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2018 | OriginalPaper | Buchkapitel

Coexistence in Three-Species Cyclic Competition: Lattice-Based Versus Lattice-Free Individual-Based Models

verfasst von : Aisling J. Daly, Ward Quaghebeur, Tim Depraetere, Jan M. Baetens, Bernard De Baets

Erschienen in: Cellular Automata

Verlag: Springer International Publishing

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Abstract

Individual-based modelling is an increasingly popular framework for modelling biological systems. Many of these models represent space as a lattice, imposing unrealistic limitations on the movement of the modelled individuals. We adapt existing models of three competing species by using a lattice-free approach, thereby improving the realism of the spatial dynamics. We retrieve the same qualitative dynamics as the lattice-based approach. However, by facilitating a higher spatial heterogeneity and allowing for small spatial refuges to form and persist, the maintenance of coexistence is promoted. This corresponds well with experimental results.

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Literatur
1.
Zurück zum Zitat Adamson, M.W., Morozov, A.Y.: Revising the role of species mobility in maintaining biodiversity in communities with cyclic competition. Bull. Math. Biol. 74(9), 2004–2031 (2012)MathSciNetCrossRef Adamson, M.W., Morozov, A.Y.: Revising the role of species mobility in maintaining biodiversity in communities with cyclic competition. Bull. Math. Biol. 74(9), 2004–2031 (2012)MathSciNetCrossRef
2.
Zurück zum Zitat Arsenault, D.J., Himmelman, J.H.: Size-related changes in vulnerability to predators and spatial refuge use by juvenile Iceland scallops Chlamys islandica. Mar. Ecol. Prog. Ser. 140(1–3), 115–122 (1996)CrossRef Arsenault, D.J., Himmelman, J.H.: Size-related changes in vulnerability to predators and spatial refuge use by juvenile Iceland scallops Chlamys islandica. Mar. Ecol. Prog. Ser. 140(1–3), 115–122 (1996)CrossRef
3.
Zurück zum Zitat Ashby, M.N., Rine, J., Mongodin, E.F., Nelson, K.E., Dimster-Denk, D.: Serial analysis of rRNA genes and the unexpected dominance of rare members of microbial communities. Appl. Environ. Microbiol. 73(14), 4532–4542 (2007)CrossRef Ashby, M.N., Rine, J., Mongodin, E.F., Nelson, K.E., Dimster-Denk, D.: Serial analysis of rRNA genes and the unexpected dominance of rare members of microbial communities. Appl. Environ. Microbiol. 73(14), 4532–4542 (2007)CrossRef
4.
Zurück zum Zitat Auchincloss, A.H., Riolo, R.L., Brown, D.G., Cook, J., Diez Roux, A.V.: An agent-based model of income inequalities in diet in the context of residential segregation. Am. J. Prev. Med. 40(3), 303–311 (2011)CrossRef Auchincloss, A.H., Riolo, R.L., Brown, D.G., Cook, J., Diez Roux, A.V.: An agent-based model of income inequalities in diet in the context of residential segregation. Am. J. Prev. Med. 40(3), 303–311 (2011)CrossRef
5.
Zurück zum Zitat Avelino, P.P., Bazeia, D., Losano, L., Menezes, J., de Oliveira, B.F.: Spiral patterns and biodiversity in lattice-free Lotka-Volterra models, pp. 1–5. arXiv preprint arXiv 1710 (2017) Avelino, P.P., Bazeia, D., Losano, L., Menezes, J., de Oliveira, B.F.: Spiral patterns and biodiversity in lattice-free Lotka-Volterra models, pp. 1–5. arXiv preprint arXiv 1710 (2017)
