Book contents
- The Species–Area Relationship
- Ecology, Biodiversity and Conservation
- The Species–Area Relationship
- Copyright page
- Contents
- Contributors
- Foreword
- Preface
- Part I Introduction and History
- Part II Diversity–Area Relationships: The Different Types and Underlying Factors
- Part III Theoretical Advances in Species–Area Relationship Research
- 7 Mathematical Expressions for the Species–Area Relationship and the Assumptions behind the Models
- 8 Biodiversity Scaling on a Continuous Plane: Geometric Underpinnings of the Nested Species–Area Relationship
- 9 Species Accumulation Curves and Extreme Value Theory
- 10 The Species–Area Relationship: Idiosyncratic or Produced by ‘Laws Acting around Us’?
- 11 The Species–Area Relationships of Ecological Neutral Theory
- 12 On the Interface of Food Webs and Spatial Ecology: The Trophic Dimension of Species–Area Relationships
- Part IV The Species–Area Relationship in Applied Ecology
- Part V Future Directions in Species–Area Relationship Research
- Index
- References
7 - Mathematical Expressions for the Species–Area Relationship and the Assumptions behind the Models
from Part III - Theoretical Advances in Species–Area Relationship Research
Published online by Cambridge University Press: 11 March 2021
Book contents
- The Species–Area Relationship
- Ecology, Biodiversity and Conservation
- The Species–Area Relationship
- Copyright page
- Contents
- Contributors
- Foreword
- Preface
- Part I Introduction and History
- Part II Diversity–Area Relationships: The Different Types and Underlying Factors
- Part III Theoretical Advances in Species–Area Relationship Research
- 7 Mathematical Expressions for the Species–Area Relationship and the Assumptions behind the Models
- 8 Biodiversity Scaling on a Continuous Plane: Geometric Underpinnings of the Nested Species–Area Relationship
- 9 Species Accumulation Curves and Extreme Value Theory
- 10 The Species–Area Relationship: Idiosyncratic or Produced by ‘Laws Acting around Us’?
- 11 The Species–Area Relationships of Ecological Neutral Theory
- 12 On the Interface of Food Webs and Spatial Ecology: The Trophic Dimension of Species–Area Relationships
- Part IV The Species–Area Relationship in Applied Ecology
- Part V Future Directions in Species–Area Relationship Research
- Index
- References
Summary
Although the species–area relationship (SAR) is commonly presumed to be either a power law or to follow the logarithmic relationship, a large number of other mathematical expressions have been proposed to describe the relationship. These models can be divided into four general categories, distinguishing between asymptotic and non-asymptotic, and between convex upward and sigmoid models (in arithmetic space). The choice of regression model should not be determined by best fit alone; rather, the choice should relate to the purpose of fitting mathematical models to SAR data: either descriptive, explicative or predictive. Therefore, we should choose models that are likely to result from expected ecological patterns. We argue that neither (accumulative) sample-area SARs (saSARs) nor island SARs (ISARs) have upper asymptotes and ISARs may be sigmoid if the smallest islands (finest scales) are included. Amongst the 30 different models we review here, few are non-asymptotic. Both the power model and logarithmic model return convex non-asymptotic curves, whereas the second persistence (P2) model and the quadratic logarithmic model consistently return sigmoid curves without asymptotes. We add the Tjørve-hybrid to this shortlist, as it can be useful when neither the power nor the logarithmic model provides a good fit to saSAR data.
