Received 24 September; accepted 16 November 2004; doi:10.1038/nature03211.1. MacArthur, R. H. & Wilson, E. O. The Theory of Island Biogeography (Princeton Univ. Press,Princeton, 1969).2. Fisher, R. A., Corbet, A. S. & Williams, C. B. The relation between the number of species and thenumber of individuals in a random sample of an animal population. J. Anim. Ecol. 12, 42–58 (1943).3. Preston, F. W. The commonness, and rarity, of species. Ecology 41, 611–627 (1948).4. Brown, J. H. Macroecology (Univ. Chicago Press, Chicago, 1995).5. Hubbell, S. P. A unified theory of biogeography and relative species abundance and its application totropical rain forests and coral reefs. Coral Reefs 16, S9–S21 (1997).6. Hubbell, S. P. The Unified Theory of Biodiversity and Biogeography (Princeton Univ. Press, Princeton,2001).7. Caswell, H. Community structure: a neutral model analysis. Ecol. Monogr. 46, 327–354 (1976).8. Bell, G. Neutral macroecology. Science 293, 2413–2418 (2001).9. Elton, C. S. Animal Ecology (Sidgwick and Jackson, London, 1927).10. Gause, G. F. The Struggle for Existence (Hafner, New York, 1934).11. Hutchinson, G. E. Homage to Santa Rosalia or why are there so many kinds of animals? Am. Nat. 93,145–159 (1959).12. Huffaker, C. B. Experimental studies on predation: dispersion factors and predator-prey oscillations.Hilgardia 27, 343–383 (1958).13. Paine, R. T. Food web complexity and species diversity. Am. Nat. 100, 65–75 (1966).14. MacArthur, R. H. Geographical Ecology (Harper & Row, New York, 1972).15. Laska, M. S. & Wootton, J. T. Theoretical concepts and empirical approaches to measuring interactionstrength. Ecology 79, 461–476 (1998).16. McGill, B. J. Strong and weak tests of macroecological theory. Oikos 102, 679–685 (2003).17. Adler, P. B. Neutral models fail to reproduce observed species-area and species-time relationships inKansas grasslands. Ecology 85, 1265–1272 (2004).18. Connell, J. H. The influence of interspecific competition and other factors on the distribution of thebarnacle Chthamalus stellatus. Ecology 42, 710–723 (1961).19. Paine, R. T. Ecological determinism in the competition for space. Ecology 65, 1339–1348 (1984).20. Wootton, J. T. Prediction in complex communities: analysis of empirically-derived Markov models.Ecology 82, 580–598 (2001).21. Wootton, J. T. Markov chain models predict the consequences of experimental extinctions. Ecol. Lett.7, 653–660 (2004).22. Paine, R. T. Food-web analysis through field measurements of per capita interaction strength. Nature355, 73–75 (1992).23. Moore, J. C., de Ruiter, P. C. & Hunt, H. W. The influence of productivity on the stability of real andmodel ecosystems. Science 261, 906–908 (1993).24. Rafaelli, D. G. & Hall, S. J. in Food Webs: Integration of Pattern and Dynamics (eds Polis, G. &Winemiller, K.) 185–191 (Chapman and Hall, New York, 1996).25. Wootton, J. T. Estimates and tests of per-capita interaction strength: diet, abundance, and impact ofintertidally foraging birds. Ecol. Monogr. 67, 45–64 (1997).26. Kokkoris, G. D., Troumbis, A. Y. & Lawton, J. H. Patterns of species interaction strength in assembledtheoretical competition communities. Ecol. Lett. 2, 70–74 (1999).27. Drossel, B., McKane, A. & Quince, C. The impact of nonlinear functional responses on the long-termevolution of food web structure. J. Theor. Biol. 229, 539–548 (2004).Acknowledgements I thank the Makah Tribal Council for providing access to Tatoosh Island;J. Sheridan, J. Salamunovitch, F. Stevens, A. Miller, B. Scott, J. Chase, J. Shurin, K. Rose, L. Weis,R. Kordas, K. Edwards, M. Novak, J. Duke, J. Orcutt, K. Barnes, C. Neufeld and L. Weintraub forfield assistance; and NSF, EPA (CISES) and the Andrew W. Mellon foundation for partial financialsupport.Competing interests statement The author declares that he has no competing financial interests.Correspondence and requests for materials should be addressed to J.T.W.([email protected])...............................................................Evolutionary dynamics on graphsErez Lieberman1,2, Christoph Hauert1,3& Martin A. Nowak11Program for Evolutionary Dynamics, Departments of Organismic andEvolutionary Biology, Mathematics, and Applied Mathematics, HarvardUniversity, Cambridge, Massachusetts 02138, USA2Harvard-MIT Division of Health Sciences and Technology, MassachusettsInstitute of Technology, Cambridge, Massachusetts, USA3Department of Zoology, University of British Columbia, Vancouver, BritishColumbia V6T 1Z4, Canada.............................................................................................................................................................................Evolutionary dynamics have been traditionally studied in thecontext of homogeneous or spatially extended populations1–4.Here we generalize population structure by arranging individ-uals on a g raph. Each vertex represents an indiv idual. Theweighted edges denote rep roductive rates which govern howoften individuals place offspring into adjacent vertices. Thehomogeneous population, described by the Moran process3,isthe special case of a fully connected graph with evenly weightededges. Spatial structures are described by graphs where verticesare connected with their nearest neighbours. We also exploreevolution on random and scale-free networks5–7. We determinethe fixation prob ability of m utants, and characterize thosegraphs for which fixation behav iour is identical to that of ahomogeneous populati on7. Furthermore, some graphs act assuppressors and others as amplifiers of selection. It is evenpossible to find g raphs that guarantee the fixation of anyadvantageous mutant. We also study frequency-dependent selec-tion and show t hat the outcome of evolutionary games candepend entirely on the structure of the underlying graph. Evolu-tionary graph theory has many fascinating applications rangingfrom ecology to multi-cellular organization and economics.Evolutionary dynamics act on populations. Neither genes, norcells, nor individuals evolve; only populations evolve. In smallpopulations, random drift dominates, whereas large populationsFigure 1 Models of evolution. a, The Moran process describes stochastic evolution of afinite population of constant size. In each time step, an individual is chosen forreproduction with a probability proportional to its fitness; a second individual is chosen fordeath. The offspring of the first individual replaces the second. b, In