6.
Zurück zum Zitat Beppu, K., Izri, Z., Gohya, J., Eto, K., Ichikawa, M., Maeda, Y.T.: Geometry-driven collective ordering of bacterial vortices. Soft Matter 13(29), 5038–5043 (2017)CrossRef Beppu, K., Izri, Z., Gohya, J., Eto, K., Ichikawa, M., Maeda, Y.T.: Geometry-driven collective ordering of bacterial vortices. Soft Matter 13(29), 5038–5043 (2017)CrossRef
7.
Zurück zum Zitat Bernard, E.P., Krauth, W.: Two-step melting in two dimensions: first-order liquid-hexatic transition. Phys. Rev. Lett. 107(15), 155704 (2011)CrossRef Bernard, E.P., Krauth, W.: Two-step melting in two dimensions: first-order liquid-hexatic transition. Phys. Rev. Lett. 107(15), 155704 (2011)CrossRef
8.
Zurück zum Zitat Buss, L.W.: Competitive networks: nontransitive competitive relationships in cryptic coral reef environments. Am. Nat. 113(2), 223–234 (1979)CrossRef Buss, L.W.: Competitive networks: nontransitive competitive relationships in cryptic coral reef environments. Am. Nat. 113(2), 223–234 (1979)CrossRef
9.
Zurück zum Zitat Chang, H.C., Wang, L.C.: A simple proof of Thue’s theorem on circle packing, pp. 1–4. arXiv preprint arXiv 1708 (2010) Chang, H.C., Wang, L.C.: A simple proof of Thue’s theorem on circle packing, pp. 1–4. arXiv preprint arXiv 1708 (2010)
10.
Zurück zum Zitat Finke, D.L., Denno, R.F.: Spatial refuge from intraguild predation: implications for prey suppression and trophic cascades. Oecologia 149(2), 265–275 (2006)CrossRef Finke, D.L., Denno, R.F.: Spatial refuge from intraguild predation: implications for prey suppression and trophic cascades. Oecologia 149(2), 265–275 (2006)CrossRef
11.
Zurück zum Zitat Ginovart, M.: INDISIM, an individual-based discrete simulation model to study bacterial cultures. J. Theor. Biol. 214(2), 305–319 (2002)CrossRef Ginovart, M.: INDISIM, an individual-based discrete simulation model to study bacterial cultures. J. Theor. Biol. 214(2), 305–319 (2002)CrossRef
12.
Zurück zum Zitat Gonnella, G., Lamura, A., Suma, A.: Phase segregation in a system of active dumbbells. Int. J. Mod. Phys. C 25(12), 1441004 (2014)CrossRef Gonnella, G., Lamura, A., Suma, A.: Phase segregation in a system of active dumbbells. Int. J. Mod. Phys. C 25(12), 1441004 (2014)CrossRef
13.
Zurück zum Zitat Grimm, V., Berger, U., DeAngelis, D.L., Polhill, J.G., Giske, J., Railsback, S.F.: The ODD protocol: a review and first update. Ecol. Model. 221(23), 2760–2768 (2010)CrossRef Grimm, V., Berger, U., DeAngelis, D.L., Polhill, J.G., Giske, J., Railsback, S.F.: The ODD protocol: a review and first update. Ecol. Model. 221(23), 2760–2768 (2010)CrossRef
14.
Zurück zum Zitat Hurlbert, S.H.: The measurement of niche overlap and some relatives. Ecology 59(1), 67–77 (1978)CrossRef Hurlbert, S.H.: The measurement of niche overlap and some relatives. Ecology 59(1), 67–77 (1978)CrossRef
15.
Zurück zum Zitat Kerr, B., Riley, M.A., Feldman, M.W., Bohannan, B.J.M.: Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors. Nature 418(6894), 171–174 (2002)CrossRef Kerr, B., Riley, M.A., Feldman, M.W., Bohannan, B.J.M.: Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors. Nature 418(6894), 171–174 (2002)CrossRef
16.
