Interplay of spatial dynamics and local adaptation shapes species lifetime distributions and species–area relationships

  • Tobias RoggeEmail author
  • David Jones
  • Barbara Drossel
  • Korinna T. Allhoff


The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local disturbances. Yet, both distributions have been discussed in mostly separate communities. Here, we study both patterns simultaneously using a spatially explicit, evolutionary meta-food web model, consisting of a grid of patches, where each patch contains a local food web. Species survival depends on predation and competition interactions, which in turn depend on species body masses as the key traits. The system evolves due to the migration of species to neighboring patches, the addition of new species as modifications of existing species, and local extinction events. The structure of each local food web thus emerges in a self-organized manner as the highly non-trivial outcome of the relative time scales of these processes. Our model generates a large variety of complex, multi-trophic networks and therefore serves as a powerful tool to investigate ecosystems on long temporal and large spatial scales. We find that the observed lifetime distributions and species–area relations resemble power laws over appropriately chosen parameter ranges and thus agree qualitatively with empirical findings. Moreover, we observe strong finite-size effects, and a dependence of the relationships on the trophic level of the species. By comparing our results to simple neutral models found in the literature, we identify the features that affect the values of the exponents.


Evolutionary assembly Trophic interactions Body mass evolution Metapopulations Dispersal 



The bachelor thesis of Johannes Reinhard contributed to the initial stage of this study by demonstrating that including a spontaneous extinction rate is essential for obtaining an ongoing species turnover.

Supplementary material

12080_2019_410_MOESM1_ESM.pdf (1023 kb)
(PDF 0.99 MB)