Keywords
- Type
- Chapter
- Information
- The Species–Area RelationshipTheory and Application, pp. 157 - 184Publisher: Cambridge University PressPrint publication year: 2021
References
Arrhenius, O. (1920a) Distribution of the species over the area. Meddelanden från Kungliga Vetenskapsakademiens Nobelinstitut, 4, 1–6.Google Scholar
Arrhenius, O. (1923) On the relation between species and area – A reply. Ecology, 4, 90–91.Google Scholar
Barrett, K., Wait, D. A. & Anderson, W. B. (2003) Small island biogeography in the Gulf of California: Lizards, the subsidized island biogeography hypothesis, and the small island effect. Journal of Biogeography, 30, 1575–1581.Google Scholar
Braun-Blanquet, J. & Jenny, H. (1926) Vegetations-entwicklung und bodenbildung in der alpine stufe der Zentralalpen (Klimaxgebiet des Caricion curvulae). Denkschriften Schweizerische Naturforsch Gesellschaft, 63, 183–344.Google Scholar
Brenner, W. (1921) Växtgeografiska studier i Barõsunds skärgård. Acta Sociatatis pro Fauna et Flora Fennica, 49, 1–151.Google Scholar
Brown, J. H. (1971) Mammals on mountaintops: Nonequilibrium insular biogeography. The American Naturalist, 105, 467–478.Google Scholar
Cain, S. A. (1934) Studies of virgin hardwood forest: II, A comparison of quadrat sizes in a quantitative phytosociological study of Nash's Woods, Posey County, Indiana. The American Midland Naturalist, 15, 529–566.Google Scholar
Cain, S. A. (1938) The species–area curve. The American Midland Naturalist, 19, 573–581.Google Scholar
Clench, H. K. (1979) How to make regional lists of butterflies: Some thoughts. Journal of the Lepidopterists' Society, 33, 216–231.Google Scholar
Cody, M. L., Moran, R., Rebman, J. & Thompson, H. (2002) Plants. A new island biogeography of the Sea of Cortés (ed. by Case, T. J., Cody, M. L. and Ezcurra, E.), pp. 63–111. New York: Oxford University Press.Google Scholar
Colwell, R. K. & Coddington, J. A. (1994) Estimating terrestrial biodiversity through extrapolation. Philosophical Transactions of the Royal Society B: Biological Sciences, 345, 101–118.Google Scholar
Colwell, R. K., Chang, X. M. & Chang, J. (2004) Interpolating, extrapolating, and comparing incidence-based species accumulation curves. Ecology, 85, 2717–2727.Google Scholar
Condit, R., Hubbell, S. P., LaFrankie, J. V., Sukumar, R., Monokaran, 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.Google Scholar
Crawley, M. J. & Harral, J. E. (2001) Scale dependence in plant biodiversity. Science, 291, 864–868.Google Scholar
Darlington, P. J. (1957) Zoogeography: The geographical distribution of animals. New York: John Wiley.Google Scholar
Delsol, R., Loreau, M. & Haegeman, B. (2018) The relationship between spatial scaling of biodiversity and ecosystem stability. Global Ecology & Biogeography, 27, 439–449.Google Scholar
Dengler, J. (2008) Pitfalls in small-scale species–area sampling and analysis. Folia Geobotanica, 43, 269–287.Google 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
Deshaye, J. & Morisset, P. (1988) Floristic richness, area and habitat diversity in a hemiarctic archipelago. Journal of Biogeography, 15, 747–757.CrossRefGoogle Scholar
Diamond, J.M. (1975) Assembly of species communities. Ecology and evolution of communities (ed. by Cody, M. L. and Diamond, J. M.), pp. 342–444. Cambridge, MA: Belknap Press.Google Scholar
Dony, J. G. (1977) Species–area relationships in an area of intermediate size. Journal of Ecology, 65, 475–484.Google Scholar
Drakare, S., Lennon, J. J. & Hillebrand, H. (2006) The imprint of geographical, evolutionary and ecological context on species–area relationships. Ecology Letters, 9, 215–227.CrossRefGoogle ScholarPubMed
Fattorini, S. (2006) Detecting biodiversity hotspots by species–area relationships: A case study of Mediterranean beetles. Conservation Biology, 20, 1169–1180.Google Scholar
Fattorini, S. (2007a) Levels of endemism are not necessarily biased by the co-presence of species with different range sizes: A case study of Vilekin and Chikatunov's models. Journal of Biogeography, 34, 994–1007.Google Scholar
Fattorini, S. (2007b) To fit or not to fit? A poorly fitting procedure produces inconsistent results when the species–area relationship is used to locate hotspots. Biological Conservation, 16, 2531–2538.Google Scholar
Fattorini, S. & Fowles, A. P. (2005) A biogeographical analysis of the tenebrionid beetles (Coleoptera, Tenebrionidae) of the island of Thasos in the context of the Aegean Islands (Greece). Journal of Natural History, 39, 3919–3949.CrossRefGoogle Scholar
