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Dragging in mutualistic networks
A simple and bounded model of population dynamics for mutualistic networks
1. | Complex System Group, Technical University of Madrid, Av. Puerta Hierro 4, 28040-Madrid |
2. | Área de Biodiversidad y Conservación, Dept. Biología y Geología, Universidad Rey Juan Carlos, 28933 Móstoles, Spain |
3. | Instituto de Física Interdisciplinar y Sistemas Complejos IFISC (CSIC-UIB), 07122 Palma de Mallorca |
References:
[1] |
D. Balcan, V. Colizza, B. Gonçalves, H. Hu, J. J. Ramasco and A. Vespignani, Multiscale mobility networks and the spatial spreading of infectious diseases, Proceedings of the National Academy of Sciences USA, 106 (2009), 21484-21489.
doi: 10.1073/pnas.0906910106. |
[2] |
J. Bascompte and P. Jordano, Plant-animal mutualistic networks: The architecture of biodiversity, The Annual Review of Ecology, Evolution, and Systematics, 38 (2007), 567-593.
doi: 10.1146/annurev.ecolsys.38.091206.095818. |
[3] |
U. Bastolla, M. A. Fortuna, A. Pascual-García, A. Ferrera, B. Luque and J. Bascompte, The architecture of mutualistic networks minimizes competition and increases biodiversity, Nature, 458 (2009), 1018-1020.
doi: 10.1038/nature07950. |
[4] |
U. Bastolla, M. Lässig, S. C. Manrubia and A. Valleriani, Biodiversity in model ecosystems, II: Species assembly and food web structure, Journal of Theoretical Biology, 235 (2005), 531-539.
doi: 10.1016/j.jtbi.2005.02.006. |
[5] |
W. Feller, On the logistic law of growth and its empirical verifications in biology, Acta Biotheoretica, 5 (1940), 51-66.
doi: 10.1007/BF01602862. |
[6] |
J. P. Gabriel, F. Saucy and L. F. Bersier, Paradoxes in the logistic equation?, Ecological Modelling, 185 (2005), 147-151.
doi: 10.1016/j.ecolmodel.2004.10.009. |
[7] |
J. R. Groff, Exploring dynamical systems and chaos using the logistic map model of population change, American Journal of Physics, 81 (2013), 725-732.
doi: 10.1119/1.4813114. |
[8] |
L. Gustafsson and M. Sternad, Bringing consistency to simulation of population models-Poisson simulation as a bridge between micro and macro simulation, Mathematical Biosciences, 209 (2007), 361-385.
doi: 10.1016/j.mbs.2007.02.004. |
[9] |
C. A. Johnson and P. Amarasekare, Competitionfor benefits can promote the persistence of mutualistics interactions, Journal of Theoretical Biology, 328 (2013), 54-64.
doi: 10.1016/j.jtbi.2013.03.016. |
[10] |
E. Kuno, Some strange properties of the logistic equation defined with r and k: Inherent defects or artifacts?, Researches on population ecology, 14 (1991), 33-39. |
[11] |
T. R. Malthus, An Essay on the Principle of Population or a View of Its Past and Present Effects on Human Happiness; with an Inquiry into Our Prospects Respecting the Future Removal on Mitigation of the Evils which It Occasions, 1st edition, Roger Chew Weightman, Washington, 1798. Available from: http://opac.newsbank.com/select/shaw/17975. |
[12] |
R. May, Models for two interacting populations, in Theoretical Ecology. Principles and Applications, $2^{nd}$ edition (ed. R. May), 1981, 78-104. |
[13] |
J. D. Murray, Mathematical Biology I: An Introduction, $3^{rd}$ edition, Springer-Verlag, New York, 2002. |
[14] |
R. Pearl, The biology of population growth, Zeitschrift für Induktive Abstammungs- und Vererbungslehre, 49 (1929), 336-338.
doi: 10.1007/BF01847581. |
[15] |
E. Stokstad, Will malthus continue to be wrong?, Science, 309 (2005), p102.
doi: 10.1126/science.309.5731.102. |
[16] |
P. F. Verhulst, Recherches mathematiques sur la loi d'accroissement de la population [Mathematical researches into the law of population growth increase], Nouveaux Memoires de l'Academie Royale des Sciences et Belles-Lettres de Bruxelles, 18 (1845), 1-42. |
[17] |
V. Volterra, Fluctuations in the abundance of a species considered mathematically, Nature, 118 (1926), 558-560.
doi: 10.1038/118558a0. |
[18] |
D. H. Wright, A simple, stable model of mutualism incorporating handling time, The American Naturalist, 134 (1989), 664-667.
