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A mutualism-parasitism system modeling host and parasite with mutualism at low density
1. | School of Mathematics and Computational Science, Sun Yat-sen University, Guangzhou 510275, China |
2. | US Geological Survey/Biological Resources Division and Department of Biology, University of Miami, Coral Gables, FL 33124, United States |
References:
[1] |
A. J. Belsky, Does herbivory benefit plants? A review of the evidence, American Naturalist, 127 (1986), 870-892.
doi: 10.1086/284531. |
[2] |
R. S. Cantrell, C. Cosner and S. Ruan, Intraspecific interference and consumer-resource dynamics, Discrete and Continuous Dynamical Systems Ser. B, 4 (2004), 527-546.
doi: 10.3934/dcdsb.2004.4.527. |
[3] |
M. I. Dyer, M. L. Turner and T. R. Seastedt, Herbivory and its consequences, Ecological Applications, 3 (1993), 10-16.
doi: 10.2307/1941781. |
[4] |
A. J. Lotka, "Elements of Physiological Biology," Dover Publications, New York, 1956. |
[5] |
J. Herrera, Acorn predation and seedling production in a low-density population of cork oak (Quercus suber L.), Forest Ecology and Management, 76 (1995), 197-201.
doi: 10.1016/0378-1127(95)03566-S. |
[6] |
D. W. Hilbert, D. M. Smith, J. K. Detling and M. I. Dyer, Relative growth rates and the grazing optimization hypothesis, Oecologia, 51 (1981), 14-18.
doi: 10.1007/BF00344645. |
[7] |
J. Hofbauer and K. Sigmund, "Evolutionary Games and Population Dynamics," Cambridge University Press, Cambridge, 1998. |
[8] |
J. N. Holland and D. L. DeAngelis, Consumer-resource theory predicts dynamic transitions between outcomes of interspecific interactions, Ecological Letters, 12 (2009), 1357-1366. |
[9] |
J. N. Holland and D. L. DeAngelis, A consumer-resource approach to the density-dependent population dynamics of mutualism, Ecology, 5 (2010), 1286-1295.
doi: 10.1890/09-1163.1. |
[10] |
K. Kielland, J. P. Bryant and R. W. Ruess, Moose herbivory and carbon turnover of early successional stands in interior Alaska, Oikos, 80 (1997), 25-30.
doi: 10.2307/3546512. |
[11] |
Y. Li, Z. L. Feng, R. Swihart, J. P. Bryant and N. Huntly, Modeling the impact of plant toxicity on plant-herbivore dynamics, Journal of Dynamics and Differential Equations, 18 (2006), 1021-1024.
doi: 10.1007/s10884-006-9029-y. |
[12] |
R. M. May, "Stability and Complexity in Model Ecosystems," Princeton University Press, Princeton, 1974. |
[13] |
S. J. McNaughton, Serengeti migratory wildebeest: Facilitation of energy flow by grazing, Science, 191 (1976), 92-94.
doi: 10.1126/science.191.4222.92. |
[14] |
S. J. McNaughton, Grazing as an optimization process: Grass-ungulate relationships in the Serengeti, American Naturalist, 113 (1979), 691-703.
doi: 10.1086/283426. |
[15] |
M. Miyaki and K. Kikuzawa, Dispersal of Quercus mongolica acorns in a broad-leaved deciduous forest. 2. Scatterhoarding by mice, Forest Ecology and Management, 25 (1988), 9-16.
doi: 10.1016/0378-1127(88)90130-2. |
[16] |
E. M. Molvar and R. T. Bowyer, Costs and benefits of group living in a recently social ungulate: The Alaskan moose, Journal of Mammalogy, 75 (1994), 621-630.
doi: 10.2307/1382509. |
[17] |
J. D. Murray, "Mathematical Biology," Second edition, Biomathematics, 19, Springer-Verlag, Berlin, 1993. |
[18] |
C. Neuhauser and J. Fargione, A mutualism-parasitism continuum model and its application to plant-mycorrhizae interactions, Ecological Modelling, 177 (2004), 337-352.
doi: 10.1016/j.ecolmodel.2004.02.010. |
[19] |
I. M. Pérez-Ramos and T. Maran, Factors affecting post-dispersal seed predation in two coexisting oak species: Microhabitat, burial and exclusion of large herbivores, Forest Ecology and Management, 255 (2008), 3506-3514.
doi: 10.1016/j.foreco.2008.02.032. |
[20] |
Y. Wang, H. Wu and S. Ruan, Periodic orbits near heteroclinic cycles in a cyclic replicator system, J. Math. Biol., in press.
doi: 10.1007/s00285-011-0435-3. |
[21] |
Y. Wang, D. L. DeAngelis and J. N. Holland, Uni-directional consumer-resource theory characterizing transitions of interaction outcomes, Ecological Complexity, 8 (2011), 249-257.
doi: 10.1016/j.ecocom.2011.04.002. |
[22] |
Y. Wang and D. L. DeAngelis, Transitions of interaction outcomes in a uni-directional consumer-resource system, J. Theoretical Biology, 280 (2011), 43-49.
doi: 10.1016/j.jtbi.2011.03.038. |
[23] |
Y. Wang and H. Wu, A mutualism-competition model characterizing competitors with mutualism at low density, Mathematical and Computer Modeling, 53 (2011), 1654-1663.