Fisher, R. A., Corbet, A. S. & Williams, C. B. (1943) The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12, 42–58.Google Scholar
Flather, C. H. (1996) Fitting species-accumulation functions and assessing regional land use impacts on avian diversity. Journal of Biogeography, 23, 155–168.Google Scholar
Fridley, J. D., Peet, R. K., Wentworth, T. R. & White, P. S. (2005) Connection fine- and broad-scale species–area relationships of southeastern U.S. flora. Ecology, 86, 1172–1177.Google Scholar
Gentile, G. & Argano, R. (2005) Island biogeography of the Mediterranean Sea: The species–area relationship for terrestrial isopods. Journal of Biogeography, 32, 1715–1726.Google Scholar
Gitay, H., Roxburgh, S. H. & Wilson, J. B. (1991) Species–area relations in a New-Zealand tussock grassland, with implications for nature-reserve design and for community structure. Journal of Vegetation Science, 2, 113–118.Google Scholar
Goodall, D. W. (1952) Quantitative aspects of plant distribution. Biological Reviews, 27, 194–242.Google Scholar
Gotelli, N. & Colwell, R. K. (2001) Quantifying biodiversity: Procedures and pitfalls in the measurement and comparison of species richness. Ecology Letters, 4, 379–391.Google Scholar
Green, J. L. & Ostling, A. (2003) Endemics–area relationships: The influence of species dominance and spatial aggregation. Ecology, 84, 3090–3097.Google Scholar
Green, J. L. & Plotkin, J. B. (2007) A statistical theory for sampling species abundances. Ecology Letters, 10, 1037–1045.Google Scholar
Guilhaumon, F., Gimenez, O., Gaston, K. J. & Mouillot, D. (2008) Taxonomic and regional uncertainty in species–area relationships and the identification of richness hotspots. Proceedings of the National Academy of Sciences USA, 105, 15458–15463.Google Scholar
Hanski, I., Zurita, G. A., Bellocq, M. I. & Rybicki, J. (2013) Species–fragmented area relationship. Proceedings of the National Academy of Sciences USA, 110, 12715–12720.Google Scholar
Harte, J., Blackburn, T. & Ostling, A. (2001) Self-similarity and the relationship between abundance and range size. The American Naturalist, 157, 374–386.Google Scholar
Harte, J., Kinzig, A. & Green, J. (1999) Self-similarity in the distribution and abundance of species. Science, 284, 334–336.Google Scholar
He, F. & Hubbell, S. P. (2011) Species–area relationships always overestimate extinction rates from habitat loss. Nature, 473, 368–371.CrossRefGoogle ScholarPubMed
He, F. & Hubbell, S. P. (2013) Estimating extinction from species–area relationships: Why the numbers do not add up. Ecology, 94, 1905–1912.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, 83, 1185–1198.Google Scholar
Hopkins, B. (1955) The species–area relations of plant communities. Journal of Ecology, 43, 409–426.Google Scholar
Hopkins, B. & Skellam, J. G. (1954) A new method for determining the type of distribution of plant individuals. Annals of Botany, 18, 213–217.Google Scholar
Hubbell, S. P. (2001) The unified neutral theory of biodiversity and biogeography. Princeton, NJ: Princeton University Press.Google Scholar
Irie, H. & Tokita, K. (2012) Species–area relationship for power-law species abundance distribution. International Journal of Biomathematics, 5, 1260014.Google Scholar
Kangas, P. (1987) On the use of species area curves to predict extinctions. Bulletin of the Ecological Society of America, 68, 158–162.Google Scholar
Keeley, J. E. & Fotheringham, C. J. (2005) Plot shape effects on plant species diversity measurements. Journal of Vegetation Science, 16, 249–256.Google Scholar
Keil, P., Pereira, H. M., Cabral, J. S., Chase, J. M., May, F., Martins, I. S. & Winter, M. (2018) Spatial scaling of extinction rates: Theory and data reveal nonlinearity and a major upscaling and downscaling challenge. Global Ecology & Biogeography, 27, 2–13.Google Scholar
Keil, P., Storch, D. & Jetz, W. (2015) On the decline of biodiversity due to area loss. Nature Communications, 6, 8837.Google Scholar
Kobayashi, S. (1974) The species–area relation I. A model for discrete sampling. Researches on Population Ecology, 15, 223–237.Google Scholar
Kobayashi, S. (1975) The species–area relation II. A second model for continuous sampling. Researches on Population Ecology, 16, 265–280.Google Scholar
Krishnamari, R., Kumar, A. & Harte, J. (2004) Estimating species richness at large spatial scales using data from small discrete plots. Ecography, 27, 637–642.Google Scholar