Zurück zum Zitat Kirkup, B.C., Riley, M.A.: Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo. Nature 428(6981), 412–414 (2004)CrossRef Kirkup, B.C., Riley, M.A.: Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo. Nature 428(6981), 412–414 (2004)CrossRef
17.
Zurück zum Zitat Kreft, J.U., Booth, G., Wimpenny, J.W.T.: BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144(12), 3275–3287 (1998)CrossRef Kreft, J.U., Booth, G., Wimpenny, J.W.T.: BacSim, a simulator for individual-based modelling of bacterial colony growth. Microbiology 144(12), 3275–3287 (1998)CrossRef
18.
Zurück zum Zitat Kreft, J.U., Picioreanu, C., Wimpenny, J.W.T., van Loosdrecht, M.C.M.: Individual-based modelling of biofilms. Microbiology 147(Pt 11), 2897–2912 (2001)CrossRef Kreft, J.U., Picioreanu, C., Wimpenny, J.W.T., van Loosdrecht, M.C.M.: Individual-based modelling of biofilms. Microbiology 147(Pt 11), 2897–2912 (2001)CrossRef
19.
Zurück zum Zitat Laird, R.A., Schamp, B.S.: Does local competition increase the coexistence of species in intransitive networks? Ecology 89(1), 237–247 (2008)CrossRef Laird, R.A., Schamp, B.S.: Does local competition increase the coexistence of species in intransitive networks? Ecology 89(1), 237–247 (2008)CrossRef
20.
Zurück zum Zitat Laird, R.A., Schamp, B.S.: Species coexistence, intransitivity, and topological variation in competitive tournaments. J. Theor. Biol. 256(1), 90–95 (2009)MathSciNetCrossRef Laird, R.A., Schamp, B.S.: Species coexistence, intransitivity, and topological variation in competitive tournaments. J. Theor. Biol. 256(1), 90–95 (2009)MathSciNetCrossRef
21.
Zurück zum Zitat Landau, L., Lifshitz, E.: EM Lifshitz Theory of Elasticity, 3rd edn. Pergamon Press, Oxford (1986) Landau, L., Lifshitz, E.: EM Lifshitz Theory of Elasticity, 3rd edn. Pergamon Press, Oxford (1986)
22.
23.
Zurück zum Zitat Luisa, M., et al.: Mitigation measures for pandemic influenza in Italy: an individual-based model considering different scenarios. PLOS One 3(3), e1790 (2008)CrossRef Luisa, M., et al.: Mitigation measures for pandemic influenza in Italy: an individual-based model considering different scenarios. PLOS One 3(3), e1790 (2008)CrossRef
24.
Zurück zum Zitat Mattson, W., Rice, B.M.: Near-neighbor calculations using a modified cell-linked list method. Comput. Phys. Commun. 119(2), 135–148 (1999)CrossRef Mattson, W., Rice, B.M.: Near-neighbor calculations using a modified cell-linked list method. Comput. Phys. Commun. 119(2), 135–148 (1999)CrossRef
25.
Zurück zum Zitat May, R.M., Leonard, W.J.: Nonlinear aspects of competition between three species. Soc. Ind. Appl. Math. 29(2), 243–253 (1975)MathSciNetCrossRef May, R.M., Leonard, W.J.: Nonlinear aspects of competition between three species. Soc. Ind. Appl. Math. 29(2), 243–253 (1975)MathSciNetCrossRef
26.
Zurück zum Zitat Neuhauser, C.: Mathematical challenges in spatial ecology. Not. AMS 48(11), 1304–1314 (2001)MathSciNetMATH Neuhauser, C.: Mathematical challenges in spatial ecology. Not. AMS 48(11), 1304–1314 (2001)MathSciNetMATH
27.
Zurück zum Zitat Osborne, J.M., Fletcher, A.G., Pitt-Francis, J.M., Maini, P.K., Gavaghan, D.J.: Comparing individual-based approaches to modelling the self-organization of multicellular tissues. PLOS Comput. Biol. 13(2), 1–34 (2017)CrossRef Osborne, J.M., Fletcher, A.G., Pitt-Francis, J.M., Maini, P.K., Gavaghan, D.J.: Comparing individual-based approaches to modelling the self-organization of multicellular tissues. PLOS Comput. Biol. 13(2), 1–34 (2017)CrossRef
