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Evolutionary dynamics of a multi-trait semelparous model
On a two-patch predator-prey model with adaptive habitancy of predators
1. | Department of Applied Mathematics, University of Western Ontario, London, ON N6A 5B7, Canada |
2. | Department of Applied Mathematics, University of Western Ontario, London, Ontario N6A 5B7 |
References:
[1] |
P. A. Abrams, R. Cressman and V. Křivan, The role of behavioral dynamics in determining the patch distributions of interacting species, The American Naturalist, 169 (2007), 505-518.
doi: 10.1086/511963. |
[2] |
D. M. Buss and H. Greiling, Adaptive individual differences, Journal of Personality, 67 (1999), 209-243.
doi: 10.1111/1467-6494.00053. |
[3] |
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), 249-271.
doi: 10.1080/17513750701450227. |
[4] |
R. S. Cantrell, C. Cosner and Y. Lou, Evolutionary stability of ideal free dispersal strategies in patchy environments, Journaal of Mathematical Biology, 65 (2012), 943-965.
doi: 10.1007/s00285-011-0486-5. |
[5] |
M. E. Clark, T. G. Wolcott, D. L. Wolcott and A. H. Hines, Foraging behavior of an estuarine predator, the blue crab Callinectes sapidus in a patchy environment, Ecography, 23 (2000), 21-31. |
[6] |
S. Creel and N. M. Dreel, The African Wild Dog: Behavior, Ecology, and Conservation, Princeton University Press, 2002. |
[7] |
R. Cressman and V. Křivan, Migration dynamics for the ideal free distribution, The American Naturalist, 168 (2006), 384-397.
doi: 10.1086/506970. |
[8] |
R. Cressman and V. Křivan, Two-patch population models with adaptive dispersal: The effects of varying dispersal speeds, Journal of Mathematical Biology, 67 (2013), 329-358.
doi: 10.1007/s00285-012-0548-3. |
[9] |
R. Cressman, V. Křivan and J. Garay, Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments, The American Naturalist, 164 (2004), 473-489.
doi: 10.1086/423827. |
[10] |
S. D. Fretwell and J. S. Calver, On territorial behavior and other factors influencing habitat distribution in birds, Acta Biotheoretica, 19 (1969), 37-44. |
[11] |
J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM Journal on Mathematical Analysis, 20 (1989), 388-395.
doi: 10.1137/0520025. |
[12] |
J. Hofbauer and K. Sigmund, Evolutionray Games and Population Dynamics, Cambridge University Press, 1998.
doi: 10.1017/CBO9781139173179. |
[13] |
C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, Memoirs of the Entomological Society of Canada, 97 (1965), 5-60.
doi: 10.4039/entm9745fv. |
[14] |
V. Křivan, The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs, The American Naturalist, 170 (2007), 771-782. |
[15] |
V. Křivan and R. Cressman, On evolutionary stability in predator-prey models with fast behavioral dynamics, Evolutionary Ecology Research, 11 (2009), 227-251. |
[16] |
Y. Kuang and Y. Takeuchi, Predator-prey dynamics in models of prey dispersal in two-patch environments, Mathematical Biosciences, 120 (1994), 77-98.
doi: 10.1016/0025-5564(94)90038-8. |
[17] |
S. A. Levin, Dispersion and population interactions, The American Naturalist, 108 (1974), 207-228.
doi: 10.1086/282900. |
[18] |
J. D. Murray, Mathematical Biology, I, An Introduction, Springer, 2002. |
[19] |
I. Scharf, E. Nulman, O. Ovadia and A. Bouskila, Efficiency evaluation of two competing foraging modes under different conditions, The American Naturalist, 168 (2006), 350-357.
doi: 10.1086/506921. |
[20] |
R. D. Seitz, R. N. Lipcius, A. H. Hines and D. B. Eggleston, Density-dependent predation, habitat variation, and the persistence of marine bivalve prey, Ecology, 82 (2001), 2435-2451. |
[21] |
J. E. Staddon, Adaptive Behaviour and Learning, CUP Archive, 1983. |
[22] |
C. Starr, R. Taggart, C. Evers and L. Starr, Biology: The Unity And Diversity of Life, Yolanda Cossio, 2009. |
[23] |
H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM Journal on Mathematical Analysis, 24 (1993), 407-435.
doi: 10.1137/0524026. |
[24] |
W. Wang and Y. Takeuchi, Adaptation of prey and predators between patches, Journal of Theoretical Biology, 258 (2009), 603-613.
doi: 10.1016/j.jtbi.2009.02.014. |
[25] |
D. K. Wasko and M. Sasa, Food resources influence spatial ecology, habitat selection, and foraging behavior in an ambush-hunting snake (Viperidae: Bothrops asper): an experimental study, Zoology, 115 (2012), 179-187.
