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8 - Biodiversity Scaling on a Continuous Plane: Geometric Underpinnings of the Nested Species–Area Relationship

from Part III - Theoretical Advances in Species–Area Relationship Research

Published online by Cambridge University Press:  11 March 2021

By
Arnošt L. Šizling  and
David Storch
Edited by
Thomas J. Matthews ,
Kostas A. Triantis  and
Robert J. Whittaker
Thomas J. Matthews
Affiliation:
University of Birmingham
Kostas A. Triantis
Affiliation:
National and Kapodistrian University of Athens
Robert J. Whittaker
Affiliation:
University of Oxford
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Summary

The slope and shape of the nested species–area relationship (SAR) can be derived using geometrical considerations. The local slope of the nested SAR is determined by mean species occupancy at a given scale. Thus, any factor that affects the scale dependent occupancy patterns of individual species will affect the overall shape of the nested SAR. Using only geometric considerations, we can derive not only the formula relating mean occupancy to the overall nested SAR slope, but also the overall triphasic shape of the nested SAR. The relatively shallow slope of the nested SAR at intermediate spatial scales, which can be well approximated by a power law, can be attributed to the scale independent (approximately fractal) spatial distribution of individual species. The shape and slope of the nested SAR are linked to beta diversity patterns as well as to the species abundance distribution (SAD), although we argue that the SAD is in fact a derived pattern which cannot be used to construct the nested SAR. In general, geometrical considerations provide a first-order explanation of the nested SAR, while biological factors affect the basic parameters of species distributions and thus act to determine the specific nested SAR in any given case.

Keywords

Macroecologybiodiversityspecies richnessscalepower lawspatial aggregationindividuals–area relationshipspecies turnoverhabitat heterogeneity
Type
Chapter
Information
The Species–Area Relationship
Theory and Application
 , pp. 185 - 210
Publisher: Cambridge University Press
Print publication year: 2021