28.
Zurück zum Zitat Railsback, S.F., Grimm, V.: Agent-Based and Individual-Based Modeling: A Practical Introduction. Princeton University Press, Princeton (2011)MATH Railsback, S.F., Grimm, V.: Agent-Based and Individual-Based Modeling: A Practical Introduction. Princeton University Press, Princeton (2011)MATH
29.
Zurück zum Zitat Railsback, S.F., Lytinen, S.L., Jackson, S.K.: Agent-based simulation platforms: review and development recommendations. Simulation 82(9), 609–623 (2006)CrossRef Railsback, S.F., Lytinen, S.L., Jackson, S.K.: Agent-based simulation platforms: review and development recommendations. Simulation 82(9), 609–623 (2006)CrossRef
30.
Zurück zum Zitat Reichenbach, T., Mobilia, M., Frey, E.: Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448(7157), 1046–1049 (2007)CrossRef Reichenbach, T., Mobilia, M., Frey, E.: Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature 448(7157), 1046–1049 (2007)CrossRef
31.
Zurück zum Zitat Schelling, T.C.: Dynamic models of segregation. J. Math. Sociol. 1(2), 143–186 (1969)CrossRef Schelling, T.C.: Dynamic models of segregation. J. Math. Sociol. 1(2), 143–186 (1969)CrossRef
32.
Zurück zum Zitat Taylor, D.R., Aarssen, L.W.: Complex competitive relationships among genotypes of three perennial grasses: implications for species coexistence. Am. Nat. 136(3), 305–327 (1990)CrossRef Taylor, D.R., Aarssen, L.W.: Complex competitive relationships among genotypes of three perennial grasses: implications for species coexistence. Am. Nat. 136(3), 305–327 (1990)CrossRef
33.
Zurück zum Zitat Touhami, A., Nysten, B., Dufrêne, Y.: Nanoscale mapping of the elasticity of microbial cells by atomic force microscopy. Microbiology 19(11), 4539–4543 (2003) Touhami, A., Nysten, B., Dufrêne, Y.: Nanoscale mapping of the elasticity of microbial cells by atomic force microscopy. Microbiology 19(11), 4539–4543 (2003)
34.
Zurück zum Zitat Verlet, L.: Computer “experiments” on classical fluids. Phys. Rev. 159(1), 98–103 (1967)CrossRef Verlet, L.: Computer “experiments” on classical fluids. Phys. Rev. 159(1), 98–103 (1967)CrossRef
35.
Zurück zum Zitat Vukov, J., Szolnoki, A., Szabó, G.: Diverging fluctuations in a spatial five-species cyclic dominance game. Phys. Rev. E - Statist. Nonlinear Soft Matter Phys. 88(2), 1–8 (2013)CrossRef Vukov, J., Szolnoki, A., Szabó, G.: Diverging fluctuations in a spatial five-species cyclic dominance game. Phys. Rev. E - Statist. Nonlinear Soft Matter Phys. 88(2), 1–8 (2013)CrossRef
36.
Zurück zum Zitat Wilsey, B.J.: Realistically low species evenness does not alter grassland species-richness - productivity relationships. Ecology 85(10), 2693–2700 (2004)CrossRef Wilsey, B.J.: Realistically low species evenness does not alter grassland species-richness - productivity relationships. Ecology 85(10), 2693–2700 (2004)CrossRef
Metadaten
Titel
Coexistence in Three-Species Cyclic Competition: Lattice-Based Versus Lattice-Free Individual-Based Models
verfasst von
Aisling J. Daly
Ward Quaghebeur
Tim Depraetere
Jan M. Baetens
Bernard De Baets
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-99813-8_10

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