. Abrams, Habitat choice in predator-prey systems: Spatial instability due to interacting adaptive movements, Am Nat, 169 (2007), 581-594.
doi: 10.1086/512688. |
[4] |
P. A. Abrams, R. Cressman and V. Křivan, The role of behavioral dynamics in determining the patch distributions of interacting species, Am Nat, 169 (2007), 505-518.
doi: 10.1086/511963. |
[5] |
K. Argasinski, Dynamic multipopulation and density dependent evolutionary games related to replicator dynamics. A metasimplex concept, Math Biosci, 202 (2006), 88-114.
doi: 10.1016/j.mbs.2006.04.007. |
[6] |
L. Arnold, W. Horsthemke and J. W. Stucki, The influence of external real and white noise on the Lotka-Volterra model, Biom. J., 21 (1979), 451-471.
doi: 10.1002/bimj.4710210507. |
[7] |
J. S. Brown and B. P. Kotler, Hazardous duty pay and the foraging cost of predation, Ecol Lett, 7 (2004), 999-1014.
doi: 10.1111/j.1461-0248.2004.00661.x. |
[8] |
J. S. Brown, J. W. Laundré and M. Gurung, The ecology of fear: Optimal foraging, game theory, and trophic interactions, J Mammal, 80 (1999), 385-399.
doi: 10.2307/1383287. |
[9] |
E. L. Charnov, Optimal foraging: Attack strategy of a mantid, Am Nat, 110 (1976), 141-151.
doi: 10.1086/283054. |
[10] |
R. Cressman, Evolutionary Dynamics and Extensive Form Games, MIT Press, Cambridge, MA, USA, 2003. |
[11] |
R. Cressman and J. Garay, The effects of opportunistic and intentional predators on the herding behavior of prey, Ecol, 92 (2011), 432-440.
doi: 10.1890/10-0199.1. |
[12] |
R. Cressman and V. Křivan, Two-patch population models with adaptive dispersal: The effects of varying dispersal speeds, J Math Biol, 67 (2013), 329-358.
doi: 10.1007/s00285-012-0548-3. |
[13] |
M. M. Dehn, Vigilance for predators: Detection and dilution effects, Behav. Ecol. Sociobiol., 26 (1990), 337-342. |
[14] |
F. Dercole and S. Rinaldi, Analysis of Evolutionary Processes, Princeton University Press, Princeton, USA, 2008. |
[15] |
U. Dieckmann and R. Law, The dynamical theory of coevolution: A derivation from stochastic ecological processes, J. Math. Biol., 34 (1996), 579-612.
doi: 10.1007/BF02409751. |
[16] |
W. A. Foster and J. E. Treherne, Evidence for the dilution effect in the selfish herd from fish predation on a marine insect, Nature, 293 (1981), 466-467.
doi: 10.1038/293466a0. |
[17] |
D. Fudenberg and D. K. Levine, The Theory of Learning in Games, MIT Press, Cambridge, MA, USA, 1998. |
[18] |
G. F. Gause, The Struggle for Existence, Williams and Wilkins, Baltimore, 1934.
doi: 10.1097/00010694-193602000-00018. |
[19] |
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, Evol. Ecol., 12 (1998), 35-57. |
[20] |
J. Hofbauer and E. Hopkins, Learning in perturbed asymmetric games, Games Econ Behav, 52 (2005), 133-152.
doi: 10.1016/j.geb.2004.06.006. |
[21] |
J. Hofbauer and K. Sigmund, The Theory of Evolution and Dynamical Systems, Cambridge University Press, Cambridge, 1988. |