Kunin, W. E., Harte, J., He, F., Hui, C., Jobe, R. T., Ostling, A., Polce, C., Šizling, A., Smith, A. B., Smith, K., Smart, S. M., Storch, D., Tjørve, E., Ugland, K.-I., Ulrich, W. & Varma, V. (2018) Upscaling biodiversity: Estimating the species–area relationship from small samples. Ecological Monographs, 88, 170–187.Google Scholar
Lennon, J. J., Kunin, W. E. & Hartley, S. (2002) Fractal species distributions do not produce power-law species–area relationships. Oikos, 97, 378–386.Google Scholar
Lennon, J. J., Kunin, W. E., Hartley, S. & Gaston, K. J. (2007) Species distribution patterns, diversity scaling and testing for fractals in Southern African birds. Scaling biodiversity (ed. by Storch, D., Marquet, P. and Brown, J.), pp. 51–76. Cambridge: Cambridge University Press.Google Scholar
Lomolino, M. V. (2000) Ecology’s most general, yet protean pattern: The species–area relationship. Journal of Biogeography, 27, 17–26.Google Scholar
Lomolino, M. V. (2001) The species–area relationship: New challenges for an old pattern. Progress in Physical Geography, 25, 1–21.Google Scholar
Lomolino, M. V. (2002) ‘… there are areas too small, and areas too large to show clear diversity patterns…’ R. H. MacArthur (1972: 191). Journal of Biogeography, 29, 555–557.Google Scholar
Lomolino, M. V. & Weiser, M. D. (2001) Towards a more general species–area relationship: Diversity of all islands, great and small. Journal of Biogeography, 28, 431–445.Google Scholar
MacArthur, R. H. & Wilson, E. O. (1963) An equilibrium theory of insular zoogeography. Evolution, 17, 373–387.Google Scholar
MacArthur, R. H. & Wilson, E. O. (1967) The theory of island biogeography. Princeton, NJ: Princeton University Press.Google Scholar
Maddux, R. D. (2004) Self-similarity and the species–area relationship. The American Naturalist, 163, 616–626.Google Scholar
Malyshev, L. I. (1991) Some quantitative approaches to problems of comparative floristics. Quantitative approaches in phytogeography (ed. by Nimis, P. L. and Crovello, T. J.), pp. 15–33. Dordrecht: Kluwer Academic Publishers.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
Matthews, T. J., Borregaard, M. K., Guilhaumon, F., Triantis, K. A. & Whittaker, R. J. (2016a) On the form of species–area relationships in habitat islands and true islands. Global Ecology & Biogeography, 25, 847–858.Google Scholar
Matthews, T. J., Steinbauer, M., Tzirkalli, E., Triantis, K. A. & Whittaker, R. J. (2014) Thresholds and the species–area relationship: A synthetic analysis of habitat island datasets. Journal of Biogeography, 41, 1018–1028.Google Scholar
Matthews, T. J., Triantis, K. A., Rigal, F., Borregaard, M. K., Guilhaumon, F. & Whittaker, R. J. (2016b) Island species–area relationships and species accumulation curves are not equivalent: An analysis of habitat island datasets. Global Ecology & Biogeography, 25, 607–618.Google Scholar
Miller, R. I. & Wiegert, R. G. (1989) Documenting completeness, species–area relations, and the species-abundance distribution of a regional flora. Ecology, 70, 16–22.Google Scholar
Olszewski, T. D. (2004) A unified mathematical framework for the measurement of richness and evenness within and among multiple communities. Oikos, 104, 377–387.Google Scholar
Palmer, M. W. (1990) The estimation of species richness by extrapolation. Ecology, 71, 1195–1198.Google Scholar
Pereira, M. & Daily, G. C. (2006) Biodiversity dynamics in countryside landscapes. Ecology, 87, 1877–1885.Google Scholar
Picard, N., Karambé, M. & Birnbaum, P. (2004) Species–area curve and spatial pattern. Écoscience, 11, 45–54.Google Scholar
Pimm, S. L. & Askins, R. A. (1995) Forest loss predict bird extinctions in eastern North America. Proceedings of the National Academy of Sciences USA, 92, 9343–9347.Google Scholar
Plotkin, J. B., Potts, M. D., Leslie, N., Manokaran, N., LaFrankie, J. & Ashton, P. S. (2000) Species–area curves, spatial aggregation, and habitat specialization in tropical forests. Journal of Theoretical Biology, 207, 81–99.Google Scholar
Preston, F. W. (1960) Time and space and the variation of species. Ecology, 41, 611–627.Google Scholar
Preston, F. W. (1962) The canonical distribution of commonness and rarity: Part I & II. Ecology, 43 , 185–215, 410–432.Google Scholar
Rosenzweig, M. L. (1995) Species diversity in space and time. Cambridge: Cambridge University Press.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 curves. Global Ecology & Biogeography, 13, 479–484.Google Scholar