doi: 10.1016/j.zool.2011.10.001. |
show all references
References:
[1] |
P. A. Abrams, R. Cressman and V. Křivan, The role of behavioral dynamics in determining the patch distributions of interacting species, The American Naturalist, 169 (2007), 505-518.
doi: 10.1086/511963. |
[2] |
D. M. Buss and H. Greiling, Adaptive individual differences, Journal of Personality, 67 (1999), 209-243.
doi: 10.1111/1467-6494.00053. |
[3] |
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), 249-271.
doi: 10.1080/17513750701450227. |
[4] |
R. S. Cantrell, C. Cosner and Y. Lou, Evolutionary stability of ideal free dispersal strategies in patchy environments, Journaal of Mathematical Biology, 65 (2012), 943-965.
doi: 10.1007/s00285-011-0486-5. |
[5] |
M. E. Clark, T. G. Wolcott, D. L. Wolcott and A. H. Hines, Foraging behavior of an estuarine predator, the blue crab Callinectes sapidus in a patchy environment, Ecography, 23 (2000), 21-31. |
[6] |
S. Creel and N. M. Dreel, The African Wild Dog: Behavior, Ecology, and Conservation, Princeton University Press, 2002. |
[7] |
R. Cressman and V. Křivan, Migration dynamics for the ideal free distribution, The American Naturalist, 168 (2006), 384-397.
doi: 10.1086/506970. |
[8] |
R. Cressman and V. Křivan, Two-patch population models with adaptive dispersal: The effects of varying dispersal speeds, Journal of Mathematical Biology, 67 (2013), 329-358.
doi: 10.1007/s00285-012-0548-3. |
[9] |
R. Cressman, V. Křivan and J. Garay, Ideal free distributions, evolutionary games, and population dynamics in multiple-species environments, The American Naturalist, 164 (2004), 473-489.
doi: 10.1086/423827. |
[10] |
S. D. Fretwell and J. S. Calver, On territorial behavior and other factors influencing habitat distribution in birds, Acta Biotheoretica, 19 (1969), 37-44. |
[11] |
J. K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM Journal on Mathematical Analysis, 20 (1989), 388-395.
doi: 10.1137/0520025. |
[12] |
J. Hofbauer and K. Sigmund, Evolutionray Games and Population Dynamics, Cambridge University Press, 1998.
doi: 10.1017/CBO9781139173179. |
[13] |
C. S. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, Memoirs of the Entomological Society of Canada, 97 (1965), 5-60.
doi: 10.4039/entm9745fv. |
[14] |
V. Křivan, The Lotka-Volterra predator-prey model with foraging-predation risk trade-offs, The American Naturalist, 170 (2007), 771-782. |
[15] |
V. Křivan and R. Cressman, On evolutionary stability in predator-prey models with fast behavioral dynamics, Evolutionary Ecology Research, 11 (2009), 227-251. |
[16] |
Y. Kuang and Y. Takeuchi, Predator-prey dynamics in models of prey dispersal in two-patch environments, Mathematical Biosciences, 120 (1994), 77-98.
doi: 10.1016/0025-5564(94)90038-8. |
[17] |
S. A. Levin, Dispersion and population interactions, The American Naturalist, 108 (1974), 207-228.
doi: 10.1086/282900. |
[18] |
J. D. Murray, Mathematical Biology, I, An Introduction, Springer, 2002. |
[19] |
I. Scharf, E. Nulman, O. Ovadia and A. Bouskila, Efficiency evaluation of two competing foraging modes under different conditions, The American Naturalist, 168 (2006), 350-357.
doi: 10.1086/506921. |
[20] |
R. D. Seitz, R. N. Lipcius, A. H. Hines and D. B. Eggleston, Density-dependent predation, habitat variation, and the persistence of marine bivalve prey, Ecology, 82 (2001), 2435-2451. |
[21] |
J. E. Staddon, Adaptive Behaviour and Learning, CUP Archive, 1983. |
[22] |
C. Starr, R. Taggart, C. Evers and L. Starr, Biology: The Unity And Diversity of Life, Yolanda Cossio, 2009. |
[23] |
H. R. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM Journal on Mathematical Analysis, 24 (1993), 407-435.
doi: 10.1137/0524026. |
[24] |
W. Wang and Y. Takeuchi, Adaptation of prey and predators between patches, Journal of Theoretical Biology, 258 (2009), 603-613.
doi: 10.1016/j.jtbi.2009.02.014. |
[25] |
D. K. Wasko and M. Sasa, Food resources influence spatial ecology, habitat selection, and foraging behavior in an ambush-hunting snake (Viperidae: Bothrops asper): an experimental study, Zoology, 115 (2012), 179-187.
doi: 10.1016/j.zool.2011.10.001. |
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