[22] |
J. Hofbauer and K. Sigmund, Evolutionary Games and Population Dynamics, Cambridge University Press, Cambridge, 1998.
doi: 10.1017/CBO9781139173179. |
[23] |
C. S. Holling, Some characteristics of simple types of predation and parasitism, Can. Entomol., 91 (1959), 385-398.
doi: 10.4039/Ent91385-7. |
[24] |
R. Huey and E. R. Pianka, Ecological consequences of foraging mode, Ecol, 62 (1981), 991-999.
doi: 10.2307/1936998. |
[25] |
V. Křivan, Optimal foraging and predator-prey dynamics, Theor Popul Biol, 49 (1996), 265-290. |
[26] |
V. Křivan, The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs, Am Nat, 170 (2007), 771-782. |
[27] |
V. Křivan and E. Sirot, Habitat selection by two competing species in a two-habitat environment, Am Nat, 160 (2002), 214-234. |
[28] |
J. H. Lü, G. R. Chen and S. C. Zhang, Dynamical analysis of a new chaotic attractor, Int. J. Bifur. Chaos Appl. Sci. Eng., 12 (2002), 1001-1015. |
[29] |
R. H. MacArthur and E. R. Pianka, On optimal use of a patchy environment, Am Nat, 100 (1966), 603-609.
doi: 10.1086/282454. |
[30] |
M. Parker and A. Kamenev, Mean extinction time in predator-prey model, J Stat Phys, 141 (2010), 201-216.
doi: 10.1007/s10955-010-0049-y. |
[31] |
M. L. Rosenzweig and R. H. MacArthur, Graphical representation and stability conditions of predator-prey interactions, Am Nat, 97 (1963), 209-223.
doi: 10.1086/282272. |
[32] |
L. Samuelson and J. Zhang, Evolutionary stability in asymmetric games, J. Econ. Theory, 57 (1992), 363-391.
doi: 10.1016/0022-0531(92)90041-F. |
[33] |
I. Scharf, E. Nulman, O. Ovadia and A. Bouskila, Efficiency evaluation of two competing foraging modes under different conditions, Am Nat, 168 (2006), 350-357.
doi: 10.1086/506921. |
[34] |
O. J. Schmitz, Behavior of predators and prey and links with population level processes. In Ecology of Predator-Prey Interactions (eds. P. Barbosa and I. Castellanos ), 256-278, Oxford University Press, 2005. |
[35] |
O. J. Schmitz, V. Křivan and O. Ovadia, Trophic cascades: The primacy of trait-mediated indirect interactions, Ecol Lett, 7 (2004), 153-163.
doi: 10.1111/j.1461-0248.2003.00560.x. |
[36] |
T. W. Schoener, Theory of feeding strategies, Annu Rev Ecol Syst, 2 (1971), 369-404.
doi: 10.1146/annurev.es.02.110171.002101. |
[37] |
J. G. Skellam, The mathematical foundations underlying the use of line transects in animal ecology, Biometrics, 14 (1958), 385-400.
doi: 10.2307/2527881. |
[38] |
D. W. Stephens and J. R. Krebs, Foraging Theory, Princeton University Press, Princeton, New Jersey, USA, 1986. |
[39] |
T. L. Vincent and J. S. Brown, Evolutionary Game Theory, Natural Selection, and Darwinian Dynamics, Cambridge University Press, Cambridge, UK, 2005.
doi: 10.1017/CBO9780511542633. |
[40] |
E. E. Werner and B. R. Anholt, Ecological consequences of the trade-off between growth and mortality rates mediated by foraging activity, Am Nat, 142 (1993), 242-272.
doi: 10.1086/285537. |
[41] |
W. B. Yapp, The theory of line transects, Bird Study, 3 (1956), 93-104.
doi: 10.1080/00063655609475840. |
[1] |
Jinfeng Wang, Hongxia Fan. Dynamics in a Rosenzweig-Macarthur predator-prey system with quiescence. Discrete and Continuous Dynamical Systems - B, 2016, 21 (3) : 909-918. doi: 10.3934/dcdsb.2016.21.909 |
[2] |
Xiaoli Liu, Dongmei Xiao. Bifurcations in a discrete time Lotka-Volterra predator-prey system. Discrete and Continuous Dynamical Systems - B, 2006, 6 (3) : 559-572. doi: 10.3934/dcdsb.2006.6.559 |
[3] |
S. Nakaoka, Y. Saito, Y. Takeuchi. Stability, delay, and chaotic behavior in a Lotka-Volterra predator-prey system. Mathematical Biosciences & Engineering, 2006, 3 (1) : 173-187. doi: 10.3934/mbe.2006.3.173 |
[4] |
