Letter | Published:

Universal scaling relations in food webs


The structure of ecological communities is usually represented by food webs1,2,3. In these webs, we describe species by means of vertices connected by links representing the predations. We can therefore study different webs by considering the shape (topology) of these networks4,5. Comparing food webs by searching for regularities is of fundamental importance, because universal patterns would reveal common principles underlying the organization of different ecosystems. However, features observed in small food webs1,2,3,6 are different from those found in large ones7,8,9,10,11,12,13,14,15. Furthermore, food webs (except in isolated cases16,17) do not share18,19 general features with other types of network (including the Internet, the World Wide Web and biological webs). These features are a small-world character4,5 and a scale-free (power-law) distribution of the degree4,5 (the number of links per vertex). Here we propose to describe food webs as transportation networks20 by extending to them the concept of allometric scaling20,21,22 (how branching properties change with network size). We then decompose food webs in spanning trees and loop-forming links. We show that, whereas the number of loops varies significantly across real webs, spanning trees are characterized by universal scaling relations.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.


  1. 1

    Lawton, J. H. in Ecological Concepts (ed. Cherret, J. M.) 43–78 (Blackwell Scientific, Oxford, 1989)

  2. 2

    Pimm, S. L. Food Webs (Chapman & Hall, London, 1982)

  3. 3

    Cohen, J. E., Briand, F. & Newman, C. M. Community Food Webs: Data and Theory Biomathematics 20 (Springer, Berlin, 1990)

  4. 4

    Strogatz, S. H. Exploring complex networks. Nature 410, 268–276 (2001)

  5. 5

    Albert, R. & Barabási, A.-L. Statistical mechanics of complex networks. Rev. Mod. Phys. 74, 47–97 (2002)

  6. 6

    Cohen, J. E. Ecologists' Co-Operative Web Bank 1.00 (The Rockfeller Univ., New York, 1989)

  7. 7

    Goldwasser, L. & Roughgarden, J. Construction and analysis of a large Caribbean food web. Ecology 74, 1216–1233 (1993)

  8. 8

    Christian, R. R. & Luczkovich, J. J. Organizing and understanding a winter's seagrass foodweb network through effective trophic levels. Ecol. Mod. 117, 99–124 (1999)

  9. 9

    Martinez, N. D., Hawkins, B. A., Dawah, H. A. & Feifarek, B. P. Effects of sampling effort on the characterization of food web structure. Ecology 80, 1044–1055 (1999)

  10. 10

    Memmott, J., Martinez, N. D. & Cohen, J. E. Predators, parasitoids and pathogens: species richness, trophic generality and body sizes in a natural web. J. Anim. Ecol. 69, 1–15 (2000)

  11. 11

    Hall, S. J. & Raffaelli, D. Food web patterns: lessons from a species-rich web. J. Anim. Ecol. 60, 823–842 (1991)

  12. 12

    Martinez, N. D. Artifacts or attributes? Effects of resolution on the Little Rock Lake food web. Ecol. Monogr. 61, 367–392 (1991)

  13. 13

    Huxham, M., Beaney, S. & Raffaelli, D. Do parasites reduce the chances of triangulation in a real food web? Oikos 76, 284–300 (1996)

  14. 14

    Polis, G. A. Complex trophic interactions in deserts: an empirical critique of food web theory. Am. Nat. 138, 123–155 (1991)

  15. 15

    Warren, P. H. Spatial and temporal variation in the structure of a freshwater food web. Oikos 55, 299–311 (1989)

  16. 16

    Montoya, J. M. & Solé, R. V. Small world patterns in food webs. J. Theor. Biol. 214, 405–412 (2002)

  17. 17

    Williams, R. J., Berlow, E. L., Dunne, J. A. & Barabási, A.-L. Two degrees of separation in complex food webs. Proc. Natl Acad. Sci. USA 99, 12913–12916 (2002)

  18. 18

    Camacho, J., Guimerà, R. & Amaral, L. A. N. Robust patterns in food web structure. Phys. Rev. Lett. 88, 228102 (2002)

  19. 19

    Dunne, J. A., Williams, R. J. & Martinez, N. D. Food-web structure and network theory: the role of connectance and size. Proc. Natl Acad. Sci. USA 99, 12917–12922 (2002)

  20. 20

    Banavar, J. R., Maritan, A. & Rinaldo, A. Size and form in efficient transportation networks. Nature 399, 130–132 (1999)

  21. 21

    West, G. B., Brown, J. H. & Enquist, B. J. A general model for the origin of allometric scaling laws in biology. Science 276, 122–126 (1997)

  22. 22

    West, G. B., Brown, J. H. & Enquist, B. J. The fourth dimension of life: fractal geometry and allometric scaling of organisms. Science 284, 1677–1679 (1999)

  23. 23

    Caldarelli, G., Higgs, P. G. & McKane, A. J. Modelling coevolution in multispecies communities. J. Theor. Biol. 193, 345–358 (1998)

  24. 24

    Williams, R. J. & Martinez, N. D. Simple rules yield complex food webs. Nature 404, 180–183 (2000)

  25. 25

    Rodriguez-Iturbe, I. & Rinaldo, A. Fractal River Basins: Chance and Self-Organization (Cambridge Univ. Press, Cambridge, 1996)

  26. 26

    McMahon, T. A. & Bonner, J. T. On Size and Life (Scientific American Library, New York, 1983)

  27. 27

    Martinez, N. D. Constant connectance in community food webs. Am. Nat. 139, 1208–1218 (1992)

  28. 28

    Dunne, J. A., Williams, R. J. & Martinez, N. D. Network structure and biodiversity loss in food webs: robustness increases with connectance. Ecol. Lett. 5, 558–567 (2002)

  29. 29

    Cousins, S. H. Species diversity measurements: choosing the right index. Trends Ecol. Evol. 6, 190–192 (1991)

  30. 30

    Drossel, B., Higgs, P. G. & McKane, A. J. The influence of predator–prey population dynamics on the long-term evolution of food web structure. J. Theor. Biol. 208, 91–107 (2001)

Download references


We acknowledge support from the FET Open Project IST-2001-33555 COSIN.

Author information

Correspondence to Guido Caldarelli.

Rights and permissions

Reprints and Permissions

About this article

Further reading

Figure 1: Computation of Ai and Ci from a spanning tree of the food web.
Figure 2: Scaling of C against A.


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.