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21 - Biodiversity power laws

Published online by Cambridge University Press:  05 August 2012

Pablo A. Marquet
Affiliation:
Pontificia Universidad Católica de Chile, CASEB, IEB, The Santa Fe Institute
Sebastian R. Abades
Affiliation:
Pontificia Universidad Católica de Chile
Fabio A. Labra
Affiliation:
Pontificia Universidad Católica de Chile
David Storch
Affiliation:
Charles University, Prague
Pablo Marquet
Affiliation:
Pontificia Universidad Catolica de Chile
James Brown
Affiliation:
University of New Mexico
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Summary

Introduction

The last ten years have been marked by important discoveries and scientific advances in our understanding of biodiversity. The emergence of new fields, such as bioinformatics, ecoinformatics, and computational ecology (Helly et al., 1995; Spengler, 2000; Green et al., 2005) has brought about an informational revolution by making available massive data sets on the composition, distribution and abundance of biodiversity from local to global scales and from genes to ecosystems. This has in turn changed biodiversity sciences, expanding the scale of analysis of ecological systems wherein biodiversity resides. While the 1970s and 1980s were marked by studies at local scales, the 1990s were marked by gaining access to regional, continental and global scale analyses. In parallel, and in part as a consequence of the above trend, there has been a shift from approaches that emphasize the highly variable and idiosyncratic nature of ecological systems to a view that emphasizes the action of first principles, natural laws and zeroth order approaches (the macroscopic approach hereafter).

The small-scale approach can be illustrated by a representative quotation from Diamond and Case (1986, p. x): “The answers to general ecological questions are rarely universal laws, like those of physics. Instead, the answers are conditional statements such as: for a community of species with properties A1 and A2 in habitat B and latitude C, limiting factors X2 and X5 are likely to predominate.”

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Scaling Biodiversity , pp. 441 - 461
Publisher: Cambridge University Press
Print publication year: 2007

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References

Adler, R., Feldman, R. & Taqqu, M. S. (eds.) (1998). A Practical Guide to Heavytails: Statistical Techniques for Analyzing Heavy-Tailed Distributions. Boston: Birkhauser.Google Scholar
Allen, A. P., Li, B. & Charnov, E. L. (2001). Population fluctuations, power laws and mixtures of lognormal distributions. Ecology Letters, 4, 1–3.CrossRefGoogle Scholar
Amaral, L. A. N., Buldyrev, S. V., Havlin, S., Salinger, M. A. & Stanley, H. E. (1998). Power law scaling for a system of interacting units with complex internal structure. Physical Review Letters, 80, 1385–1388.CrossRefGoogle Scholar
Anderson, R. M., Gordon, D. M., Crawley, M. J. & Hassell, M. P. (1982). Variability in the abundance of animal and plant species, Nature, 296, 245–248.CrossRefGoogle Scholar
Arino, A. & Pimm, S. L. (1995). On the nature of population extremes. Evolutionary Ecology, 9, 429–443.CrossRefGoogle Scholar
Bak, P. (1996). How Nature Works. The Science of Self-Organized Criticality. New York: Springer-Verlag.Google Scholar
Bak, P., Tang, C. & Wiesenfeld, K. (1987). Self-organized criticality: an explanation of 1/f noise. Physical Review Letters, 59, 381–384.CrossRefGoogle ScholarPubMed
Banavar, J. R., Green, J. L., Harte, J. & Maritan, A. (1999). Finite size scaling in ecology. Physical Review Letters, 83, 4212–4214.CrossRefGoogle Scholar
Bell, G. (2000). The distribution of abundance in neutral communities. American Naturalist, 155, 606–617.CrossRefGoogle ScholarPubMed
Biney, J. J., Dowrick, N. J., Fisher, A. J. & Newman, M. E. J. (1992). The Theory of Critical Phenomena. Oxford: Clarendon Press.Google Scholar
Blackburn, T. M., Lawton, J. H. & Pimm, S. L. (1993). Non-metabolic explanations for the relationship between body size and animal abundance. Journal of Animal Ecology, 62, 694–702.CrossRefGoogle Scholar