doi: 10.1016/j.mcm.2010.12.033. |
[24] |
K. M. Stewart, R. T. Bowyer, R. W. Ruess, B. L. Dick and J. G. Kie, Herbivore optimization by North American elk: Consequences for theory and management, Wildlife Monographs, 167 (2006), 1-24. |
[25] |
V. Volterra, Fluctuation in the abundance of a species considered mathematically, Nature, 118 (1926), 558-560.
doi: 10.1038/118558a0. |
show all references
References:
[1] |
A. J. Belsky, Does herbivory benefit plants? A review of the evidence, American Naturalist, 127 (1986), 870-892.
doi: 10.1086/284531. |
[2] |
R. S. Cantrell, C. Cosner and S. Ruan, Intraspecific interference and consumer-resource dynamics, Discrete and Continuous Dynamical Systems Ser. B, 4 (2004), 527-546.
doi: 10.3934/dcdsb.2004.4.527. |
[3] |
M. I. Dyer, M. L. Turner and T. R. Seastedt, Herbivory and its consequences, Ecological Applications, 3 (1993), 10-16.
doi: 10.2307/1941781. |
[4] |
A. J. Lotka, "Elements of Physiological Biology," Dover Publications, New York, 1956. |
[5] |
J. Herrera, Acorn predation and seedling production in a low-density population of cork oak (Quercus suber L.), Forest Ecology and Management, 76 (1995), 197-201.
doi: 10.1016/0378-1127(95)03566-S. |
[6] |
D. W. Hilbert, D. M. Smith, J. K. Detling and M. I. Dyer, Relative growth rates and the grazing optimization hypothesis, Oecologia, 51 (1981), 14-18.
doi: 10.1007/BF00344645. |
[7] |
J. Hofbauer and K. Sigmund, "Evolutionary Games and Population Dynamics," Cambridge University Press, Cambridge, 1998. |
[8] |
J. N. Holland and D. L. DeAngelis, Consumer-resource theory predicts dynamic transitions between outcomes of interspecific interactions, Ecological Letters, 12 (2009), 1357-1366. |
[9] |
J. N. Holland and D. L. DeAngelis, A consumer-resource approach to the density-dependent population dynamics of mutualism, Ecology, 5 (2010), 1286-1295.
doi: 10.1890/09-1163.1. |
[10] |
K. Kielland, J. P. Bryant and R. W. Ruess, Moose herbivory and carbon turnover of early successional stands in interior Alaska, Oikos, 80 (1997), 25-30.
doi: 10.2307/3546512. |
[11] |
Y. Li, Z. L. Feng, R. Swihart, J. P. Bryant and N. Huntly, Modeling the impact of plant toxicity on plant-herbivore dynamics, Journal of Dynamics and Differential Equations, 18 (2006), 1021-1024.
doi: 10.1007/s10884-006-9029-y. |
[12] |
R. M. May, "Stability and Complexity in Model Ecosystems," Princeton University Press, Princeton, 1974. |
[13] |
S. J. McNaughton, Serengeti migratory wildebeest: Facilitation of energy flow by grazing, Science, 191 (1976), 92-94.
doi: 10.1126/science.191.4222.92. |
[14] |
S. J. McNaughton, Grazing as an optimization process: Grass-ungulate relationships in the Serengeti, American Naturalist, 113 (1979), 691-703.
doi: 10.1086/283426. |
[15] |
M. Miyaki and K. Kikuzawa, Dispersal of Quercus mongolica acorns in a broad-leaved deciduous forest. 2. Scatterhoarding by mice, Forest Ecology and Management, 25 (1988), 9-16.
doi: 10.1016/0378-1127(88)90130-2. |
[16] |
E. M. Molvar and R. T. Bowyer, Costs and benefits of group living in a recently social ungulate: The Alaskan moose, Journal of Mammalogy, 75 (1994), 621-630.
doi: 10.2307/1382509. |
[17] |
J. D. Murray, "Mathematical Biology," Second edition, Biomathematics, 19, Springer-Verlag, Berlin, 1993. |
[18] |
C. Neuhauser and J. Fargione, A mutualism-parasitism continuum model and its application to plant-mycorrhizae interactions, Ecological Modelling, 177 (2004), 337-352.
doi: 10.1016/j.ecolmodel.2004.02.010. |
[19] |
I. M. Pérez-Ramos and T. Maran, Factors affecting post-dispersal seed predation in two coexisting oak species: Microhabitat, burial and exclusion of large herbivores, Forest Ecology and Management, 255 (2008), 3506-3514.
doi: 10.1016/j.foreco.2008.02.032. |
[20] |
Y. Wang, H. Wu and S. Ruan, Periodic orbits near heteroclinic cycles in a cyclic replicator system, J. Math. Biol., in press.
doi: 10.1007/s00285-011-0435-3. |
[21] |
Y. Wang, D. L. DeAngelis and J. N. Holland, Uni-directional consumer-resource theory characterizing transitions of interaction outcomes, Ecological Complexity, 8 (2011), 249-257.
doi: 10.1016/j.ecocom.2011.04.002. |
[22] |
Y. Wang and D. L. DeAngelis, Transitions of interaction outcomes in a uni-directional consumer-resource system, J. Theoretical Biology, 280 (2011), 43-49.
doi: 10.1016/j.jtbi.2011.03.038. |
[23] |
Y. Wang and H. Wu, A mutualism-competition model characterizing competitors with mutualism at low density, Mathematical and Computer Modeling, 53 (2011), 1654-1663.
doi: 10.1016/j.mcm.2010.12.033. |
[24] |
K. M. Stewart, R. T. Bowyer, R. W. Ruess, B. L. Dick and J. G. Kie, Herbivore optimization by North American elk: Consequences for theory and management, Wildlife Monographs, 167 (2006), 1-24. |
[25] |
V. Volterra, Fluctuation in the abundance of a species considered mathematically, Nature, 118 (1926), 558-560.
doi: 10.1038/118558a0. |
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