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On richness and evenness within and between communities

  • Martin A. Buzas (a1) and Lee-Ann C. Hayek (a2)


Although there is extraordinary interest in the quantitative measurement of species diversity, published statements on the behavior of the components of species diversity are contradictory and lead to opposite conclusions. In this paper, we demonstrate that the confusion is due to two key oversights: (1) whether or not biological sampling is carried out within or between communities; and (2) determination of the statistical distribution underlying a biological community, which is crucial for the evaluation of all of the components of diversity measurement.

The problem of sampling “within” a population or community is basically distinct from the equivalent integration of structure and diversity measurement “between” differing multispecies populations. “Within-community sampling” is defined as a set of biological samples from a statistical population that has a particular statistical distribution or a constant value for the associated parameter(s). As the number of individuals increases along with the number of species, for a log series distribution, the diversity measures of Shannon's H, log series or Fisher's α, and Simpson's Index 1/λ remain constant while the evenness measures of Buzas-Gibson's E and Pielou's J decrease. For a log-normal distribution, J will remain constant while E decreases and α, 1/λ, and H increase. No single measure of evenness remains constant over all statistical distributions, so if constancy as a type of independence is required, the appropriate distribution must first be determined. Each species ensemble is mathematically fixed by the applicable statistical distribution.

In contrast, “between-community sampling” is defined as a set of biological samples from different statistical distributions and/or the same distribution with differing parametric values. If sampling is between communities and S increases while the number of individuals remains constant, then all the other measures considered here increase. The exception is the broken stick, for which E remains constant while H, J, α, and 1/λ increase.

Herein we propose and justify the use of the log-series distribution (with regression on the information decomposition equation) as a null model for determination of community structure and demonstrate that the community structure of a Miocene bed at Calvert Cliffs, Maryland, is a log series by use of this new unified methodology.



