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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

Relative abundance distributions of species : the need to have a new look at them

Ulrich W.

Polish Journal of Ecology

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2001

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Vol. 49, nr 4

391-405

EN

This paper shows that recent models of relative abundances (RADs) like the log-normal model or sequential breakage or nich apportionment models are not able to describe and explain RADs found in natural communities because they are derived from a classical niche concept and assume strong past or present interspecific competition. None of them refers especially to temporal variability and functional niche dimensions. The present paper identifie three basic features of natural communities (unimodal species-weight distributions, abundance-weight distributions with more or less marked upper boundaries, and species density fluctuations that can be modelled by four different random processes). Modelling communities with these basic features resulted in RADs that only in part could be described by classical models but that had shapes often found in sampling from larger natural communities. No single distribution like the canonical log-normal appeared that may serve as a general null-model but RAD and evolutionary strategy (r- or K selection) seem to be related. The shape of relative abundance distributions was found to depend on the number of species even if all parameter setting of the generating distributions were identical. This indicates that classical evenness indices (that assume independence of species number) might not be appropriate to compare communities with different numbers of species. It appeared that RAD and body weight related community patterns have to be studied together.

3

On the scale dependence of evenness

Ulrich W.

Polish Journal of Ecology

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2001

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Vol. 49, nr 1

91-94

EN

A recently reported (Wilson et al. 1999) effect of spatial scale on evenness is studied and it is shown that such a pattern is not necessarily an effect of changes in community structure at different scales but may simply result as a byproduct from constrains introduced by maximum and minimum allowed densities due to the sampling procedure. Evenness is found to be constant only if the species area relationship of the community under study has exactly the parameter values that are given by the parameter values of the relative abundance distribution of the community. Because such a situation will seldom occur under natural circumstances scale dependence of the evenness (and of related descriptors of structure) is expected to be a general feature.

4

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.

5

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.