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3 Polish Journal of Ecology

3 Ulrich W.

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

Ulrich W.

Polish Journal of Ecology

2001

Vol. 49, nr 2

159-175

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.

On species-area relationships. 1, fit of power function and exponential model

Ulrich W.

Polish Journal of Ecology

2000

Vol. 48, nr 1

3-20

A FORTRAN program is developed that generates model assemblages on the basis of three basic features of animal communities: the species-weight relationship, the density-weightrelationship, and the minimal density. Samplings from random placed individuals of such assemblages revealed the influence of the sampling method (sequential adding, nested and non-nested), the scale, and the underlying relative abundance distribution on resulting species-area relationships (SPARs). It is concluded that the type of the species-area relationship is not an intrinsic factor of an assemblage but depends especially on the sampling method and the unit of area. The fraction of species found only once in the sample (singletons) was the major factor influencing the model that fitted the SPAR best (at low fractions the exponential, at higher fractions the power function model). All sampling and structural factors that influence the fraction of singletons also influence the fit of the SPAR model. A mathematical derivation showed that at a certain fraction of singletons in the sample a shift from the power function to the exponential model is expected independent of assemblage type. This shift will occur between 20 and 30% singletons.

On species-area relationship. 3, The intercept of the power function and the exponential model

Ulrich W.

Polish Journal of Ecology

2000

Vol. 48, nr 1

37-48

Using model assemblages the dependence of the intercept of the power function and the exponential model of species-area relationships on slope and factor value were studied. It is shown that the quotient of intercept and total species number in the assemblage (A[unit]/S[a]) can be interpreted as a relation between local and regional diversity and linked with species-area relations. Two general relations are derived and tested combining both concepts: z=a/ln[area] [...] with z being the slope of the power function model, H the Shannon diversity, Beta, Beta[1] and Beta[2] constants, and a the constant of the relation between S[unit]/S[a] and z. It is concluded that with the above functions species-area relationships can be used to infer the relation between local and regional species numbers and to compute regional diversities.