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1

Species area relations generated by theoretical relative abundance distributions : parameter values, model fit and relation to species saturation studies

Ulrich W.

Polish Journal of Ecology

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2001

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Vol. 49, nr 1

67-77

EN

Using model assemblages and random samplings the relations between 8 relative abundance distributions (RADs)(broken stick,log-series, power fraction, random fraction, Sugihara fraction, and two types of Zipf-Mandelbrot models) and resulting species-area relationship (SPARs) were studied. It is shown that the model fit of the power function and the exponential SPAR model depends mainly on the number of species per unit of area, the fraction of singletons in the sample, and the total species number in the assemblage. Sugihara and power fraction RADs did not necessarily led to power function SPARs but are characterized byrelatively high slope values in comparison to other distributions. Random placement and sampling of individuals of Zipf-Mandelbrot and log-series distributions resulted in curvilinear local vs. regional plots and the slope value z of the power function SPAR was not necessarily constant but could be forced to become constant by introducing a correction factor into the power function SPAR. The implications of these findings for detecting local species saturation are discussed.

2

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

Ulrich W.

Polish Journal of Ecology

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2001

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Vol. 49, nr 2

159-175

EN

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.

3

Models of relative abundance distributions. 1, Model fitting by stochastic models

Ulrich W.

Polish Journal of Ecology

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2001

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Vol. 49, nr 2

145-147

EN

The present paper studies possibilities to discriminate between 9 stochastic models of relative abundance distributions (RADs). It develops a new test statistic for fitting based on least square distances and tests the applicability of methods described so far. The paper identifies three basic shapes of RADs termed power fraction, random assortment and Zipf-Mandelbrot type shape. It is shown that even a correct identification of the shape of a given data set requires that this data set is replicated more than 10 times. Estimates of necessary sample sizes for real animal or plant communities revealed that for communities with 20 to 100 species at least 200 to 500 times the species number is necessary for a correct model identification. The implications of these findings for the applicability of models of relative abundance distributions are discussed.

4

Estimating species numbers by extrapolation : a cautionary note

Ulrich W.

Polish Journal of Ecology

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2001

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Vol. 49, nr 3

299-305

EN

This paper evaluates the accuracy any estimator of species may achieve if only a limited fraction (up to 3/4) of the species number in the community has been sampled. From the impossibility to infer the relative abundance distribution (RAD) the rare and not sampled species follow it is shown that it is only possible to give a lower and an upper boundary of the species number. The lower boundary may be inferred either from a fit of a log-normal type RAD or by a graphical method. In the latter case, the lower boundary is S[min]=(ln(d[min]-2icpt) / slope with d[min] being the minimal possible relative density in the community and icpt and slope being the intercept and the slope of the geometric series fitted through the linear part of the log-normal distribution. The upper boundary is found through an extrapolation of this geometric series up to d[min][S[max]=(ln(d[min])-icpt)/slope]. For any estimator to work d[min] has to be known.