The competitive exclusion principle versus biodiversity through competitive segregation and further adaptation to spatial heterogeneities

Theoretical Population Biology

Volumn 69, Issue 1, 2006, Pages 94-109

  López Gómez, Julián ^a   Molina Meyer, Marcela ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

Competitive exclusion principle; Lazaro species in zoo paleontology; Mathematical foundations in ecology; Refuge patches; Segregation; Spatial random dispersion

Indexed keywords

BIODIVERSITY; COMMUNITY ECOLOGY; COMPETITION (ECOLOGY); ECOLOGICAL THEORY;

ANIMAL; ANIMAL BEHAVIOR; ARTICLE; BIODIVERSITY; BIOLOGICAL MODEL; COMPETITIVE BEHAVIOR; ECOSYSTEM; POPULATION DYNAMICS;

ANIMALS; BEHAVIOR, ANIMAL; BIODIVERSITY; COMPETITIVE BEHAVIOR; ECOSYSTEM; MODELS, BIOLOGICAL; POPULATION DYNAMICS;

EID: 29144443884     PISSN: 00405809     EISSN: 10960325     Source Type: Journal    
DOI: 10.1016/j.tpb.2005.08.004     Document Type: Article

References (61)

1. M. Begon, J.L. Harper, and C.R. Townsend Ecology, Individual, Populations and Communities 1990 Blackwell Scientific Publications Cambridge, Massachusets
2. M. Begon, J.L. Harper, and C.R. Townsend Ecology 1996 Blackwell Science Oxford
3. G.E. Belovsky, C. Mellison, C. Larson, P.A. Zandt, and Van Experimental studies of extinction dynamics Science 286 1999 1175 1177
4. J. Blat, and K.J. Brown Bifurcation of steady state solutions in predator-prey and competition systems Proc. R. Soc. Edinburgh 97A 1984 21 34
5. S. Cano-Casanova, and J. López-Gómez Varying domains in a general class of sublinear elliptic problems El. J. Differential Equations 74 2004 1 41
6. R.S. Cantrell, C. Cosner, and W.F. Fagan Competitive reversals inside ecological reserves: the role of external habitat degradation J. Math. Biol. 37 1998 491 533
7. R.S. Cantrell, C. Cosner, and S. Ruan Intraspecific interference and consumer-resource dynamics Discrete Contin. Dyn. Syst. Ser. B 4 2004 527 546
8. C. Canuto, M.Y. Hussaini, A. Quarteroni, and T.A. Zang Spectral Methods in Fluid Dynamics. Springer Series in Computational Physics 1988 Springer Berlin
9. P. Chesson, and N. Huntly The roles of harsh and fluctuating conditions in the dynamics of ecological communities Am. Nat. 150 1997 519 553
10. M.J. Crawley Plant Ecology 1986 Blackwell Scientific Publications Oxford
11. J.M. Cushing Two species competition in a periodic environment J. Math. Biol. 10 1980 385 390
12. J.M. Cushing, S. Levarge, N. Chitnis, and S.M. Henson Some discrete competition models and the competitive exclusion principle J. Difference Equations Appl. 10 2004 1139 1151
13. A. Dobson, and M. Meagher The population dynamics of brucellosis in Yellowstone National Park Ecology 177 1996 1026 1036
14. J. Edmunds, J.M. Cushing, R.F. Costantino, M.H. Shandelle, B. Dennis, and R.A. Desharnais Park's Tribolium competition experiments: a non-equilibrium species coexistence hypothesis J. Anim. Ecol. 72 2003 703 712
15. J.C. Eilbeck The pseudo-spectral method and path-following in reaction diffusion bifurcation studies SIAM J. Sci. Statist. Comput. 7 1986 599 610
16. J.C. Eilbeck, J.E. Furter, and J. López-Gómez Coexistence in the competition model with diffusion J. Differential Equations 107 1994 96 139
17. W.F. Fagan, R.S. Cantrell, and C. Cosner How habitat edges change species interactions Am. Nat. 153 1999 165 182
18. R.A. Fisher The way of advance of advantageous genes Ann. Eugen. 7 1937 353 369
19. J.E. Furter, and J. López-Gómez Diffusion-mediated permanence problem for a heterogeneous Lotka-Volterra competition model Proc. R. Soc. Edinburgh 127A 1997 281 336
20. F. Goreaud, M. Loreau, and C. Millier Spatial structure and survival of an inferior competitor: a theoretical model of neighborhood competition in plants Ecol. Model. 158 2002 1 19
21. M. Hirsch Stability and convergence in strongly monotone dynamical systems J. Reine Ang. Math. 383 1988 1 58
22. E.E. Holmes, M.A. Lewis, J.E. Banks, and R.R. Veit Partial differential equations in ecology: spatial interactions and population dynamics Ecology 75 1994 17 29
23. Jablonski, D., 1996. Background extinction versus mass extinction. The logic of extinctions. In: Agustí, J. (Ed.), Metatemas, vol. 42. Tusquets, Barcelona 1996.
24. Kauffman, E.G., Harries, P.J., 1996. The consequence of mass extinctions. The logic of extinctions. In: Agustí, J. (Ed.), Metatemas, vol. 42. Tusquets, Barcelona 1996.
25. S.A. Levin Dispersion and population interactions Am. Nat. 108 1974 207 228