doi: 10.1086/285003. |
show all references
References:
[1] |
D. Balcan, V. Colizza, B. Gonçalves, H. Hu, J. J. Ramasco and A. Vespignani, Multiscale mobility networks and the spatial spreading of infectious diseases, Proceedings of the National Academy of Sciences USA, 106 (2009), 21484-21489.
doi: 10.1073/pnas.0906910106. |
[2] |
J. Bascompte and P. Jordano, Plant-animal mutualistic networks: The architecture of biodiversity, The Annual Review of Ecology, Evolution, and Systematics, 38 (2007), 567-593.
doi: 10.1146/annurev.ecolsys.38.091206.095818. |
[3] |
U. Bastolla, M. A. Fortuna, A. Pascual-García, A. Ferrera, B. Luque and J. Bascompte, The architecture of mutualistic networks minimizes competition and increases biodiversity, Nature, 458 (2009), 1018-1020.
doi: 10.1038/nature07950. |
[4] |
U. Bastolla, M. Lässig, S. C. Manrubia and A. Valleriani, Biodiversity in model ecosystems, II: Species assembly and food web structure, Journal of Theoretical Biology, 235 (2005), 531-539.
doi: 10.1016/j.jtbi.2005.02.006. |
[5] |
W. Feller, On the logistic law of growth and its empirical verifications in biology, Acta Biotheoretica, 5 (1940), 51-66.
doi: 10.1007/BF01602862. |
[6] |
J. P. Gabriel, F. Saucy and L. F. Bersier, Paradoxes in the logistic equation?, Ecological Modelling, 185 (2005), 147-151.
doi: 10.1016/j.ecolmodel.2004.10.009. |
[7] |
J. R. Groff, Exploring dynamical systems and chaos using the logistic map model of population change, American Journal of Physics, 81 (2013), 725-732.
doi: 10.1119/1.4813114. |
[8] |
L. Gustafsson and M. Sternad, Bringing consistency to simulation of population models-Poisson simulation as a bridge between micro and macro simulation, Mathematical Biosciences, 209 (2007), 361-385.
doi: 10.1016/j.mbs.2007.02.004. |
[9] |
C. A. Johnson and P. Amarasekare, Competitionfor benefits can promote the persistence of mutualistics interactions, Journal of Theoretical Biology, 328 (2013), 54-64.
doi: 10.1016/j.jtbi.2013.03.016. |
[10] |
E. Kuno, Some strange properties of the logistic equation defined with r and k: Inherent defects or artifacts?, Researches on population ecology, 14 (1991), 33-39. |
[11] |
T. R. Malthus, An Essay on the Principle of Population or a View of Its Past and Present Effects on Human Happiness; with an Inquiry into Our Prospects Respecting the Future Removal on Mitigation of the Evils which It Occasions, 1st edition, Roger Chew Weightman, Washington, 1798. Available from: http://opac.newsbank.com/select/shaw/17975. |
[12] |
R. May, Models for two interacting populations, in Theoretical Ecology. Principles and Applications, $2^{nd}$ edition (ed. R. May), 1981, 78-104. |
[13] |
J. D. Murray, Mathematical Biology I: An Introduction, $3^{rd}$ edition, Springer-Verlag, New York, 2002. |
[14] |
R. Pearl, The biology of population growth, Zeitschrift für Induktive Abstammungs- und Vererbungslehre, 49 (1929), 336-338.
doi: 10.1007/BF01847581. |
[15] |
E. Stokstad, Will malthus continue to be wrong?, Science, 309 (2005), p102.
doi: 10.1126/science.309.5731.102. |
[16] |
P. F. Verhulst, Recherches mathematiques sur la loi d'accroissement de la population [Mathematical researches into the law of population growth increase], Nouveaux Memoires de l'Academie Royale des Sciences et Belles-Lettres de Bruxelles, 18 (1845), 1-42. |
[17] |
V. Volterra, Fluctuations in the abundance of a species considered mathematically, Nature, 118 (1926), 558-560.
doi: 10.1038/118558a0. |
[18] |
D. H. Wright, A simple, stable model of mutualism incorporating handling time, The American Naturalist, 134 (1989), 664-667.
doi: 10.1086/285003. |
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