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Anscombe, F. J. 1950. Sampling theory of the negative binomial and logarithmic series distribution. Biometrika 37(3/4):358382.
Bastow, W. J., Steel, J. B., King, W. M., and Gitay, H. 1999. The effect of spatial scale on evenness. Journal of Vegetation Science 10:463468.
Berger, W. H., and Parker, F. L. 1970. Diversity of planktonic foraminifera in deep-sea sediments. Science 168:13451347.
Brian, M. V. 1953. Species frequencies in random samples from animal populations. Journal of Animal Ecology 22:5764.
Bulla, L. 1994. An index of evenness and its associated diversity measure. Oikos 70:167171.
Bulmer, M. G. 1974. On fitting the Poisson lognormal distribution to species-abundance data. Biometrics 30:101110.
Buzas, M. A., and Culver, S. J. 1999. Understanding regional species diversity through the log series distribution of occurrences. Diversity and Distributions 5:187195.
Buzas, M. A., and Gibson, T. G. 1969. Species diversity: benthonic Foraminifera in western north Atlantic. Science 163:7275.
Buzas, M. A., and Gibson, T. G. 1990. Spatial distribution of Miocene foraminifera at Calvert Cliffs, Maryland. Smithsonian Contributions to Paleobiology 68:135.
Buzas, M. A., and Hayek, L. C. 1996. Biodiversity resolution: an integrated approach. Biodiversity Letters 3:4043.
Buzas, M. A., and Hayek, L. C. 1998. SHE analysis for biofacies identification. Journal of Foraminiferal Research 28:233239.
Buzas, M. A., Smith, R. K., and Beem, K. A. 1977. Ecology and systematics of Foraminifera in two Thalassia habitats, Jamaica, West Indies. Smithsonian Contributions to Paleobiology 31:1139.
Buzas, M. A., Koch, C. F., Culver, S. J., and Sohl, N. F. 1982. On the distribution of species occurrence. Paleobiology 8:143150.
Camargo, J. A. 1995. On measuring species evenness and other associated parameters of community structure. Oikos 74:538542.
Caswell, H. 1976. Community structure: a neutral model analysis. Ecological Monographs 46:327354.
DeBenedictis, P. A. 1973. On the correlations between certain diversity indices. American Naturalist 107:295302.
Engen, S. 1974. On species frequency models. Biometrika 61:263270.
Fager, E. W. 1972. Diversity: a sampling study. American Naturalist 106(949):293310.
Fisher, R. A., Corbet, A. S., and 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 12:4258.
Gotelli, N. J., and Colwell, R. K. 2001. Quantifying biodiversity: procedures and pitfalls in the measurement and comparison of species richness. Ecology Letters 4:379391.
Gray, J. S. 1987. Species-abundance patterns. Pp. 53–44 in Gee, J. H. R. and Giller, P. S., eds. Organization of communities: past and present. Blackwell Scientific, Oxford.
Gray, J. S. 2000. The measurement of marine species diversity, with an application to the benthic fauna of the Norwegian continental shelf. Journal of Experimental Marine Biology and Ecology 250:2349.
Hayek, L. C., and Buzas, M. A. 1997. Surveying natural populations. Columbia University Press, New York.
Hayek, L. C., and Buzas, M. A. 1998. SHE analysis: an integrated approach to the analysis of forest biodiversity. Pp. 311321in Dallmeier, F. and Comiskey, J., eds. Forest biodiversity research, monitoring and modelling: conceptual background and Old World case studies. UNESCO and Parthenon, Paris.
Hill, M. O. 1973. Diversity and evenness: a unifying notation and its consequences. Ecology 54:427432.
Hubbell, S. P. 1997. A unified theory of biogeography and relative species abundance and its application to tropical rain forests and coral reefs. Coral Reefs 16(Suppl.):921.
Hubbell, S. P. 2001. The unified neutral theory of biodiversity and biogeography. Princeton University Press, Princeton, N.J.
Hughes, R. G. 1986. Theories and models of species abundance. American Naturalist 128:879899.
Hurlbert, S. H. 1971. The nonconcept of species diversity: a critique and alternative parameters. Ecology 52:577586.
Izsak, J., and Hunter, P. R. 1992. Serotype abundance distributions in reports of Salmonella incidents in domestic livestock as indicators of the population biology of Salmonella infections. Functional Ecology 6:154159.
Kempton, R. A. 1979. The structure of species abundance and measurement of diversity. Biometrics 35:307321.
Lloyd, M., and Ghelardi, R. J. 1964. A table for calculating the equitability component of species diversity. Journal of Animal Ecology 33:217225.
MacArthur, R. H. 1957. On the relative abundance of bird species. Proceedings of the National Academy of Sciences USA 43:293295.
Magurran, A. E. 1988. Ecological diversity and its Measurement. Princeton University Press, Princeton, N.J.
May, R. M. 1975. Patterns of species abundance and diversity. Pp. 81120in Cody, M. L. and Diamond, J. M., eds. Ecology and evolution of communities. Belknap Press of Harvard University Press, Cambridge.
Murray, J. W. 2002. Patterns in the cumulative increase in species from foraminiferal time-series. Marine Micropaleontology 48:121.
Osterman, L., Buzas, M. A., and Hayek, L. A. 2002. SHE analysis for biozonation of benthic foraminiferal assemblages from Western Arctic Ocean. Palaios 17:297303.
Parker, F. L. 1954. Distribution of the foraminifera in the northeastern Gulf of Mexico. Bulletin of the Museum of Comparative Zoology 111:453588.
Peet, R. K. 1975. Relative diversity indices. Ecology 56:496498.
Peters, S. E. 2004. Evenness of Cambrian-Ordovician benthic communities in North America. Paleobiology 30:325346.
Peters, S. E., and Bork, K. B. 1999. Species-abundance models: an ecological approach to inferring paleoenvironment and resolving paleoecological change in the Waldron Shale (Silurian). Palaios 14:234245.
Pielou, E. C. 1966. The measurement of diversity in different types of biological collections. Journal of Theoretical Biology 13:131144.
Pielou, E. C. 1975. Ecological diversity. Wiley-Interscience, New York.
Pisces Conservation Ltd. 2002. Species diversity and richness III. Pisces Conservation, Lymington, U.K.
Preston, F. W. 1948. The commonness, and rarity, of species. Ecology 29:254283.
Routledge, R. D. 1983. Evenness indices: are any admissible? Oikos 40:149151.
Schneider, T. D. 2003. Some lessons for molecular biology from information theory. Pp. 229237in Schneider, T. D., ed. Entropy measures, maximum entropy principle and emerging applications. Springer, New York.
Shannon, C. E. 1948. A mathematical theory of communication. Bell System Technical Journal 27:379423,623–656.
Simpson, E. H. 1949. Measurement of diversity. Nature 163:688.
Simpson, G. G. 1964. Species density of North American recent mammals. Systematic Zoology 13:5773.
Smith, B., and Wilson, J. B. 1996. A consumer's guide to evenness indices. Oikos 76:7082.
Stirling, G., and Wilsey, B. 2001. Empirical relationships between species richness, evenness and proportional diversity. American Naturalist 158:286299.
Taylor, L. R., Kempton, R. A., and Woiwood, I. P. 1976. Diversity statistics and the log-series model. Journal of Animal Ecology 45:255272.
Tokeshi, M. 1993. Species abundance patterns and community structure. Advances in Ecological Research 24:111186.
Ulrich, W. 2001. Models of relative abundance distributions. II. Diversity and evenness statistics. Polish Journal of Ecology 49:159175.
Weiher, E., and Keddy, P. A. 1999. Relative abundance and evenness patterns along diversity and biomass gradients. Oikos 87:355361.
Wiens, J. A., Crist, T. O., Day, R. H., Murphy, S. M., and Hayward, G. D. 1996. Effects of the Exxon Valdez oil spill on marine bird communities in Prince William Sound, Alaska. Ecological Applications 6:828841.
Williams, C. B. 1953. The relative abundance of different species in a wild animal population. Journal of Animal Ecology 22:1431.
Willis, J. C. 1922. Age and area. Cambridge University Press, Cambridge.


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