Boag, B., Hackett, C. A. & Topham, P. B. (1992). The use of Taylor power law to describe the aggregated distribution of gastrointestinal nematodes of sheep. International Journal of Parasitology, 22, 267–270.CrossRefGoogle Scholar
Brock, W. A. (1999). Scaling in economics: a reader's guide. Industrial and Corporate Change, 8, 409–446.CrossRefGoogle Scholar
Brose, U., Ostling, A., Harrison, K. & Martinez, N. D. (2004). Unified spatial scaling of species and their trophic interactions. Nature, 428, 167–171.CrossRefGoogle ScholarPubMed
Brown, J. H. (1995). Macroecology. Chicago: University of Chicago Press.Google Scholar
Brown, J. H. & Maurer, B. A. (1989). Macroecology: the division of food and space among species on continents. Science, 243, 1145–1150.CrossRefGoogle ScholarPubMed
Brown, J. H. & West, G. B. (2000). Scaling in Biology. New York: Oxford University Press.Google Scholar
Brown, J. H., Mehlman, D. W. & Stevens, G. C. (1995). Spatial variation in abundance. Ecology, 76, 2028–2043.CrossRefGoogle Scholar
Brown, J. H., Gupta, V. K., Li, B-L, Milne, B. T., Restrepo, C. & West, G. B. (2002). The fractal nature of nature: power laws, ecological complexity and biodiversity. Philosophical Transactions of the Royal Society of London, Series B, 357, 619–626.CrossRefGoogle ScholarPubMed
Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. (2004). Toward a metabolic theory of ecology. Ecology, 85, 1771–1789.CrossRefGoogle Scholar
Calder, W. A. III (1983). Ecological scaling: mammals and birds. Annual Review of Ecology and Systematics, 14, 213–230.CrossRefGoogle Scholar
Calder, W. A. III (1984). Size, Function and Life History. Cambridge, MA: Harvard University Press.Google Scholar
Cardy, J. L. (ed.) (1988). Finite-size scaling. New York: North Holland.Google Scholar
Chave, J. & Levin, S. A. (2003). Scale and scaling in ecological and economic systems. Environmental Resource Economics, 26, 527–557.CrossRefGoogle Scholar
Christensen, K., Danon, L., Scanlon, T. & Bak, P. (2002). Unified scaling law for earthquakes. Proceedings of the National Academy of Sciences of the USA, 99, 2509–2513.CrossRefGoogle ScholarPubMed
Clark, J. S., Silman, M., Kern, R., Macklin, E. & HilleRisLambers, J. (1999). Seed dispersal near and far: patterns across temperate and tropical forests. Ecology, 80, 1475–1494.CrossRefGoogle Scholar
Cyr, H. (1997). Does inter-annual variability in population density increase with time?Oikos, 79, 549–558.CrossRefGoogle Scholar
Dennis, B. & Patil, G. P. (1988). Applications in ecology. In Lognormal Distributions: Theory and Applications, ed. Crow, E. L. & Shimizu, K., pp. 303–330. New York: Marcel Dekker.Google Scholar
Diamond, J. M. & Case, T. (eds.) (1986). Community Ecology. New York: Harper and Row.Google Scholar
Diserud, O. H. & Engen, S. (2000). A general and dynamic species abundance model, embracing the lognormal and the gamma models. American Naturalist, 155, 497–511.CrossRefGoogle ScholarPubMed
Fenner, T., Levene, M. & Loizou, G. (2005). A stochastic evolutionary model exhibiting power-law behaviour with an exponential cutoff. Physica A, 355, 641–656.CrossRefGoogle Scholar
Ferrier, R. & Cazelles, B. (1999). Universal power laws govern intermittent rarity in communities of interacting species. Ecology, 80, 1505–1521.CrossRefGoogle Scholar
Frontier, S. (1985). Diversity and structure in aquatic ecosystems. Oceanography and Marine Biology Annual Review, 23, 253–312.Google Scholar
Fu, D., Pammolli, F., Buldyrev, S. V., et al. (2005). The growth of business firms: theoretical framework and empirical evidence. Proceedings of the National Academy of Sciences of the USA, 102, 18801–18806.CrossRefGoogle ScholarPubMed
Garlaschelli, D., Caldarelli, G. & Pietronero, L. (2003). Universal scaling relations in food webs. Nature, 423, 165–168.CrossRefGoogle ScholarPubMed
Gaston, K. J. & Blackburn, T. M. (2000). Patterns and Processes in Macroecology. Oxford: Blackwell Science.CrossRefGoogle Scholar