  1. Allhoff KT, Drossel B (2013) When do evolutionary food web models generate complex structures?. J Theor Biol 334:122–129. CrossRefPubMedGoogle Scholar
  2. Allhoff KT, Ritterskamp D, Rall BC, Drossel B, Guill C (2015) Evolutionary food web model based on body masses gives realistic networks with permanent species turnover. Sci Rep 5:10955. CrossRefGoogle Scholar
  3. Allhoff KT, Weiel EM, Rogge T, Drossel B (2015) On the interplay of speciation and dispersal: an evolutionary food web model in space. J Theor Biol 366:46–56. CrossRefGoogle Scholar
  4. Arrhenius O (1921) Species and area. J Ecol 9(1):95–99CrossRefGoogle Scholar
  5. Azaele S, Suweis S, Grilli J, Volkov I, Banavar JR, Maritan A (2016) Statistical mechanics of ecological systems: neutral theory and beyond. Rev Mod Phys 88:035,003. CrossRefGoogle Scholar
  6. Bak P, Sneppen K (1993) Punctuated equilibrium and criticality in a simple model of evolution. Phys Rev Lett 71(24):4083CrossRefGoogle Scholar
  7. Barnosky AD, Matzke N, Tomiya S, Wogan GO, Swartz B, Quental TB, Marshall C, McGuire JL, Lindsey EL, Maguire KC et al (2011) Has the earth’s sixth mass extinction already arrived? Nature 471(7336):51–57CrossRefGoogle Scholar
  8. Barter E, Gross T (2017) Spatial effects in meta-foodwebs. Sci Report 7 (9980):2045–2322. Google Scholar
  9. Bertuzzo E, Suweis S, Mari L, Maritan A, Rodríguez-Iturbe I, Rinaldo A (2011) Spatial effects on species persistence and implications for biodiversity. Proc Natl Acad Sci 108(11):4346–4351. CrossRefPubMedGoogle Scholar
  10. Binzer A, Brose U, Curtsdotter A, Eklöf A, Rall BC, Riede JO, de Castro F (2011) The susceptibility of species to extinctions in model communities. Basic Appl Ecol 12(7):590–599. CrossRefGoogle Scholar
  11. Bolchoun L, Drossel B, Allhoff KT (2017) Spatial topologies affect local food web structure and diversity in evolutionary metacommunities. Sci Rep 7:1818CrossRefGoogle Scholar
  12. Brännström Å, Loeuille N, Loreau M, Dieckmann U (2011) Emergence and maintenance of biodiversity in an evolutionary food-web model. Theor Ecol 4(4):467–478CrossRefGoogle Scholar
  13. Calcagno V, Jarne P, Loreau M, Mouquet N, David P (2017) Diversity spurs diversification in ecological communities. Nature 8(15):810Google Scholar
  14. Caldarelli G, Higgs PG, McKane AJ (1998) Modelling coevolution in multispecies communities. J Theor Biol 193:345–358. arXiv:adap-org/9801003v2 CrossRefGoogle Scholar
  15. Caswell H, Cohen JE (1993) Local and regional regulation of species-area relations: a patch-occupancy model. Species diversity in ecological communities 7:99–107Google Scholar
  16. Chesson P (2000) Mechanisms of maintenance of species diversity. Annu Rev Ecol Syst 31(1):343–366CrossRefGoogle Scholar
  17. Connor EF, McCoy ED (1979) The statistics and biology of the species-area relationship. Am Nat 113 (6):791–833CrossRefGoogle Scholar
  18. Dengler J (2009) Which function describes the species–area relationship best? A review and empirical evaluation. J Biogeogr 36(4):728–744CrossRefGoogle Scholar
  19. Desmet P, Cowling R (2004) Using the species–area relationship to set baseline targets for conservation. Ecol Soc 9(2):11CrossRefGoogle Scholar
  20. Drakare S, Lennon JJ, Hillebrand H (2006) The imprint of the geographical, evolutionary and ecological context on species–area relationships. Ecol Lett 9(2):215–227CrossRefGoogle Scholar
  21. Drossel B (1998) Extinction events and species lifetimes in a simple ecological model. Phys Rev Lett 81:5011–5014. CrossRefGoogle Scholar
  22. Drossel B (2001) Biological evolution and statistical physics. Adv Phys 50(2):209–295. CrossRefGoogle Scholar
  23. Drossel B, Higgs PG, McKane AJ (2001) The influence of predator-prey population dynamics on the long-term evolution of food web structure. J Theor Biol 208(1):91–107. CrossRefPubMedGoogle Scholar
  24. Durrett R, Levin S (1996) Spatial models for species-area curves. J Theor Biol 179(2):119–127CrossRefGoogle Scholar
  25. Gaston K, Blackburn T (2008) Pattern and process in macroecology. John Wiley & SonsGoogle Scholar
  26. Gleason HA (1922) On the relation between species and area. Ecology 3(2):158–162CrossRefGoogle Scholar
  27. Gomulkiewicz R, Holt RD (1995) When does evolution by natural selection prevent extinction? Evolution 49(1):201–207CrossRefGoogle Scholar
  28. Gravel D, Canard E, Guichard F, Mouquet N (2011) Persistence increases with diversity and connectance in trophic metacommunities. PloS one 6(5):e19,374CrossRefGoogle Scholar
  29. Guill C, Drossel B (2008) Emergence of complexity in evolving niche-model food webs. J Theor Biol 251(1):108–120. CrossRefPubMedGoogle Scholar
  30. Hairston NG, Ellner SP, Geber MA, Yoshida T, Fox JA (2005) Rapid evolution and the convergence of ecological and evolutionary time. Ecol Lett 8(10):1114–1127CrossRefGoogle Scholar
  31. Hanski I (1991) Single-species metapopulation dynamics: concepts, models and observations. Biol J Linn Soc 42(1-2):17–38CrossRefGoogle Scholar
  32. Hanski I (1994) A practical model of metapopulation dynamics. J Anim Ecol 63(1):151–162. CrossRefGoogle Scholar
  33. He F, Legendre P (1996) On species-area relations. Am Nat 148(4):719–737CrossRefGoogle Scholar
  34. He F, Legendre P (2002) Species diversity patterns derived from species–area models. Ecology 83(5):1185–1198Google Scholar
  35. Holt RD, Lawton JH, Polis GA, Martinez ND (1999) Trophic rank and the species–area relationship. Ecology 80(5):1495–1504Google Scholar
  36. Keitt TH, Stanley HE (1998) Dynamics of north american breeding bird populations. Nature 393:257–260. CrossRefGoogle Scholar
