Evolutionary Ecology

, Volume 23, Issue 2, pp 187–205 | Cite as

Two-patch model of spatial niche segregation

Original Paper

Abstract

Spatial niche segregation between two habitats and the related adaptive dynamics are investigated. Independent population regulations operate in the two patches by a single resource in each. The populations migrate between the habitats with a constant rate. In line with a general mathematical concept published elsewhere, the niche of a species is described by the measures of the two-way interactions between the species and the resources. Increasing migration rate tends to equalize the population sizes between the habitats and diminish the dependence of the niches on the environmental tolerances of the species. In line with the expectations, when two species coexist, their realized niches are more segregated than their fundamental ones. We demonstrate that robust coexistence requires sufficient niche segregation. That is, the parameter range that allows coexistence of the two species shrinks to nil when the niche-differences between the species disappear. In turn, niche segregation requires separation of tolerances and sufficiently low migration rate. For the evolutionary study we assume a continuous, clonally inherited character that has different optima at the two patches. Evolution of this trait may end up in an intermediate “generalist” optimum, or it can branch and leads to a dimorphic population. The condition of the latter outcome is in line with the conditions that allow niche segregation: the patches have to be sufficiently different and the migration has to be sufficiently low.

Keywords

Niche theory Habitat segregation Fundamental and realized niche Regulation Limiting similarity Adaptive dynamics 

Notes

Acknowledgements

We thank Péter Szabó for commenting on the previous version of the manuscript, Tamás Czárán, Odo Diekmann, Mats Gyllenberg, Mathew Leibold, Hans Metz, Beáta Oborny, Liz Pásztor and István Scheuring for discussions. This work was supported from OTKA grants T049689, TS049885.

Supplementary material

10682_2007_9212_MOESM1_ESM.pdf (93 kb)
ESM1 (PDF 93 KB)