Rui Xu, M.A.J. Chaplain, F.A. Davidson. Periodic solutions of a discrete nonautonomous Lotka-Volterra predator-prey model with time delays. Discrete and Continuous Dynamical Systems - B, 2004, 4 (3) : 823-831. doi: 10.3934/dcdsb.2004.4.823 |
[5] |
Michael Y. Li, Xihui Lin, Hao Wang. Global Hopf branches and multiple limit cycles in a delayed Lotka-Volterra predator-prey model. Discrete and Continuous Dynamical Systems - B, 2014, 19 (3) : 747-760. doi: 10.3934/dcdsb.2014.19.747 |
[6] |
Xun Cao, Xianyong Chen, Weihua Jiang. Bogdanov-Takens bifurcation with $ Z_2 $ symmetry and spatiotemporal dynamics in diffusive Rosenzweig-MacArthur model involving nonlocal prey competition. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022031 |
[7] |
Yuzo Hosono. Traveling waves for the Lotka-Volterra predator-prey system without diffusion of the predator. Discrete and Continuous Dynamical Systems - B, 2015, 20 (1) : 161-171. doi: 10.3934/dcdsb.2015.20.161 |
[8] |
Wenjie Li, Lihong Huang, Jinchen Ji. Globally exponentially stable periodic solution in a general delayed predator-prey model under discontinuous prey control strategy. Discrete and Continuous Dynamical Systems - B, 2020, 25 (7) : 2639-2664. doi: 10.3934/dcdsb.2020026 |
[9] |
Wei Feng, Nicole Rocco, Michael Freeze, Xin Lu. Mathematical analysis on an extended Rosenzweig-MacArthur model of tri-trophic food chain. Discrete and Continuous Dynamical Systems - S, 2014, 7 (6) : 1215-1230. doi: 10.3934/dcdss.2014.7.1215 |
[10] |
Qizhen Xiao, Binxiang Dai. Heteroclinic bifurcation for a general predator-prey model with Allee effect and state feedback impulsive control strategy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1065-1081. doi: 10.3934/mbe.2015.12.1065 |
[11] |
Minzhen Xu, Shangjiang Guo. Dynamics of a delayed Lotka-Volterra model with two predators competing for one prey. Discrete and Continuous Dynamical Systems - B, 2021 doi: 10.3934/dcdsb.2021287 |
[12] |
P. Auger, N. H. Du, N. T. Hieu. Evolution of Lotka-Volterra predator-prey systems under telegraph noise. Mathematical Biosciences & Engineering, 2009, 6 (4) : 683-700. doi: 10.3934/mbe.2009.6.683 |
[13] |
Yueding Yuan, Yang Wang, Xingfu Zou. Spatial dynamics of a Lotka-Volterra model with a shifting habitat. Discrete and Continuous Dynamical Systems - B, 2019, 24 (10) : 5633-5671. doi: 10.3934/dcdsb.2019076 |
[14] |
Li Ma, Shangjiang Guo. Bifurcation and stability of a two-species diffusive Lotka-Volterra model. Communications on Pure and Applied Analysis, 2020, 19 (3) : 1205-1232. doi: 10.3934/cpaa.2020056 |
[15] |
Wei Feng, Jody Hinson. Stability and pattern in two-patch predator-prey population dynamics. Conference Publications, 2005, 2005 (Special) : 268-279. doi: 10.3934/proc.2005.2005.268 |
[16] |
Miljana JovanoviĆ, Marija KrstiĆ. Extinction in stochastic predator-prey population model with Allee effect on prey. Discrete and Continuous Dynamical Systems - B, 2017, 22 (7) : 2651-2667. doi: 10.3934/dcdsb.2017129 |
[17] |
Dingyong Bai, Jianshe Yu, Yun Kang. Spatiotemporal dynamics of a diffusive predator-prey model with generalist predator. Discrete and Continuous Dynamical Systems - S, 2020, 13 (11) : 2949-2973. doi: 10.3934/dcdss.2020132 |
[18] |
Xiao He, Sining Zheng. Protection zone in a modified Lotka-Volterra model. Discrete and Continuous Dynamical Systems - B, 2015, 20 (7) : 2027-2038. doi: 10.3934/dcdsb.2015.20.2027 |
[19] |
Guihong Fan, Gail S. K. Wolkowicz. Chaotic dynamics in a simple predator-prey model with discrete delay. Discrete and Continuous Dynamical Systems - B, 2021, 26 (1) : 191-216. doi: 10.3934/dcdsb.2020263 |
[20] |
Liang Zhang, Zhi-Cheng Wang. Spatial dynamics of a diffusive predator-prey model with stage structure. Discrete and Continuous Dynamical Systems - B, 2015, 20 (6) : 1831-1853. doi: 10.3934/dcdsb.2015.20.1831 |
2020 Impact Factor: 1.327
Tools
Metrics
Other articles
by authors
[Back to Top]