Gautestad, A. O. & Mysterud, I. (2005). Instrinsic scaling complexity in animal dispersion and abundance. American Naturalist, 165, 44–55.CrossRefGoogle Scholar
Gisiger, T. (2001). Scale invariance in biology: coincidence or footprint of an universal mechanism?Biological Reviews, 76, 161–209.CrossRefGoogle ScholarPubMed
Green, J. L., Hastings, A., Arzberger, P., et al. (2005). Complexity in ecology and conservation: mathematical, statistical, and computational challenges. BioScience, 55, 501–510.CrossRefGoogle Scholar
Gutenberg, B. & Richter, C. F. (1944). Frequency of earthquakes in California. Bulletin of Seismological Society of America, 34, 185–188.Google Scholar
Halley, J. (1996). Ecology, evolution and 1/f noise. Trends in Ecology and Evolution, 11, 33–37.CrossRefGoogle Scholar
Halley, J. & Inchausti, P. (2002). Lognormality in ecological time series. Oikos, 99, 518–530.CrossRefGoogle Scholar
Halley, J. & Inchausti, P. (2004). The increasing importance of 1/f noises as models of ecological variability. Fluctuation and Noise Letters, 4, R1–R26.CrossRefGoogle Scholar
Hanski, I. & Tiainen, J. (1989). Bird ecology and Taylor variance-mean regression. Annales Zoologici Fennici, 26, 213–217.Google Scholar
Harte, J., Kinzig, A. & Green, J. (1999). Self-similarity in the distribution and abundance of species. Science, 284, 334–336.CrossRefGoogle ScholarPubMed
Harte, J., Blackburn, T. & Ostling, A. (2001). Self-similarity and the relationship between abundance and range size. American Naturalist, 157, 374–386.Google ScholarPubMed
Helly, J., Case, T., Davis, F., Levin, S. A. & Michener, W. (eds.) (1995). The State of Computational Ecology. San Diego, CA: San Diego Super Computer Center.Google Scholar
Hubbell, S. P. (1997). A unified theory of biogeography and relative species abundance and its application to tropical rain forest and coral reefs. Coral Reefs, 16, 9–21.CrossRefGoogle Scholar
Hubbell, S. P. (2001). A Unified Theory of Biodiversity and Biogeography. Princeton: Princeton University Press.Google Scholar
Hurlbert, A. H. (2004). Species-energy relationships and habitat complexity in bird communities. Ecology Letters, 7, 714–720.CrossRefGoogle Scholar
Inchausti, P. & Halley, J. (2001). Investigating long-term ecological variability using the Global Population Dynamics Database. Science, 293, 655–657.CrossRefGoogle ScholarPubMed
Inchausti, P. & Halley, J. (2002). The temporal variability and spectral colour of animal populations. Evolutionary Ecology Research, 4, 1033–1048.Google Scholar
Inchausti, P. & Halley, J. (2003). On the relation between temporal variability and persistence time in animal populations. Journal of Animal Ecology, 72, 899–908.CrossRefGoogle Scholar
Ives, R. & Klopper, E. D. (1997). Spatial variation in abundance created by stochastic temporal variation. Ecology, 78, 1907–1913.CrossRefGoogle Scholar
Katul, G. G., Porporato, A., Nathan, R., et al. (2005). Mechanistic analytical models for long-distance seed dispersal by wind. American Naturalist, 166, 368–381.Google ScholarPubMed
Keeling, M. J. (2000). Simple stochastic models and their power-law type behaviour. Theoretical Population Biology, 58, 21–31.CrossRefGoogle ScholarPubMed
Keitt, T. H. & Marquet, P. A. (1996). Extinction cascades in introduced Hawaiian birds suggest self-organized criticality. Journal of Theoretical Biology, 182, 161–167.CrossRefGoogle Scholar
Keitt, T. H. & Stanley, H. E. (1998). Dynamics of North American breeding bird populations. Nature, 393, 257–260.CrossRefGoogle Scholar
Keitt, T. H., Amaral, L. A. N., Buldyrev, S. V. & Stanley, H. E. (2002). Scaling in the growth of geographically subdivided populations: invariant patterns from a continent-wide biological survey. Philosophical Transactions of the Royal Society of London, Series B, 357, 627–633.CrossRefGoogle ScholarPubMed
Kot, M., Lewis, M. A. & Driessche, P. (1996). Dispersal data and the spread of invading organisms. Ecology, 77, 2027–2042.CrossRefGoogle Scholar
Labra, F. A. (2005). Uso de energia desde los individuos a las comunidades: escalamiento y universalidad. Ph.D. dissertation, Pontificia Universidad Católica de Chile, Santiago.
