Title:

Models of relative abundance distributions. 2, Diversity and evenness statistics

Subtitle:

Diversity and evenness statistics

Creator:

Ulrich, Werner

Contributor:

Polish Academy of Sciences. Institute of Ecology

Publisher:

Polish Academy of Sciences. Institute of Ecology. Publishing Office

Place of publishing:

Dziekanów Leśny

Date issued/created:

2001

Description:

Pages 159-175 : illustrations ; 27 cm ; Bibliographical references (pages 173-175)

Type of object:

Journal/Article

Subject and Keywords:

relative abundance distributions ; diversity ; evenness ; power fraction ; random assortment ; Zipf-Mandelbrot Model

Abstract:

The recent concepts of diversity and evenness and their definitions are discussed. It is shown that especially the ambiguities in defining evenness has led to confusion about evenness measures and their applicability. Definitions of diversity and evenness from parameters of relative abundance distributions avoid such ambiguities. In this paper diversity is defined as the negative inverse of the slope of the relative abundance distribution in a semilogarithmic plot and evenness as the arcus tangens transformed shaping parameter. Diversity and evenness depend therefore on the type of relative abundance distribution and diversities from communities of different types of relative abundance distributions (power fraction, random assortment or Zipf-Mandelbrot type) cannot be compared directly. The properties of these newly defined diversity and evenness indices and their behavior in samples are discussed. It is shown that Tokeshi's newly developed power fraction model may serve as a universal basis for defining diversity and evenness indices.

References:

