Revising the Role of Species Mobility in Maintaining Biodiversity in Communities with Cyclic Competition

Bulletin of Mathematical Biology

Volumn 74, Issue 9, 2012, Pages 2004-2031

  Adamson, M W ^a   Morozov, A Y ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

Co invasion; Complexity; Dispersal rate; Excitable system; Homogeneous environment; Patterns of spread; Spatial ecology; Spatiotemporal chaos; Spiral waves

Indexed keywords

EID: 84864766997     PISSN: 00928240     EISSN: 15229602     Source Type: Journal    
DOI: 10.1007/s11538-012-9743-z     Document Type: Article

References (78)

1. Alzahrani, E. O., Davidson, F. A., & Dodds, N. (2010). Travelling waves in near-degenerate bistable competition models. Math. Model. Nat. Phenom., 5(5), 13-35.
2. Alzahrani, E. O., Davidson, F. A., & Dodds, N. (2011). Reversing invasion in bistable systems. J. Math. Biol. doi: 10. 1007/s00285-011-0490-9.
3. Amarasekare, P. (2003). Competitive coexistence in spatially structured environments: A synthesis. Ecol. Lett., 6, 1109-1122.
4. Boerlijst, M. C., & Hogeweg, P. (1995). Spatial gradients enhance persistence of hypercycles. Physica D, 88, 29-39.
5. Boerlijst, M. C., Lamers, M. E., & Hogeweg, P. (1993). Evolutionary consequences of spiral waves in a host-parasitoid system. Proc. R. Soc. Lond. B, 253, 15-18.
6. Buss, L. W., & Jackson, J. B. (1979). Competitive networks: Nontransitive competitive relationships in cryptic coral reef environments. Am. Nat., 113, 223-234.
7. Cameron, D. D., White, A., & Antonovics, J. (2009). Parasite-grass-forb interactions and rock-paper-scissor dynamics: Predicting the effects of the parasitic plant Rhinanthus minor on host plant communities. J. Ecol., 97, 1311-1319.
8. Cantrell, R. S., & Cosner, C. (2003). Spatial ecology via reaction-diffusion equations. Chichester: Wiley.
9. Chesson, P. (2000). Mechanisms of maintenance of species diversity. Annu. Rev. Ecol. Syst., 31, 342-366.
10. Crosby, A. W. (1986). Ecological imperialism. The biological expansion of Europe, 900-1900. Cambridge: Cambridge University Press.
11. Davis, M. B., Calcote, R. R., Sugita, S., & Takahara, H. (1998). Patchy invasion and the origin of a hemlock-hardwoods forest mosaic. Ecology, 79, 2641-2659.
12. Ducharme, M. B., Larochelle, J., & Richard, D. (1989). Thermogenic capacity in gray and black morphs of the gray squirrel, Sciurus Carolinensis. Physiol. Zool., 62, 1273-1292.
13. Durrett, R., & Levin, S. (1998). Spatial aspects of interspecific competition. Theor. Popul. Biol., 53, 30-43.
14. Frachebourg, L., Krapivsky, P. L., & Ben-Naim, E. (1996). Spatial organization in cyclic Lotka-Volterra systems. Phys. Rev. E, 54, 6186-6200.
15. Frean, M., & Abraham, R. (2001). Rock-scissors-paper and the survival of the weakest. Proc. R. Soc. Lond. B, 268, 1323-1327.
16. Gause, G. F. (1934). The struggle for existence. New York: Hafner Publishing Company.
17. Gilpin, M. E. (1975). Limit cycles in competition communities. Am. Nat., 109, 51-60.
18. Gurney, W. S. C., Veitch, A. R., Cruickshank, I., & McGeachin, G. (1998). Circles and spirals: Population persistence in a spatially explicit predator-prey model. Ecology, 79, 2516-2530.
19. Hanski, I. (1994). Spatial scale, patchiness and population dynamics on land. Philos. Trans. R. Soc. Lond. B, 343, 19-25.
20. Hardin, G. (1960). The competitive exclusion principle. Science, 131, 1292-1298.
21. Hauert, C., De Monte, S., Hofbauer, J., & Sigmund, K. (2002). Replicator dynamics for optional public good games. J. Theor. Biol., 218, 187-194.
22. Hosono, Y. (1998). The minimal speed of traveling fronts for a diffusive Lotka-Volterra competition model. Bull. Math. Biol., 60, 435-448.
23. Huisman, J., Johansson, A. M., Folmer, E. O., & Weissing, F. J. (2001). Towards a solution of the plankton paradox: The importance of physiology and life history. Ecol. Lett., 4, 408-411.
24. Hutchinson, G. E. (1961). The paradox of the plankton. Am. Nat., 95, 137-145.