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References

Adler, P. B. & Lauenroth, W. K. (2003) The power of time: Spatiotemporal scaling of species diversity. Ecology Letters, 6, 749–756.CrossRefGoogle Scholar
Adler, P. B., White, E. P., Lauenroth, W. K., Kaufman, D. M., Rassweiler, A. & Rusak, J. A. (2005) Evidence for a general species–time–area relationship. Ecology, 86, 2032–2039.CrossRefGoogle Scholar
Allen, A. P. & White, E. P. (2003) Effects of range size on species–area relationships. Evolutionary Ecology Research, 5, 493–499.Google Scholar
Arita, H. T. & Rodríguez, P. (2002) Geographic range, turnover rate and the scaling of species diversity. Ecography, 25, 541–550.Google Scholar
Arrhenius, O. (1921) Species and area. Journal of Ecology, 9, 95–99.CrossRefGoogle Scholar
Azaele, S., Muneepeerakul, R., Maritan, A., Rinaldo, A. & Rodriguez-Iturbea, I. (2008) Predicting spatial similarity of freshwater fish biodiversity. Proceedings of the National Academy of Sciences USA, 106, 7058–7062.Google Scholar
Azovsky, A. I. (2002) Size-dependent species–area relationship in benthos: Is the world more diverse for microbes? Ecography, 25, 273–282.Google Scholar
Bartha, S. & Ittzés, P. (2001) Local richness-species pool ratio: A consequence of the species–area relationship. Folia Geobotanica, 36, 9–23.CrossRefGoogle Scholar
Bonn, A., Storch, D. & Gaston, K. J. (2004) Structure of the species–energy relationship. Proceedings of the Royal Society B: Biological Sciences, 271, 1685–1691.Google Scholar
Caley, M. J. & Schluter, D. (1997) The relationship between local and regional diversity. Ecology, 78, 70–80.Google Scholar
Carey, S., Harte, J. & delMoral, R. (2006) Effect of community assembly and primary succession on the species–area relationship in disturbed ecosystems. Ecography, 29, 866–872.Google Scholar
Chiarucci, A., Viciani, D., Winter, C. & Diekmann, M. (2006) Effects of productivity on species–area curves in herbaceous vegetation: Evidence from experimental and observational data. Oikos, 115, 475–483.Google Scholar
Coleman, D. B. (1981) On random placement and species–area relations. Mathematical Biosciences, 54, 191–215.Google Scholar
Condit, R., Hubbell, S. P., Lafrankie, J. V., Sukumar, R., Manokaran, N., Foster, R. B. & Ashton, P. S. (1996) Species–area and species–individual relationships for tropical trees: A comparison of three 50-ha plots. Journal of Ecology, 84, 549–562.CrossRefGoogle Scholar
Connor, E. F. & McCoy, E. D. (1979) The statistics and biology of the species–area relationship. The American Naturalist, 113, 791–833.CrossRefGoogle Scholar
Dengler, J. (2009) Which function describes the species–area relationship best? A review and empirical evaluation. Journal of Biogeography, 36, 728–744.Google Scholar
Drakare, S., Lennon, J. L. & Hillebrand, H. (2006) The imprint of the geographical, evolutionary and ecological context on species–area relationships. Ecology Letters, 9, 215–227.Google Scholar
Finlay, B. J. (2002) Global dispersal of free-living microbial eukaryote species. Science, 296, 1061–1063.Google Scholar
Fridley, J. D., Peet, R. K., Wentworth, T. R. & White, P. S. (2005) Connecting fine- and broad-scale species–area relationships of southeastern U.S. flora. Ecology, 86, 1172–1177.Google Scholar
Gaston, K. J., Blackburn, T. M. & Lawton, J. H. (1997) Interspecific abundance–range size relationships: An appraisal of mechanisms. Journal of Animal Ecology, 66, 579–601.Google Scholar
Gaston, K. J., Evans, K. L. & Lennon, J. J. (2007) The scaling of spatial turnover: Pruning the thicket. Scaling Biodiversity. (ed. by Storch, D., Marquet, P. A. & Brown, J. H.), pp. 181–214. Cambridge: Cambridge University Press.Google Scholar
Gleason, H. A. (1922) On the relation between species and area. Ecology, 3, 158–162.CrossRefGoogle Scholar
Gray, J. S., Ugland, K. I. & Lambshead, J. (2004) On species accumulation and species–area curves. Global Ecology & Biogeography, 13, 567–568.CrossRefGoogle Scholar
Green, J. L. & Plotkin, J. B. (2007) A statistical theory for sampling species abundances. Ecology Letters, 10, 1037–1045.CrossRefGoogle ScholarPubMed
Haegeman, B. & Etienne, R. S. (2010) Entropy maximization and the spatial distribution of species. The American Naturalist, 175, E74–E90.CrossRefGoogle ScholarPubMed
Hanski, I. & Gyllenberg, M. (1997) Uniting two general patterns in the distribution of species. Science, 275, 397–400.CrossRefGoogle ScholarPubMed
Harrison, J. A., Allan, D. G., Underhill, L. G., Herremans, M., Tree, A. J., Parker, V. & Brown, C. J. (1997) The atlas of southern African birds. Vol I & II. Johannesburg: Bird Life South Africa.Google Scholar
Harte, J. & Kinzig, A. P. (1997) On the implications of species–area relationships for endemism, spatial turnover, and food web patterns. Oikos, 80, 417–427.CrossRefGoogle Scholar
Harte, J., Conlisk, E., Ostling, A., Green, J. L. & Smith, A. B. (2005) A theory of spatial structure in ecological communities at multiple spatial scales. Ecological Monographs, 75, 179–197.Google Scholar
Harte, J., Kinzig, A. & Green, J. (1999) Self-similarity in the distribution and abundance of species. Science, 284, 334–336.Google Scholar
