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1

On species-area relationships. 2, Slope and factor values of power function and exponential model

Ulrich W.

Polish Journal of Ecology

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2000

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Vol. 48, nr 1

21-35

EN

Using model assemblages generated by a FORTRAN program the parameter values of the slope of the power function and the factor of the exponential model of species-area relationships have been studied. It appeared that the slope value is not a constant independent of area and sampling method but depends strongly on grain, sampling method and model fit. The fraction of singletons in the sample proofed to be of major importance. A plot of slope against assemblage structure (estimated by the standard deviation of log2 (densities) was bell shaped with the highest slope values at intermediate SD values. A comparison of this plot with SD values from theoretical relative abundance distributions showed that log-normal distributed assemblages should have slope values that are higher than previously reported in the literature. Although it was impossible to predict the slope from the relative abundance distribution, the opposite was possible. At any given slope value there are two linked relative abundance distributions. The factor of the exponential model was more independent of sampling methods but linearily connected with sampling efficacy. A high non-linear correlation between factor and Shannon diversity was detected and a general function of this relationship developed and tested. The factor of the exponential species-area relationship may serve as an estimate of regional diversity.

2

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

Ulrich W.

Polish Journal of Ecology

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2000

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Vol. 48, nr 1

3-20

EN

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.

3

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

Ulrich W.

Polish Journal of Ecology

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2000

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Vol. 48, nr 1

37-48

EN

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.

4

Estimating species numbers by extrapolation. I, Comparing the performance of various estimators using large model communities

Ulrich W.

Polish Journal of Ecology

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1999

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Vol. 47, no 3

271-291

EN

A computer program was constructed that simulates large species assemblages (28 to 997 species) with various species - rank order distributions and degrees of aggregation of the species. From these model assemblages random samples were taken to study the performance of 14 estimators of species diversity. For 6 of the estimators correction factors are developed. In sufficiently large samples ( more than 2/3 of the true species number (TS) sampled) a corrected second order jackknife estimator gave the best results. 18% of the estimates ranged outside TS+-10%. If fewer species are represented in the sample (but more than 1/3 TS) two newly developed data analytical estimators performed better. Between 23 and 24%, respectively, of their estimates ranged outside TS+-20%. Crucial to the performance of all of the estimators is the sample size. The minimum sample size for an estimator to work has to contain at least 1/3 of the total species number.