25. Ikeda, H. (2001). Multiple travelling wave solutions of three-component systems with competition and diffusion. Methods Appl. Anal., 8(3), 479-496.
26. Ives, A. R., & Carpenter, S. R. (2007). Stability and diversity of ecosystems. Science, 317, 58.
27. Jackson, J. B. C., & Buss, L. W. (1975). Allelopathy and spatial competition among coral reef invertebrates. Proc. Natl. Acad. Sci. USA, 72, 5160-5163.
28. Jiang, L., Zhou, T., Perc, M., & Wang, B. (2011). Effects of competition on pattern formation in the rock-paper-scissors game. Phys. Rev. E, 84, 021912.
29. Károlyi, G., Neufeld, Z., & Scheuring, I. (2005). Rock-scissors-paper game in a chaotic flow: The effect of dispersion on the cyclic competition of microorganisms. J. Theor. Biol., 236, 12-20.
30. Kerr, B., Riley, M. A., Feldman, M. W., & Bohannan, J. M. (2002). Local dispersal promotes biodiversity in a real-life game of rock-paper-scissors. Nature, 418, 171-174.
31. Kim, P. J., Jeong, H. (2005). Spatio-temporal dynamics in the origin of genetic information. Physica D, 203, 88-99.
32. Kirkup, B. C., & Riley, M. A. (2004). Antibiotic-mediated antagonism leads to a bacterial game of rock-paper-scissors in vivo. Nature, 428, 412-414.
33. Kolb, A., & Alpert, P. (2003). Effects of nitrogen and salinity on growth and competition between a native grass and an invasive congener. Biol. Invasions, 5, 229-238.
34. Laird, R. A., & Schamp, B. S. (2008). Does local competition increase the coexistence of species in intransitive networks? Ecology, 89, 237-247.
35. Levin, P. S., Coyer, J. A., Petrik, R., & Good, T. P. (2002). Community-wide effects of nonindigenous species on temperate rocky reefs. Ecology, 83, 3182-3193.
36. Levine, J. M., & Hille Ris Lambers, J. (2010). The importance of niches for the maintenance of species diversity. Nature, 461, 254-257.
37. Lewis, M. A. (2000). Spread rate for a nonlinear stochastic invasion. J. Math. Biol., 41, 430-454.
38. Lewis, M. A., & Pacala, S. (2000). Modeling and analysis of stochastic invasion processes. J. Math. Biol., 41, 387-429.
39. Lewis, M., Li, B., & Weinberger, H. F. (2002). Spreading speed and linear determinacy for two-species competition models. J. Math. Biol., 45, 219-233.
40. MacArthur, R., & Levins, R. (1967). The limiting similarity, convergence, and divergence of coexisting species. Am. Nat., 101(921), 377-385.
41. May, R. M., & Leonard, W. J. (1975). Nonlinear aspects of competition between three species. SIAM J. Appl. Math., 29, 243-253.
42. Merino, S. (1996). Cyclic competition of three species in the time periodic and diffusive case. J. Math. Biol., 34, 789-809.
43. Metz, J. A. J., Nisbet, R. M., & Geritz, S. A. H. (1992). How should we define fitness for general ecological scenarios. Trends Ecol. Evol., 7, 198-202.
44. Moen, J. (1989). Diffuse competition: A diffuse concept. Oikos, 54, 260-263.
45. Morozov, A. Yu., & Li, B.-L. (2007). On the importance of dimensionality of space in models of space-mediated population persistence. Theor. Popul. Biol., 71, 278-289.
46. Morozov, A. Yu., Petrovskii, S. V., & Li, B. (2006). Spatiotemporal complexity of the patchy invasion in a predator-prey system with the Allee effect. J. Theor. Biol., 238, 18-35.
47. Müller, A. P. O., & Gallas, J. A. C. (2010). How community size affects survival chances in cyclic competition games that microorganisms play. Phys. Rev. E, 82, 052901.
48. Murray, J. D. (1989). Mathematical biology. Berlin: Springer.
49. Ni, X., Yang, R., Wang, W.-X., Lai, Y.-C., & Grebogi, C. (2010). Cyclic competition of mobile species on continuous space: pattern formation and coexistence. Phys. Rev. E, 82, 066211.
50. O'Dowd, D. J., Green, P. T., & Lake, P. S. (2003). Invasional 'meltdown' on an oceanic island. Ecol. Lett., 6, 812-817.
51. Okubo, A., Maini, P., Williamson, M. H., & Murray, J. D. (1989). On the spatial spread of the grey squirrel in Britain. Proc. R. Soc. Lond. B, 238, 113-125.
52. Paquin, C. E., & Adams, J. (1983). Relative fitness can decrease in evolving asexual populations of S. cerevisiae. Nature, 306, 368-371.