Labra, F. A., Abades, S. R. & Marquet, P. A. (2005). Scaling patterns in exotic species: distribution and abundance. In Species Invasions. Insights Into Ecology, Evolution, and Biogeography, ed. Sax, D. F., Stachowicz, J. J. & Gaines, S., pp. 421–446. Sunderland, MA: Sinauer Associates.Google Scholar
Laherrère, J. & Sornette, D. (1998). Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales. European Physical Journal B, 2, 525–539.CrossRefGoogle Scholar
Lande, R. (1993). Risk of population extinction from demographic and environmental stochasticity and random catastrophes. American Naturalist, 142, 911–927.CrossRefGoogle ScholarPubMed
Lawton, J. H. (1989). What is the relationship between population density and animal abundance?Oikos, 55, 429–434.CrossRefGoogle Scholar
Leigh, E. (1981). The average lifetime of a population in a varying environment. Journal of Theoretical Biology, 90, 213–239.CrossRefGoogle Scholar
MacArthur, R. H. (1960). On the relative abundance of species. American Naturalist, 94, 25–36.CrossRefGoogle Scholar
Magurran, A. E. & Henderson, P. A. (2003). Explaining the excess of rare species in natural species abundance distributions. Nature, 422, 714–716.CrossRefGoogle ScholarPubMed
Malamud, B. D., Turcotte, D. L., Guzzetti, F. & Reichenbach, P. (2004). Landslide inventories and their statistical properties. Earth Surface Processes and Landforms, 29, 687–712.CrossRefGoogle Scholar
Malamud, B. D., Millington, J. D. A. & Perry, G. L. W. (2005). Characterizing wildfire regimes in the United States. Proceedings of the National Academy of Sciences of the USA, 102, 4694–4699.CrossRefGoogle ScholarPubMed
Mantegna, R. N. & Stanley, H. E. (2000). An Introduction to Econophysics: Correlations and Complexity in Finance. Cambridge: Cambridge University Press.Google Scholar
Mårell, A., Ball, J. P. & Hofgaard, A. (2002). Foraging and movement paths of female reindeer: insights from fractal analysis, correlated random walks, and Levy flights. Canadian Journal of Zoology, 80, 854–865.CrossRefGoogle Scholar
Maris, H. J. & Kadanoff, L. P. (1978).Teaching the renormalization group. American Journal of Physics, 46, 652–657.CrossRefGoogle Scholar
Marquet, P. A. (2002a). The search for general principles in ecology. Nature, 418, 723.CrossRefGoogle Scholar
Marquet, P. A. (2002b). Of predators, prey, and power laws. Science, 295, 2229–2230.CrossRefGoogle Scholar
Marquet, P. A., Navarrete, S. A. & Castilla, J. C. (1990). Scaling population density to body size in rocky intertidal communities. Science, 250, 1125–1127.CrossRefGoogle ScholarPubMed
Marquet, P. A., Keymer, J. E. & Cofre, H. (2003). Breaking the stick in space: of niche models, metacommunities, and patterns in the relative abundance of species. In Macroecology: Concepts and Consequences, ed. Blackburn, T. M. & Gaston, K. J., pp. 64–84. Cambridge: Cambridge University Press.Google Scholar
Marquet, P. A., Quiñones, R. A., Abades, S. R., et al. (2005). Scaling and power-laws in ecological systems. Journal of Experimental Biology, 208, 1749–1769.CrossRefGoogle ScholarPubMed
May, R. M. (1975). Patterns of species abundance and diversity. In Ecology and Evolution in Communities, ed. Cody, M. & Diamond, J.. Princeton: Princeton University Press.Google Scholar
McGill, B. & Collins, C. (2003). A unified theory for macroecology based on spatial patterns of abundance. Evolutionary Ecology Research, 5, 469–492.Google Scholar
Milne, B. T. (1998). Motivation and beliefs of complex systems approaches in ecology. Ecosystems, 1, 449–456.CrossRefGoogle Scholar
Miramontes, O. (1995). Order-disorder transitions in the behavior of ant societies. Complexity, 1, 56–60.CrossRefGoogle Scholar
Miramontes, O. & Rohani, P. (1998). Intrinsically generated coloured noise in laboratory insect populations. Proceedings of the Royal Society of London, Series B, 265, 785–792.CrossRefGoogle Scholar
Mitzenmacher, M. (2001). A brief history of generative models for power law and log normal distributions. In Proceedings of the 39th Annual Allerton Conference on Communication, Control, and Computing, pp. 182–191. Urbana-Champagne: University of Illinois.
