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18. Gilinsky, N. L. in Analytical Paleobiology (eds Gilinsky, N. L. & Signor, P. W.) 157174 (The Paleontological Society, Knoxville, Tennessee, 1991).
19. Cleveland, W. S. & McGill, R. The many faces of a scatterplot. J. Am. Stat. Assoc. 79, 807822 (1984).
Supplementary information is available on Nature's World-Wide Web site(http://www.nature.com) or as paper copy from the London editorial ofce of Nature.
AcknowledgementsWe are indebted to the late J. Sepkoski for his fossil databases and his encouragement, and we thank M. Foote and D. Erwin for comments on the manuscript. Our work was supported by grants from the University of California and the NSF to J.W.K.
Correspondence and requests for materials should be addressed to J.W.K. (e-mail: [email protected])
.................................................................Simple rules yield complex food webs
Richard J. Williams & Neo D. MartinezRomberg Tiburon Center, Department of Biology, San Francisco State University, PO Box 855, Tiburon, California 94920, USA..............................................................................................................................................
Several of the most ambitious theories in ecology114 describe food webs that document the structure of strong and weak trophic links9 that is responsible for ecological dynamics among diverse assemblages of species4,1113. Early mechanism-based theory asserted that food webs have little omnivory and several properties that are independent of species richness14,6. This theory was overturned by empirical studies that found food webs to be much more complex5,79,1418, but these studies did not provide mechanistic explanations for the complexity9. Here we show that a remarkably simple model lls this scientic void by successfully predicting key structural properties of the most complex and comprehensive food webs in the primary literature. These properties include the fractions of species at top, intermediate and basal trophic levels, the means and variabilities of generality, vulnerability and food-chain length, and the degrees of cannibalism, omnivory, looping and trophic similarity. Using only two empirical parameters, species number and connectance, our `niche model' extends the existing `cascade model'3,19 and improves its
t ten-fold by constraining species to consume a contiguous sequence of prey in a one-dimensional trophic niche20.
We compare the abilities of two earlier models, the random and cascade models3,19, and our new niche model to predict a dozen
properties for each of seven food webs. The parameters of all models are set to synthesize webs with the empirically observed species number and...