Simberloff, D. (1992) Do species–area curves predict extinction in fragmented forests? Tropical deforestation and species extinction (ed. by Whitmore, T. C. and Sayer, J. A.), pp. 75–89. London: Chapman and Hall.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. and Brown, J. H.), pp. 77–100. Cambridge: Cambridge University Press.Google Scholar
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
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. & Gaston, K. J. (2003) Geometry of the species–area relationship in central European birds: Testing the mechanism. Journal of Animal Ecology, 72, 509–519.Google Scholar
Taylor, L. R., Woiwood, I. P. & Perry, J. N. (1978) The density-dependence of spatial behaviour and the rarity of randomness. Journal of Animal Ecology, 47, 383–406.Google Scholar
Tjørve, E. (2002) Habitat size and number in multi-habitat landscapes: A model approach based on species–area curves. Ecography, 25, 17–24.Google Scholar
Tjørve, E. (2003) Shapes and functions of species–area curves: A review of possible models. Journal of Biogeography, 30, 827–835.Google 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. (2010) How to resolve the SLOSS debate: Lessons from species-diversity models. Journal of Theoretical Biology, 264, 604–612.Google Scholar
Tjørve, E. (2012) Arrhenius and Gleason revisited: New hybrid models resolve an old controversy. Journal of Biogeography, 39, 629–639.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.Google Scholar
Tjørve, E. & Tjørve, K. M. C. (2011) Subjecting the theory of the small-island effect to Ockham's razor. Journal of Biogeography, 38, 1834–1839.Google Scholar
Tjørve, E. & Tjørve, K. M. C. (2017) Species–area relationship. eLS (Encyclopedia of Life Sciences Online), pp. 1–9. Chichester: John Wiley & Sons.Google Scholar
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) The species–area relationship: Separating the effects of species-abundance and spatial distribution. Journal of Ecology, 96, 1141–1151.Google Scholar
Tjørve, E., Tjørve, K. C. M., Šizlingová, E. & Šizling, A. L. (2018) Great theories of species diversity in space and why they were forgotten: The beginnings of a spatial ecology and the Nordic early 20th-century botanists. Journal of Biogeography, 45, 530–540.Google Scholar
Triantis, K. A., Guilhaumon, F. & Whittaker, R. J. (2012) The island species–area relationship: Biology and statistics. Journal of Biogeography, 39, 215–231.Google Scholar
Triantis, K. A., Mylonas, M., Lika, K. & Vardinoyannis, K. (2003) A model for the species–area–habitat relationship. Journal of Biogeography, 30, 19–27.Google Scholar
Turner, W. R. & Tjørve, E. (2005) Scale-dependence in species–area relationships. Ecography, 28, 721–730.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
Ulrich, W. & Buszko, J. (2005) Detecting biodiversity hotspots using species–area and endemics–area relationships. Biodiversity and Conservation, 14, 1977–1988.Google Scholar
Veech, J. A. (2000) Choice of species–area function affects identification of hotspots. Conservation Biology, 14, 140–147.Google Scholar
Veech, J. A., Crist, T. O. & Summerville, K. S. (2003) Intraspecific aggregation decreases local species diversity of arthropods. Ecology, 84, 3376–3383.Google Scholar
Williams, C. B. (1950) The application of the logarithmic series to the frequency of occurrence of plant species in quadrats. Journal of Ecology, 38, 107–138.Google Scholar
Williams, C. B. (1964) Patterns in the balance of nature and related problems in quantitative ecology. London: Academic Press.Google Scholar
Williams, M. R. (1995) An extreme-value function model of the species incidence and species–area relations. Ecology, 76, 2607–2616.Google Scholar
Williams, M. R., Lamont, B. B. & Hestridge, J. D. (2009) Species–area functions revisited. Journal of Biogeography, 36, 1994–2004.Google Scholar
Williamson, M., Gaston, K. J. & Lonsdale, W. M. (2001) The species–area relationship does not have an asymptote! Journal of Biogeography, 28, 827–830.Google Scholar
Williamson, M., Gaston, K. J. & Lonsdale, W. M. (2002) An asymptote is an asymptote and not found in species–area relationships. Journal of Biogeography, 29, 1713.Google Scholar
Wilson, E. O. (1961) The nature of the taxon cycle in the Melanesian ant fauna. The American Naturalist, 95, 169–193.Google Scholar
- 2
- Cited by