  37. Kilburn PD (1966) Analysis of the species-area relation. Ecology 47(5):831–843CrossRefGoogle Scholar
  38. Kirkpatrick M, Barton NH (1997) Evolution of a species’ range. Am Nat 150(1):1–23CrossRefGoogle Scholar
  39. Lawson D, Jensen HJ (2006) The species–area relationship and evolution. J Theor Biol 241(3):590–600CrossRefGoogle Scholar
  40. Loeuille N, Leibold M (2008) Ecological consequences of evolution in plant defenses in a metacommunity. Theor Popul Biol 74(1):34–45CrossRefGoogle Scholar
  41. Loeuille N, Loreau M (2005) Evolutionary emergence of size-structured food webs. PNAS 102(16):5761–5766. CrossRefPubMedGoogle Scholar
  42. Lomolino MV (2000) Ecology’s most general, yet protean pattern: The species-area relationship. J Biogeogr 27(1):17–26CrossRefGoogle Scholar
  43. MacArthur RH, Wilson EO (1963) An equilibrium theory of insular zoogeography. Evolution 17(4):373–387CrossRefGoogle Scholar
  44. Manrubia S, Paczuski M (1998) A simple model of large scale organization in evolution. Int J Modern Phys C 9(07):1025–1032CrossRefGoogle Scholar
  45. McCann KS, Rasmussen JB, Umbanhowar J (2005) The dynamics of spatially coupled food webs. Ecol Lett 8(5):513–523. CrossRefGoogle Scholar
  46. Mcguinness KA (1984) Species–area curves. Biol Rev 59(3):423–440CrossRefGoogle Scholar
  47. Newman M (1996) Self-organized criticality, evolution and the fossil extinction record. Proc R Soc Lond B Biol Sci 263(1376):1605–1610CrossRefGoogle Scholar
  48. Newman M, Palmer R (1999) Models of extinction: A review. arXiv:adap-org/9908002
  49. Norberg J, Urban MC, Vellend M, Klausmeier CA, Loeuille N (2012) Eco-evolutionary responses of biodiversity to climate change. Nat Clim Change 2(10):747–751. CrossRefGoogle Scholar
  50. Nunes Amaral LA, Meyer M (1999) Environmental changes, coextinction, and patterns in the fossil record. Phys Rev Lett 82:652–655. CrossRefGoogle Scholar
  51. Pantel JH, Duvivier C, Meester LD (2015) Rapid local adaptation mediates zooplankton community assembly in experimental mesocosms. Ecol Lett 18(10):992–1000CrossRefGoogle Scholar
  52. Pigolotti S, Cencini M, Molina D, Muñoz MA (2017) Stochastic spatial models in ecology: A statistical physics approach. Journal of Statistical Physics.
  53. Pigolotti S, Flammini A, Marsili M, Maritan A (2005) Species lifetime distribution for simple models of ecologies. Proc Natl Acad Sci USA 102(44):15,747–15,751. CrossRefGoogle Scholar
  54. Pillai P, Gonzalez A, Loreau M (2011) Metacommunity theory explains the emergence of food web complexity. Proc Natl Acad Sci 108(48):19,293–19,298CrossRefGoogle Scholar
  55. Pillai P, Loreau M, Gonzalez A (2010) A patch-dynamic framework for food web metacommunities. Theor Ecol 3(4):223–237. CrossRefGoogle Scholar
  56. Plitzko SJ, Drossel B (2015) The effect of dispersal between patches on the stability of large trophic food webs. Theor Ecol 8(2):233–244CrossRefGoogle Scholar
  57. Raup D (1986) Biological extinction in earth history. Science 231(4745):1528–1533. CrossRefPubMedGoogle Scholar
  58. Raup DM (1991) A kill curve for phanerozoic marine species. Paleobiology 17(1):37–48. CrossRefGoogle Scholar
  59. Raup DM, Sepkoski JJ (1982) Mass extinctions in the marine fossil record. Science 215(4539):1501–1503. CrossRefPubMedGoogle Scholar
  60. Richhardt J, Plitzko SJ, Schwarzmüller F, Drossel B (2015) The influence of the migration network topology on the stability of a small food web. Journal of Complex Networks.
  61. Rosindell J, Cornell SJ (2007) Species–area relationships from a spatially explicit neutral mpodel in an infinite landscape. Ecol Lett 10(7):586–595CrossRefGoogle Scholar
  62. Rossberg A, Ishii R, Amemiya T, Itoh K (2008) The top-down mechanism for body-mass-abundance scaling. Ecology 89(2):567–80. CrossRefGoogle Scholar
  63. Scheiner SM (2003) Six types of species-area curves. Glob Ecol Biogeogr 12(6):441–447. CrossRefGoogle Scholar
  64. Sole RV, Bascompte J (1996) Are critical phenomena relevant to large-scale evolution? Proc R Soc Lond B Biol Sci 263(1367):161–168CrossRefGoogle Scholar
  65. Tjørve E (2003) Shapes and functions of species–area curves: a review of possible models. J Biogeogr 30(6):827–835CrossRefGoogle Scholar
  66. Triantis K, Mylonas M, Lika K, Vardinoyannis K (2003) A model for the species–area–habitat relationship. J Biogeogr 30(1):19–27CrossRefGoogle Scholar
  67. Urban MC, Leibold MA, Amarasekare P, De Meester L, Gomulkiewicz R, Hochberg ME, Klausmeier CA, Loeuille N, De Mazancourt C, Norberg J et al (2008) The evolutionary ecology of metacommunities. Trends Ecol Evol 23(6):311–317. CrossRefGoogle Scholar
  68. Williams RJ, Martinez ND (2000) Simple rules yield complex food webs. Nature 404:180–182CrossRefGoogle Scholar
  69. Willis JC (1922) Age and area, The University Press, CambridgeGoogle Scholar
  70. Yodzis P, Innes S (1992) Body size and consumer-resource dynamics. Am Nat 139:1151–1175CrossRefGoogle Scholar
  71. Zaoli S, Giometto A, Maritan A, Rinaldo A (2017) Covariations in ecological scaling laws fostered by community dynamics. Proc Natl Acad Sci 114(40):10,672–10,677. CrossRefGoogle Scholar
  72. žliobaitė I, Fortelius M, Stenseth NC (2017) Reconciling taxon senescence with the red queen’s hypothesis. Nature 552(7683): 92PubMedGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Technische Universität DarmstadtInstitut für FestkörperphysikDarmstadtGermany
  2. 2.Institut d’écologie et des sciences de l’environnement de ParisUniversité Pierre et Marie CurieParisFrance
  3. 3.Institut für Evolution und ÖkologieEberhard Karls Universität TübingenTübingenGermany

Personalised recommendations