26. R. Levins Some demographic and genetic consequences of environmental heterogeneity for biological control Bull. Entomol. Soc. Am. 15 1969 237 240
27. B.T. Li, and H. Smith How many species can two resources support? SIAM J. Appl. Math. 62 2001 336 366
28. I. Loladze, Y. Kuang, J.J. Elser, and W.F. Fagan Competition and stoichiometry: coexistence of two predators on one prey Theor. Popul. Biol. 65 2004 1 15
29. López-Gómez, J., 1988. Estabilidad y Bifurcación Estática. Aplicaciones y Métodos Numéricos. Cuadernos de Matemática y Mecánica, Cursos y Seminarios Nro. 4. CONICET, Santa Fé.
30. J. López-Gómez Permanence under strong competition World Sci. Ser. Appl. Anal. 4 1995 473 488
31. J. López-Gómez The maximum principle and the existence of principal eigenvalues for some linear weighted boundary value problems J. Differential Equations 127 1996 263 294
32. J. López-Gómez Large solutions, metasolutions, and asymptotic behavior of the regular positive solutions of a class of sublinear parabolic problems Electron. J. Differential Equations Conf. 05 2000 135 171
33. López-Gómez, J., 2001. Spectral Theory and Nonlinear Functional Analysis. Research Notes in Mathematics, vol. 426. CRC Press, Boca Raton.
34. J. López-Gómez The boundary blow-up of large solutions J. Differential Equations 195 2003 25 45
35. López-Gómez, J., Molina-Meyer, M., 2004. Superlinear indefinite systems: beyond Lotka-Volterra models. J. Differential Equations, in press, corrected proof, available online 2 August 2005.
36. J. López-Gómez, and J.C. Sabina de Lis Coexistence states and global attractivity for some convective diffusive competing species models Trans. Am. Math. Soc. 347 1995 3797 3833
37. J. López-Gómez, J.C. Eilbeck, K.N. Duncan, and M. Molina-Meyer Structure of solution manifolds in a strongly coupled elliptic system IMA J. Numer. Anal. 12 1992 405 428
38. A.J. Lotka The growth of mixed populations: two species competing for a common food supply J. Washington Acad. Sci. 22 1932 461 469
39. R.M. May Theoretical Ecology. Principles and Applications 1981 Sinauer Associates Oxford
40. J.D. Murray Mathematical Biology 1989 Springer Berlin
41. C. Neuhauser Mathematical Challenges in Spatial Ecology Notices of the American Mathematical Society 48 2001 1304 1314
42. C. Neuhauser, and S.W. Pacala An explicit spatial version of the Lotka-Volterra model with interspecific competition Ann. Appl. Probab. 9 1999 1226 1259
43. A. Okubo Diffusion and Ecological Problems: Mathematical Models 1980 Springer New York
44. H.J. Oosting The Study of Plant Communities 1956 W.H. Freeman and Company San Francisco
45. S. Pacala, and M. Reiss Field experiments that test alternative hypotheses explaining successional diversity Am. Nat. 152 1998 729 737
46. T. Park Experimental studies of interspecific competition. II. Temperature, humidity and competition in two species of Tribolium Physiol. Zool. 27 1954 177 238
47. A.B. Potapov, and M. Lewis Climate and competition: the effect of moving range boundaries on habitat invasibility Bull. Math. Biol. 66 2004 975 1008
48. Quinlan, R., 2004. The competitive exclusion principle. http://www.headwaterstreams.com
49. A. Sard The measure of the critical points of differentiable maps Bull. Am. Math. Soc. 48 1942 883 890
50. E. Schrödinger What is Life? The Physical Aspect of the Living Cell 1944 Cambridge University Press Cambridge
51. N. Shigesada, and K. Kawasaki Biological Invasions: Theory and Practice 1997 Oxford University Press Oxford
52. J.G. Skellam Random dispersal in theoretical population Biometrika 38 1951 196 218
53. D. Tilman Resource Competition and Community Structure 1982 Princeton University Press Princeton
54. D. Tilman Diversity and production in European grasslands Science 285 1999 1099 1100
55. D. Tilman, and P. Kareiva Spatial Ecology 1997 Princeton University Press Princeton
56. D. Tilman, M. Mattson, and S. Langer Competition and nutrient kinetics along a temperature gradient: an experimental test of a mechanistic approach to niche theory Limneology Oceanography 26 1981 1020 1033
57. P. Turchin Quantitative analysis of movement 1998 Sinauer Sunderland, MA
58. V. Volterra Leçons sur la théorie mathématique de la lutte pour la vie 1931 Gauthir-Villars Paris
59. E.O. Wilson Sociobiology 1980 Harvard University Press Cambridge, MA
60. E.O. Wilson The Diversity of Life 1992 Harvard University Press Cambridge, MA
61. T. Yamamoto, and G. Hatta Pulsed nutrient supply as a factor inducing phytoplankton diversity Ecol. Model. 171 2004 247 270