Moritz, M. A., Morais, M. E., Summerell, L. A., Carlson, J. M. & Doyle, J. (2005). Wildfires, complexity, and highly optimized tolerance. Proceedings of the National Academy of Sciences of the USA, 102, 17912–17917.CrossRefGoogle ScholarPubMed
Newman, M. E. J. (2005). Power laws, Pareto distributions and Zipf's law. Contemporary Physics, 46, 323–351.CrossRefGoogle Scholar
Niwa, H-S. (2003). Power-law versus exponential distributions of animal group sizes. Journal of Theoretical Biology, 224, 451–457.CrossRefGoogle ScholarPubMed
Niwa, H-S. (2005). Power-law scaling in dimension-to-biomass relationship of fish schools. Journal of Theoretical Biology, 235, 419–430.CrossRefGoogle ScholarPubMed
Pascual, M. & Guichard, F. (2005). Criticality and disturbance in spatial ecological systems. Trends in Ecology and Evolution, 20, 88–95.CrossRefGoogle ScholarPubMed
Perline, R. (2005). Strong, weak and false inverse power laws. Statistical Science, 20, 68–88.CrossRefGoogle Scholar
Peters, R. H. (1983). The Ecological Implications of Body Size. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Pimm, S. L. & Redfearn, A. (1988). The variability of population-densities. Nature, 334, 613–614.CrossRefGoogle Scholar
Pimm, S., Jones, H. & Diamond, J. (1988). On the risk of extinction. American Naturalist, 132, 757–785.CrossRefGoogle Scholar
Rhodes, C. J. & Anderson, R. M. (1996). Power laws governing epidemics in isolated populations. Nature, 381, 600–602.CrossRefGoogle ScholarPubMed
Rhodes, C. J., Jensen, H. J. & Anderson, R. M. (1997). On the critical behavior of simple epidemics. Proceedings of the Royal Society of London, Series B, 264, 1639–1646.CrossRefGoogle ScholarPubMed
Rinaldo, A., Maritan, A., Cavender-Bares, K. K. & Chisholm, S. W. (2002). Cross-scale ecological dynamics and microbial size spectra in marine ecosystems. Proceedings of the Royal Society of London, Series B, 269, 2051–2059.CrossRefGoogle ScholarPubMed
Roy, M., Pascual, M. & Franc, A. (2003). Broad scaling region in a spatial ecological system. Complexity, 8, 19–27.CrossRefGoogle Scholar
Samorodnitsky, G. & Taqqu, M. S. (1994). Stable Non-Gaussian Random Processes: Stochastic Models with Infinite Variance. New York: Chapman and Hall.Google Scholar
Sauer, J. R., Peterjohn, B. G. & Link, W. A. (1994). Observer differences in the North American Breeding Bird Survey. Auk, 111, 50–62.CrossRefGoogle Scholar
Sauer, J. R., Hines, J. E. & Fallon, J. (2005). The North American Breeding Bird Survey, Results and Analysis 1966–2004. Version 2005.2. Laurel, MD: USGS Patuxent Wildlife Research Center.Google Scholar
Schmidt-Nielsen, K. (1984). Scaling: Why is Animal Size so Important?Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Solé, R. V. & Alonso, D. (1998). Random walks, fractals and the origins of rainforest diversity. Advances in Complex Systems, 1, 203–220.CrossRefGoogle Scholar
Solé, R. V., Manrubia, S. C., Luque, B., Delgado, J. & Bascompte, J. (1996). Phase transitions and complex systems. Complexity, 1, 13–26.CrossRefGoogle Scholar
Solé, R. V., Manrubia, S. C., Kauffman, S., Benton, M. & Bak, P. (1999). Criticality and scaling in evolutionary ecology. Trends in Ecology and Evolution, 14, 156–160.CrossRefGoogle ScholarPubMed
Solé, R. V., Alonso, D. & McKane, A. (2002). Self-organized instability in complex ecosystems. Philosophical Transactions of the Royal Society of London, Series B, 357, 667–681.CrossRefGoogle ScholarPubMed
Solow, A. R. (2005). Power laws without complexity. Ecology Letters, 8, 361–363.CrossRefGoogle Scholar