References

  1. Abrams PA (1983) The theory of limiting similarity. Annu Rev Ecol Syst 14:359–376CrossRefGoogle Scholar
  2. Abrams PA (1988) How should resources be counted? Theor Popul Biol 33:226–242CrossRefGoogle Scholar
  3. Abrams PA, Wilson WG (2004) Coexistence of competitors in metacommunities due to spatial variation in resource growth rates; does R * predict the outcome of competition? Ecol Lett 7:929–940CrossRefGoogle Scholar
  4. Amarasekare P (2003) Competitive coexistence in spatially structured environments: a synthesis. Ecol Lett 6:1109–1122CrossRefGoogle Scholar
  5. Armstrong RA, McGehee R (1980) Competitive exclusion. Am Nat 115:151–170CrossRefGoogle Scholar
  6. Bulmer M (1994) Theoretical evolutionary ecology. Sinauer Associates, Sunderland, MAGoogle Scholar
  7. Case TJ (2000) An illustrated guide to theoretical ecology. Oxford University PressGoogle Scholar
  8. Caswell H (2001) Matrix population methods: construction, analysis and interpretation. Sinauer AssociatesGoogle Scholar
  9. Chase JM, Leibold MA (2003) Ecological niches: linking classical and contemporary approaches. The University of Chicago Press, ChicagoGoogle Scholar
  10. Chesson P (2000a) General theory of competitive coexistence in spatially-varying environments. Theor Popul Biol 58:211–237PubMedCrossRefGoogle Scholar
  11. Chesson P (2000b) Mechanism and maintenance of species diversity. Annu Rev Ecol Syst 31:343–366CrossRefGoogle Scholar
  12. Christiansen FB (1975) Hard and soft selection in a subdivided population. Am Nat 109:11–16CrossRefGoogle Scholar
  13. Christiansen FB (1988) Frequency dependence and competition. Proc R Soc Lond B 319:587–600Google Scholar
  14. Christiansen FB, Fenchel TM (1977) Theories of populations in biological communities. Springer-Verlag, BerlinGoogle Scholar
  15. Christiansen FB, Loeschcke V (1980) Evolution and intraspecific exploitative competition. i. one locus theory for small additive gene effects. Theor Popul Biol 18:297–313CrossRefGoogle Scholar
  16. Christiansen FB, Loeschcke V (1987) Evolution and intraspecific exploitative competition. iii. one-locus theory for small additive gene effect and multidimensional resource qualities. Theor Popul Biol 31:33–46CrossRefGoogle Scholar
  17. Darwin C (1859) On the origin of species by means of natural selection, or the preservation of favoured races in the struggle for life, 1st edn. John Murray, LondonGoogle Scholar
  18. Day T (2000) Competition and the effect of spatial resource heterogeneity on evolutionary diversification. Am Nat 155:790–803PubMedCrossRefGoogle Scholar
  19. Dieckmann U, Doebeli M (1999) On the origin of species by sympatric speciation. Nature 400:354–357PubMedCrossRefGoogle Scholar
  20. Dieckmann U, Law R (1996) The dynamical theory of coevolution: a derivation from stochastic ecological processes. J Math Biol 34:579–612PubMedCrossRefGoogle Scholar
  21. Diekmann O, Gyllenberg M, Metz JAJ, Thieme HR (1998) On the formulation and analysis of general deterministic structured population models: I. Linear theory. J Math Biol 36:349–388CrossRefGoogle Scholar
  22. Diekmann O, Gyllenberg M, Huang H, Kirkilionis M, Metz JAJ, Thieme HR (2001) On the formulation and analysis of general deterministic structured population models: II. Nonlinear theory. J Math Biol 43:157–189PubMedCrossRefGoogle Scholar
  23. Diekmann O, Gyllenberg M, Metz JAJ (2003) Steady state analysis of structured population models. Theor Popul Biol 63:309–338PubMedCrossRefGoogle Scholar
  24. Dieckmann U, Doebeli M, Metz JAJ, Tautz D (eds) (2004) Adaptive speciation. Cambridge University Press, CambridgeGoogle Scholar
  25. Doebeli M, Dieckmann U (2003) Speciation along environmental gradient. Nature 421:259–264PubMedCrossRefGoogle Scholar
  26. Durinx M, Metz JAJ, Meszéna G (in press) Adaptive dynamics for physiologically structured population models. J Math BiolGoogle Scholar
  27. Elton C (1927) Animal ecology. Sidwick and Jackson, LondonGoogle Scholar
  28. Eshel I (1983) Evolutionary and continuous stability. J Theor Biol 103:99–111CrossRefGoogle Scholar
  29. Gause GF (1934) The struggle for existence. Williams and Wilkins, BaltimoreGoogle Scholar
  30. Gavrilets S (2004) Fitness landscapes and the origin of species. Monographs in population biology. Princeton University Press, PrincetonGoogle Scholar
  31. Gavrilets S (2005) “Adaptive speciation”: it is not that simple. Evolution 59:696–699Google Scholar
  32. Geritz SAH, Metz JAJ, Kisdi É, Meszéna G (1997) The dynamics of adaptation and evolutionary branching. Phys Rev Lett 78(10):2024–2027. http://www.evol.elte.hu/∼geza/GeritzPRL.pdf Google Scholar
  33. Geritz SAH, Kisdi É, Meszéna G, Metz JAJ (1998) Evolutionary singular strategies and the adaptive growth and branching of evolutionary trees. Evol Ecol 12:35–57CrossRefGoogle Scholar
  34. Goldberg DE (1990) Components of resource competition in plant communities. In: Grace JB, Tilman D (eds) Perspectives on plant competition. Academic Press, San Diego, pp 27–49Google Scholar
  35. Grinnel J (1904) The origin and distribution of the chestnut-backed chicadee. Auk 21:364–382Google Scholar
  36. Grinnel J (1914) The account of the mammals and birds of the lower colorado valley. Univ Calif Publ Zool 12:51–294Google Scholar