Harte, J., Smith, A. B. & Storch, D. (2009) Biodiversity scales from plots to biomes with a universal species–area curve. Ecology Letters, 12, 789–797.Google Scholar
He, F. & Condit, R. (2007) The distribution of species: Occupancy, scale, and rarity. Scaling biodiversity (ed. by Storch, D., Marquet, P. A. and Brown, J. H.), pp. 32–50. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
He, F. & Gaston, K. J. (2000) Estimating species abundance from occurrence. The American Naturalist, 156, 553–559.Google Scholar
He, F. & Legendre, P. (1996) On species–area relations. The American Naturalist, 148, 719–737.Google Scholar
He, F. & Legendre, P. (2002) Species diversity patterns derived from species–area models. Ecology, 85, 1185–1198.Google Scholar
Hubbell, S. P. (2001) The unified theory of biodiversity and biogeography. Princeton, NJ: Princeton University Press.Google Scholar
Jaynes, E. T. (1957) Information theory and statistical mechanics. Physical Review, 106, 620–630.Google Scholar
Jaynes, E. T. (1982) On the rationale of maximum entropy methods. Proceedings of the IEEE, 70, 939–952.Google Scholar
Koleff, P., Gaston, K. J. & Lennon, J. J. (2003) Measuring beta diversity for presence-absence data. Journal of Animal Ecology, 72, 367–382.Google Scholar
Kunin, W. E. (1997) Sample shape, spatial scale and species counts: Implications for reserve design. Biological Conservation, 82, 369–377.Google Scholar
Kunin, W. E. (1998) Extrapolating species abundances across spatial scales. Science, 281, 1513–1515.Google Scholar
Kunin, W. E., Harte, J., He, F., Hui, C., Jobe, R. T., Ostling, A., Polce, C., Šizling, A. L., Smith, A. B., Smith, K., Smart, S. M., Storch, D., Tjørve, E., Ugland, K.-I., Ulrich, W. & Varma, V. (2018) Up-scaling biodiversity: Estimating the species–area relationship from small samples. Ecological Monographs, 88, 170–187.Google Scholar
Kůrka, P., Šizling, A. L. & Rosindell, J. (2010) Analytical evidence for scale-invariance in the shape of species abundance distributions. Mathematical Biosciences, 223, 151–159.Google Scholar
Lazarina, M., Kallimanis, A. S. & Sgardelis, S. (2013) Does the universality of the species–area relationship apply to smaller scales and across taxonomic groups? Ecography, 36, 965–970.Google Scholar
Leitner, W. A. & Rosenzweig, M. L. (1997) Nested species–area curves and stochastic sampling: A new theory. Oikos, 79, 503–512.Google Scholar
Lennon, J. J., Kunin, W. E. & Hartley, S. (2002) Fractal species distributions do not produce power-law species area distribution. Oikos, 97, 378–386.CrossRefGoogle Scholar
Lepš, J. & Štursa, J. (1989) Species–area curve, life history strategies, and succession: A field test of relationships. Vegetatio, 83, 249–257.CrossRefGoogle Scholar
MacArthur, R. H. & Wilson, E. O. (1967) The theory of island biogeography. Princeton, NJ: Princeton University Press.Google Scholar
Martín, H. G. & Goldenfeld, N. (2006) On the origin and robustness of power-law species–area relationships in ecology. Proceedings of the National Academy of Sciences USA, 103, 10310–10315.Google Scholar
May, R. (1975) Patterns of species abundance and diversity. Ecology and evolution of communities (ed. by Cody, M. L. and Diamond, J. M.), pp. 81–120. Cambridge, MA: Belknap Press.Google Scholar
McGill, B. J. (2010) Towards a unification of unified theories of biodiversity. Ecology Letters, 13, 627–642.Google Scholar
McGill, B. J. & Collins, C. (2003) A unified theory for macroecology based on spatial patterns of abundance. Evolutionary Ecology Research, 5, 469–492.Google Scholar
Nachman, G. (1981) A mathematical model of the functional relationship between density and spatial distribution of a population. Journal of Animal Ecology, 50, 453–460.CrossRefGoogle Scholar
Nee, S. & Cotgreave, P. (2002) Does the species–area relationship account for the density–area relationship? Oikos, 99, 545–551.Google Scholar
Nekola, J. C. & White, P. S. (1999) Distance decay of similarity in biogeography and ecology. Journal of Biogeography, 26, 867–878.Google Scholar
O’Dwyer, J. P. & Green, J. L. (2010) Field theory for biogeography: A spatially explicit model for predicting patterns of biodiversity. Ecology Letters, 13, 87–95.CrossRefGoogle ScholarPubMed
Ovaskainen, O. & Hanski, I. (2003) The species–area relationship derived from species-specific incidence functions. Ecology Letters, 6, 903–909.Google Scholar
Pautasso, M. & Weisberg, P. J. (2008) Negative density–area relationship: The importance of zeros. Global Ecology & Biogeography, 17, 203–210.CrossRefGoogle Scholar
Preston, F. V. (1960) Time and space and the variation of species. Ecology, 41, 611–627.Google Scholar
Rosenzweig, M. L. (1995) Species diversity in space and time. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Rosenzweig, M. L. & Ziv, Y. (1999) The echo pattern of species diversity: Pattern and processes. Ecography, 22, 614–628.CrossRefGoogle Scholar
Rosindell, J. & Cornell, S. J. (2007) Species–area relationships from a spatially explicit neutral model in an infinite landscape. Ecology Letters, 10, 586–595.CrossRefGoogle Scholar