Sornette, D. (1998). Linear stochastic dynamics with nonlinear fractal properties. Physica A, 250, 295–314.CrossRefGoogle Scholar
Sornette, D. (2004). Critical Phenomena in Natural Sciences. Chaos Fractals, Selforganization and Disorder: Concepts and Tools. Heidelberg: Springer-Verlag.Google Scholar
Spengler, S. J. (2000). Computers and biology: bioinformatics in the information age. Science, 287, 1221–1223.CrossRefGoogle ScholarPubMed
Stanley, H. E. (1971). Introduction to Phase Transitions and Critical Phenomena. Oxford: Oxford University Press.Google Scholar
Stanley, H. E. (1995). Power laws and universality. Nature, 378, 554.CrossRefGoogle Scholar
Stanley, H. E. (1999). Scaling, universality, and renormalization: three pillars of modern critical phenomena. Reviews of Modern Physics, 71, 358–366.CrossRefGoogle Scholar
Stanley, H. E., Amaral, L. A. N., Gopikrishnan, P., Ivanov, P. Ch., Keitt, T. H. & Plerou, V. (2000). Scale invariance and universality: organizing principles in complex systems. Physica A, 281, 60–68.CrossRefGoogle Scholar
Stenseth, N. C. (1979). Where have all the species gone? On the nature of extinction and the Red Queen hypothesis. Oikos, 33, 196–227.CrossRefGoogle Scholar
Storch, D. & Gaston, K. J. (2004). Untangling ecological complexity on different scales of space and time. Basic and Applied Ecology, 5, 389–400.CrossRefGoogle Scholar
Storch, D., Gaston, K. J. & Cepák, J. (2002). Pink landscapes: 1/f spectra of spatial environmental variability and bird community composition. Proceedings of the Royal Society of London, Series B, 269, 1791–1796.CrossRefGoogle ScholarPubMed
Taylor, L. R. (1961). Aggregation, variance and the mean. Nature, 189, 732–735.CrossRefGoogle Scholar
Taylor, L. R. & Woiwod, I. P. (1980). Temporal stability as a density-dependent species characteristic. Journal of Animal Ecology, 49, 209–224.CrossRefGoogle Scholar
Terres, J. (1980). Audubon Society Encyclopedia of North American Birds. New York: Alfred A. Knopf.Google Scholar
Udvardy, M. (1994). National Audubon Society Field Guide to North American Birds: Western Edition. New York: Alfred A. Knopf.Google Scholar
Valen, L. (1976). Energy and evolution. Evolutionary Theory, 1, 179–229.Google Scholar
Valen, L. (1977). The Red Queen. American Naturalist, 111, 809–810.CrossRefGoogle Scholar
Valen, L. (1980). Evolution as a zero-sum game for energy. Evolutionary Theory, 4, 289–300.Google Scholar
Viswanathan, G. M., Afanasyev, V., Buldyrev, S. V., Murphy, E. J., Prince, P. A. & Stanley, H. E. (1996). Levy-flight search patterns of wandering albatrosses. Nature, 381, 413–415.CrossRefGoogle Scholar
Viswanathan, G. M., Buldyrev, S. V., Havlin, S., DaLuz, M. G. E., Raposo, E. P. & Stanley, H. E. (1999). Optimizing the success of random searches. Nature, 401, 911–914.CrossRefGoogle ScholarPubMed
Williamson, M. (1972). The Analysis of Biological Populations. London: Arnold.Google Scholar
Williamson, M. & Gaston, K. J. (2005). The lognormal distribution is not an appropriate null hypothesis for the species–abundance distribution. Journal of Animal Ecology, 74, 409–423.CrossRefGoogle Scholar
West, G. B. (1999). The origin of universal scaling laws in biology. Physica A, 263, 104–113.CrossRefGoogle Scholar
West, G. B. & Brown, J. H. (2005). The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization. Journal of Experimental Biology, 208, 1575–1592.CrossRefGoogle ScholarPubMed

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