  37. Heino M, Metz JAJ, Kaitala V (1997) Evolution of mixed maturation strategies in semelparous life-histories: the crucial role of dimensionality of feedback environment. Philos Trans R Soc Lond B Biol Sci 353:1647–1655Google Scholar
  38. Hutchinson GE (1959) Homage to Santa Rosalia, or why are so many kinds of animals? Am Nat XCIII (870):137–145Google Scholar
  39. Hutchinson GE (1978) An introduction to population ecology. Yale University Press, New HavenGoogle Scholar
  40. Krebs CJ (2001) Ecology. The experimental analysis of distribution and abundance. Benjamin Cummings, San Francisco, CAGoogle Scholar
  41. Leibold MA (1995) The niche concept revisited: mechanistic models and community context. Ecology 76(5):1371–1382CrossRefGoogle Scholar
  42. Levene H (1953) Genetic equilibrium when more than one ecological niche is available. Am Nat 87:331–333CrossRefGoogle Scholar
  43. Levin SM (1970) Community equlibria and stability, and an extension of the competitive exclusion principle. Am Nat 104(939):413–423CrossRefGoogle Scholar
  44. MacArthur RH (1969) Species packing, and what interspecies competition minimizes. Proc Natl Acad Sci USA 64:1369–1371CrossRefGoogle Scholar
  45. MacArthur RH, Levins R (1964) Competition, habitat selection and character displacement in a patchy environment. Proc Natl Acad Sci USA 51:1207–1210PubMedCrossRefGoogle Scholar
  46. MacArthur RH, Levins R (1967) The limiting similarity, convergence, and divergence of coexisting species. Am Nat 101(921):377–385CrossRefGoogle Scholar
  47. May RM (1973) Stability and complexity in model ecosystems. Princeton University Press, PrincetonGoogle Scholar
  48. May RM, MacArthur RH (1972) Niche overlap as a function of environmental variability. Proc Natl Acad Sci USA 69:1109–1113PubMedCrossRefGoogle Scholar
  49. Mayr E (1942) Systematics and the origin of species. Columbia University Press, New YorkGoogle Scholar
  50. Meszéna G, Czibula I, Geritz SAH (1997) Adaptive dynamics in a 2-patch environment: a toy model for allopatric and parapatric speciation. J Biol Syst 5:265–284. http://www.evol.elte.hu/∼geza/MeszenaEtal1997.pdf Google Scholar
  51. Meszéna G, Gyllenberg M, Jacobs FJ, Metz JAJ (2005) Link between population dynamics and dynamics of darwinian evolution. Phys Rev Lett 95:078105. URL: http://www.evol.elte.hu/∼geza/PhysRevLett_95_078105.pdf Google Scholar
  52. Meszéna G, Gyllenberg M, Pásztor L, Metz JAJ (2006) Competitive exclusion and limiting similarity: a unified theory. Theor Popul Biol 69:68–87PubMedCrossRefGoogle Scholar
  53. Metz JAJ, Diekmann O (1986) The dynamics of physiologically structured populations. Lecture notes in biomathematics, vol 68. Springer, BerlinGoogle Scholar
  54. Metz JAJ, Nisbet RM, Geritz SAH (1992) How should we define “fitness” for general ecological scenarios? Trends Ecol Evol 7:198–202CrossRefGoogle Scholar
  55. Metz JAJ, Geritz SAH, Meszéna G, Jacobs FJA, van Heerwaarden JS (1996) Adaptive dynamics, a geometrical study of the consequences of nearly faithful reproduction. In: van Strien SJ, Verduyn Lunel SM (eds) Stochastic and spatial structures of dynamical systems. North Holland, pp 183–231Google Scholar
  56. Mizera F, Meszéna G (2003) Spatial niche packing, character displacement and adaptive speciation along an environmental gradient. Evol Ecol Res 5:363–382Google Scholar
  57. Petraitis PS (1989) The representation of niche breadth and overlap on Tilman’s consumer-resource graphs. Oikos 56:289–292CrossRefGoogle Scholar
  58. Rescigno A, Richardson IW (1965) On the competitive exclusion principle. Bull Math Biophys 27:85–89PubMedCrossRefGoogle Scholar
  59. Rosenzweig ML (1978) Competitive speciation. Biol J Linn Soc (Lond) 10:275–289CrossRefGoogle Scholar
  60. Rosenzweig ML (1995) Species diversity in space and time. Cambridge University Press, CambridgeGoogle Scholar
  61. Schileven UK, Tautz D, Pääbo S (1994) Sympatric speciation suggested by monophyly of crater lake cichlids. Nature 386:629–632Google Scholar
  62. Seger J (1985) Intraspecific resource competition as a cause of sympatric spciation. In: Greenwood PJ, Harvey PM, Slatkin M (eds) Evolution. Essays in honour of John Maynard Smith. Cambridge University Press, Cambridge, pp 43–53Google Scholar
  63. Szabó P, Meszéna G (2006a) Limiting similarity revisited. Oikos 112:612–619CrossRefGoogle Scholar
  64. Szabó P, Meszéna G (2006b) Spatial ecological hierachies: coexistence on heterogeneous landscapes via scale niche diversification. Ecosystems 9:1009–1016CrossRefGoogle Scholar
  65. Szabó P, Meszéna G (2007) Multi-scale regulated plant community dynamics: mechanisms and implications. Oikos 116:233–240CrossRefGoogle Scholar
  66. Tilman D (1982) Resource equilibrium and community structure. Princeton University Press, PrincetonGoogle Scholar
  67. Via S (2001) Sympatric speciation in animals: the ugly duckling grows up. Trends Ecol Evol 16:381–390PubMedCrossRefGoogle Scholar
  68. Yodzis P (1989) Introduction to theoretical ecology. Harper & Row, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Biological PhysicsEötvös UniversityBudapestHungary

Personalised recommendations