53. Petrovskii, S. V., Kawasaki, K., Takasu, F., & Shigesada, N. (2001). Diffusive waves, dynamical stabilization and spatiotemporal chaos in a community of three competitive species. Jpn. J. Ind. Appl. Math., 18, 459-481.
54. Petrovskii, S. V., Morozov, A. Y., & Venturino, E. (2002). Allee effect makes possible patchy invasion in a predator-prey system. Ecol. Lett., 5, 345-352.
55. Prado, F., & Kerr, B. (2008). The evolution of restraint in bacterial biofilms under nontransitive competition. Evolution, 62, 538-548.
56. Reichenbach, T., Mobilia, M., & Frey, E. (2007). Mobility promotes and jeopardizes biodiversity in rock-paper-scissors games. Nature, 448, 1046-1049.
57. Richardson, D. M., Allsopp, N., D'Antonio, C. M., Milton, S. J., & Rejmanek, M. (2000). Plant invasions-the role of mutualisms. Biol. Rev., 75, 65-93.
58. Rohani, P., Lewis, T. J., Grünbaum, D., & Ruxton, G. D. (1997). Spatial self-organization in ecology: Pretty patterns or robust reality? Trends Evol. Ecol., 12(2), 70-74.
59. Roy, S., & Chattopadhyay, J. (2007). Towards a resolution of 'the paradox of the plankton': A brief overview of the proposed mechanisms. Ecol. Complex., 4, 26-33.
60. Rushton, S. P., Lurz, P., Gurnell, J., & Fuller, R. (2000). Modelling the spatial dynamics of parapoxvirus disease in red and grey squirrels: A possible cause of the decline in the red squirrel in the UK? J. Appl. Ecol., 37, 997-1012.
61. Ryabov, A. B., & Blasius, B. (2011). A graphical theory of competition on spatial resource gradients. Ecol. Lett., 14, 220-228.
62. Scheffer, M., Rinaldi, S., Huisman, J., & Weissing, F. J. (2003). Why plankton communities have no equilibrium: Solutions to the paradox. Hydrobiologia, 491, 9-18.
63. Sherratt, J. (2001). Periodic travelling waves in cyclic predator-prey systems. Ecol. Lett., 4, 30-37.
64. Sherratt, J., & Smith, M. (2008). Periodic travelling waves in cyclic populations: Field studies and reaction-diffusion models. J. R. Soc. Interface, 6, 483-505.
65. Shigesada, N., & Kawasaki, K. (1997). Biological invasions: Theory and practice. Oxford: Oxford University Press.
66. Silvertown, J., Holtier, S., Johnson, J., & Dale, P. (1992). Cellular automaton models of interspecific competition for space-The effect of pattern on process. J. Ecol., 80, 527-534.
67. Simberloff, D. (2006). Invasional meltdown 6 years later: Important phenomenon, unfortunate metaphor, or both? Ecol. Lett., 9, 912-919.
68. Simberloff, D., & Von Holle, B. (1999). Positive interactions of nonindigenous species: Invasional meltdown? Biol. Invasions, 5, 179-192.
69. Sinervo, B., & Lively, C. M. (1996). The rock-paper-scissors game and the evolution of alternative male strategies. Nature, 380, 240-243.
70. Szabó, G. (2002). Evolutionary prisoner's dilemma games with voluntary participation. Phys. Rev. E, 66, 062903.
71. Tainaka, K. (1993). Paradoxical effect in a three-candidate voter model. Phys. Lett. A, 176, 303-306.
72. Tanner, J. E., Hughes, T. P., & Connell, J. H. (1994). Species coexistence, keystone species, and succession: A sensitivity analysis. Ecology, 75, 2204-2219.
73. Thomas, J. (1995). Texts in applied mathematics: Vol. 22. Numerical partial differential equations: finite difference methods. New York: Springer.
74. Tilman, D. (1982). Resource competition and community structure. Princeton: Princeton University Press.
75. Tilman, D., May, R. M., Lehman, C. L., & Nowak, M. A. (1994). Habitat destruction and the extinction debt. Nature, 371, 65-66.
76. Tompkins, D. M., White, A. R., & Boots, M. (2003). Ecological replacement of native red squirrels by invasive greys driven by disease. Ecol. Lett., 6, 189-196.
77. With, K. A. (2001). The landscape ecology of invasive spread. Conserv. Biol., 16, 1192-1203.
78. Wonham, M. J., O'Connor, M., & Harley, C. D. G. (2005). Positive effects of a dominant invader on introduced and native mudflat species. Mar. Ecol. Prog. Ser., 289, 109-116.