Rosindell, J. & Cornell, S. J. (2009) Species–area curves, neutral models, and long-distance dispersal. Ecology, 90, 1743–1750.Google Scholar
Scheiner, S. M. (2003) Six types of species–area curves. Global Ecology & Biogeography, 12, 441–447.Google Scholar
Scheiner, S. M. (2004) A mélange of curves – Further dialogue about species–area relationships. Global Ecology & Biogeography, 13, 479–484.Google Scholar
Shmida, A. & Wilson, M. V. (1985) Biological determinants of species diversity. Journal of Biogeography, 12, 1–20.Google Scholar
Šizling, A. L. & Storch, D. (2004) Power-law species–area relationships and self-similar species distributions within finite areas. Ecology Letters, 7, 60–68.Google Scholar
Šizling, A. L. & Storch, D. (2007) Geometry of species distributions: Random clustering and scale invariance. Scaling Biodiversity (ed. by Storch, D., Marquet, P. A. & Brown, J. H.), pp. 77–99. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Šizling, A. L., Kunin, W. E., Šizlingová, E., Reif, J. & Storch, D. (2011) Between geometry and biology: The problem of universality of the species–area relationship. The American Naturalist, 178, 602–611.CrossRefGoogle ScholarPubMed
Šizling, A. L., Šizlingová, E., Tjørve, E., Tjørve, K. M. C. & Kunin, W. E. (2017) How to allow SAR collapse across local and continental scales: A resolution of the controversy between Storch et al. (2012) and Lazarina et al. (2013). Ecography, 40, 971–981.Google Scholar
Šizling, A. L., Storch, D., Reif, J. & Gaston, K. J. (2009b) Invariance in species-abundance distributions. Theoretical Ecology, 2, 89–103.Google Scholar
Šizling, A. L., Storch, D., Šizlingová, E., Reif, J. & Gaston, K. J. (2009a) Species abundance distribution results from a spatial analogy of central limit theorem. Proceedings of the National Academy of Sciences USA, 106, 6691–6695.Google Scholar
Storch, D. (2016) The theory of the nested species–area relationship: Geometric foundations of biodiversity scaling. Journal of Vegetation Science, 27, 880–891.Google Scholar
Storch, D. & Šizling, A. L. (2008) The concept of taxon invariance in ecology: Do diversity patterns vary with changes in taxonomic resolution? Folia Geobotanica, 43, 329–344.Google Scholar
Storch, D., Evans, K. L. & Gaston, K. J. (2005) The species–area–energy relationship. Ecology Letters, 8, 487–492.Google Scholar
Storch, D., Keil, P. & Jetz, W. (2012) Universal species–area and endemics–area relationships at continental scales. Nature, 488, 78–81.Google Scholar
Storch, D., Marquet, P. A. & Brown, J. H. (eds.) (2007) Scaling biodiversity. Cambridge: Cambridge University Press.Google Scholar
Storch, D., Šizling, A. L., Reif, J., Polechová, J., Šizlingová, E. & Gaston, K. J. (2008) The quest for a null model for macroecological patterns: Geometry of species distributions at multiple spatial scales. Ecology Letters, 11, 771–784.Google Scholar
Tjørve, E. (2003) Shapes and functions of species–area curves: A review of possible models. Journal of Biogeography, 30, 827–835.CrossRefGoogle Scholar
Tjørve, E. (2009) Shapes and functions of species–area curves (II): A review of new models and parameterizations. Journal of Biogeography, 36, 1435–1445.Google Scholar
Tjørve, E. & Tjørve, K. M. C. (2008) The species–area relationship, self-similarity, and the true meaning of the z-value. Ecology, 89, 3528–3533.CrossRefGoogle ScholarPubMed
Tjørve, E. & Turner, W. R. (2009) The importance of samples and isolates for species–area relationships. Ecography, 32, 391–400.Google Scholar
Tjørve, E., Kunin, W. E., Polce, C. & Tjørve, K. M. C. (2008) Species–area relationship: Separating the effects of species abundance and spatial distribution. Journal of Ecology, 96, 1141–1151.Google Scholar
Ugland, K. I., Gray, J. S. & Ellingsen, K. E. (2003) The species-accumulation curve and estimation of species richness. Journal of Animal Ecology, 72, 888–897.Google Scholar
Ugland, K. I., Gray, J. S. & Lambshead, J. D. (2005) Species accumulation curves analysed by a class of null models discovered by Arrhenius. Oikos, 108, 263–274.Google Scholar
Ulrich, W. & Buszko, J. (2003) Self-similarity and the species–area relation of Polish butterflies. Basic and Applied Ecology, 4, 263–270.Google Scholar
Virkkala, R. (1993) Ranges of northern forest passerines: A fractal analysis. Oikos, 67, 218–226.Google Scholar
White, E. P. (2007) Spatiotemporal scaling of species richness: Patterns, processes, and implications. Scaling Biodiversity (ed. by Storch, D., Marquet, P. A. and Brown, J. H.), pp. 325–346. Cambridge: Cambridge University Press.Google Scholar
Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279–338.Google Scholar
Williams, M. R. (1995) An extreme-value function model of the species incidence and species–area relationship. Ecology, 76, 2607–2616.Google Scholar
Williamson, M. H. (1988) Relationship of species number to area, distance and other variables. Analytical biogeography (ed. by Myers, A. A. & Giller, P. S.), pp. 91–115. London: Chapman & Hall.Google Scholar
Wright, D. H. (1991) Correlations between incidence and abundance are expected by chance. Journal of Biogeography, 18, 463–466.Google Scholar

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