Begon M., Harper J. L., Town send C. R. 1986 - Ecology. Individuals, Populations and Communities. Oxford.
Bulla L. I 994 - An index of evenness and its associated diversity measure - Oikos 70: 167-171 .
Camargo J. A. 1993 - Must dominance increase with the number of subordinate species in competitive interactions? - J. Theor. Biol. 161: 537-542.
Camargo J. A. 1995 - On measuring species evenness and other associated parameters of community structure - Oikos 74: 538-542.
Caswell H. 1976 - Community stmcture: a neutral model analysis - Ecol. Monogr. 46: 327-354.
Dempster J. P., Atkinson D. A., Cheesman O. D. 1995 - The spatial population dynamics of insects exploiting a patchy food resource: I. Population extinctions and regulation - Oecologia 104: 340-353.
Den Boer P. J. 1985 - Fluctuations of density and survival of carabid populations - Oecologia 67: 322-330.
Doak D. F., Bigger D., Harding E. K., Marvier M. A., O'Malley R. E., Thornson D. 1998 - The statistical inevitability of stability-diversity relationships in community ecology - Am. Nat. 151: 264-276
Frontier S. 1985 - Diversity and structure in aquatic ecosystems (In: Oceanography and Marine Biology - An Annual Review, Ed. M. Barnes) - Aberdeen, pp. 253-312.
Grady-Steed J., Harris P. M., Morin P. J. 1997 - Biodiversity regulates ecosystem predictability - Nature 390: 162-165.
Grime J. P. 1997 - Biodiversity and ecosystem functioning: the debate deepens - Science 277: 1260-1261.
Heip C. 1974 - A new index measuring evenness - J. Mar. Biol. Ass. 54: 555-557.
Hill M. O. 1973 - Diversity and evenness: a unifying notation and its consequences - Ecology 54: 427-432.\
Hill M. O. 1997 - An evenness statistic based on the abundance-weighted variance of species proportions - Oikos 79: 413-416.
Hooper D. U., Vitousek P. M. 1998 - Effects of plant composition and diversity on nutrient cycling - Ecol. Monog. 68: 121-149.
Kempton R. A., Taylor L. R. 1976 - Models and statistics for species diversity - Nature 262: 818-820.
Krebs Ch. J. 1995 - Ecology - Harper and Row, London, 800 pp.
Kvelseth T. O. 1991 - Note on biological diversity, evenness, and homogeneity measures - Oikos 62: 123-127.
Lande R. 1996 - Statistics and partitioning of species diversity, and similarity among multiple communities - Oikos 76: 5-13.
Lewontin R. C. 1972 - The apportionment of human diversity - Evol. Biol. 6: 381 -398.
Magurran A. E. 1988 - Ecological diversity and its measurement - Princeton (Univ. Press), 179 pp.
May R. M. 1975 - Patterns of species abundance and diversity (In: Ecology and Evolution of Communities, Eds. M.L. Cody, J.M. Diamond) - Cambridge, pp. 81-120.
Molinari J. 1989 - A calibrated index for the measurement ofevenness - Oikos 56: 319-326.
Motomura I. 1932 - On the statistical treatment of communities - Zool. Mag. Tokyo 44: 379-383 (in Japanese).
Naeem S., Thompson L. J., Lawler S. P., Lawton J. H., Woodfin R. M. 1994 - Declining biodiversity can alter the performance of ecosystems - Nature 368: 734-737.
Naeem S., Thompson L. J., Lawler S. P., Lawton J. H., Woodfin R. M. 1995 - Empirical evidence that declining species diversity may alter the performance of terrestrial ecosystems - Phil. Trans. R. Soc. Lond. B 347: 249-262.
Naeem S., Li S. 1997 - Biodiversity enhances ecosystem reliability - Nature 390: 507-509.
Nee S., Harvcy P. H., Cotgreave P. 1992 - Population persistence and the natural relationship between body size and abundance (In: Conservation of biodiversity for sustainable development, Eds. O. T. Sandlund, K. Hindar, A. H. D. Brown) - Oslo (Scand. Univ. Press), pp. 124-136.
Peet R. K. 1974 - The measurement of species diversity - Annu. Rev. Ecol. Syst. 5: 285-307.
Pielou E. C. 1977 - Mathematical Ecology - New York, 385 pp. Rosenzweig M. L. 1995 - Species diversity in space and time - Cambridge (Univ. Press). 436 pp.
Routledge R. D. 1983 - Evenness indices: are any admissible? - Oikos 40: 149-151.
Sankaran M. McNaughton S. J. 1999 - Determinants of biodiversity regulate compositional stability of communities - Nature 401: 691-693. Schaefer M. 1983 - Okologie - Worterbi.icher der Biologie, Jena (Fischer), 354 pp.
Smith B., Wilson J. B. 1996 - A consumer's guide to evenness indices - Oikos 76: 70-82.
Sugihara G. 1980 - Minimal community structure: an explanation of species abundance patterns - Am. Nat. 116: 770-787.
Taylor L. R. 1978 - Bates, Williams, Hutchinson: a variety of diversities - (In: Diversity of insect faunas, Eds. L.A. Mound, N. Waloff) - Oxford (Blackwell Scient. Pub.): 1-18.
Taylor L. R., Kempton R. A., Woiwod 1976 - Diversity statistics and the log-series model - J. Anim. Ecol. 45: 255-272.
Tilman D. 1996 - Biodiversity: population versus ecosystem stability - Ecology 77: 350-363.
Tilman D., Lehman Cl. L., Bristow Ch. E. 1998 - Diversity-stability relationships: statistical inevitability of ecological consequence - Am. Nat. 151: 277-282.
Tilman D. 1999 - The ecological consequences of changes in biodiversity: a search for general principles - Ecology 80: 1455-1474.
Tokeshi M. 1990 - Niche apportionment or random assortment: species abundance patterns revisited - J. Animal Ecol. 59: 1129-1146.
Tokeshi M. 1993 - Species abundance patterns and community structure - Adv. Ecol. Res. 24: 111 -186.
Tokeshi M. 1996 - Power fraction: a new explanation of relative abundance patterns in species-rich assemblages - Oikos 75: 543-550.
Ulrich W. 1999a - Estimating species numbers by extrapolation I: comparing the performance of various estimators using large model communities - Pol. J. Ecol.: 47: 271-291.
Ulrich W. 1999b - Temporal stability of community structure of the parasitic Hymenoptera in a beech forest on limestone - Pol. J. Ecol. 47: 257-270.
Ulrich W. 2001a - On the scale dependence of evenness - Pol. J. Ecol. 49: 91-94.
Ulrich W. 2001b - Models of relative abundance distributions I: model fitting by stochastic models - Pol. J. Ecol. 49: 145-157.
Weiher E., Keddy P.A. 1999 - Relative abundance and evenness patterns along diversity and biomass gradients - Oikos 87: 355-361.
Whittaker R. H. 1972 - Evolution and measurement of species diversity - Taxon 21: 213-251.
Wilson J. B., Steel J. B., King W. McG., Gitay H. 1999 - The effect of spatial scale on evenness - J. Veg. Science 10: 463-468.

Relation:

Polish Journal of Ecology

Volume:

49

Issue:

2

Start page:

159

End page:

175

Resource type:

Text

Detailed Resource Type:

Article

Resource Identifier:

ISSN 1505-2249

Source:

MiIZ PAN, call no. P.2840 ; click here to follow the link

Language:

eng

Language of abstract:

Rights:

Creative Commons Attribution BY 3.0 PL license

Terms of use:

Copyright-protected material. [CC BY 3.0 PL] May be used within the scope specified in Creative Commons Attribution BY 3.0 PL license, full text available at: ; -

Digitizing institution:

Museum and Institute of Zoology of the Polish Academy of Sciences

Original in:

Library of the Museum and Institute of Zoology of the Polish Academy of Sciences

Projects co-financed by:

Operational Program Digital Poland, 2014-2020, Measure 2.3: Digital accessibility and usefulness of public sector information; funds from the European Regional Development Fund and national co-financing from the state budget.

Access:

Open