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Predictions from data

Predictions from data

-value# testssample

-value# testssample sizemeans.d.error0.005126846.910.413.6%0.0101513650.310.612.5%0.0201427149.45.76.8%0.0201038751.43.95.6%Table 5.6. Richness estimates and error terms for perturbed communityThe two average richness predictions that appear in Table 5.5 are closer to the ideal average of50.0 than are the average predictions shown in Table 5.6. This is due to the data being lessvariable, given that samples came from a smooth, idealized community. At the same time, weobserve that in both tables the error term for intensity 0.005 is larger than the error term forintensity 0.010. This makes sense because the samples are twice as large in the second case.The results displayed in Table 5.6 show a similar trend in accuracy; the error estimate declines instep with higher sampling ratios. The last set of (10) samples in Table 5.4 were drawn from amuch “larger” community, a perturbed version of LJ[10.0, 4000.0] x 50. This not only illustratesthe method’s wide applicability, but provides an extra data point when plotting estimation erroras a function of sample size. (See the end of Section 5.) The average richness estimate for all fourtests is 49.5, acceptably close to 50.5.4.2 The one-step methodIn this method the second step of the two-step method is used in the same manner, but with adifferent input -- the raw data itself, instead of the best fit. There is, therefore, no first step tospeak of. Tests of the one-step method parallel those of the two-step method, with the firstseries of experiments performed on the idealized community LJ[2.0, 3000] x 50. The remainingtests focus on perturbed versions of the same community. The series two tests thus assess theaccuracy of the one-step method, enabling a direct comparison of the results.r-value# testssample sizemeans.d.error0.005106853.08.910.4%0.0101513649.14.05.7%Table 5.7. Richness and error estimates for idealized community16

-value# testssample sizemeans.d.error0.005146852.010.913.2%0.0101413651.910.312.6%0.0201427151.47.08.4%0.0201038751.43.45.7%Table 5.8. Richness and error estimates for the perturbed communitiesResults of the first series of experiments on the idealized community LJ[2.0, 3000] x 50 aresummarized in Table 5.7, while those for perturbed versions appear in Table 5.8.Apart from what appear to be significantly higher error terms in the one-step method, there islittle to choose between the two methods. Given that the mean richness estimate is independentof intensity, one can arrive at a slightly more refined richness estimate of 49.98 % for the twostepmethod and 51.05 % for the one-step method, both applying to the idealized community.The foregoing results arise from the idealized community, of course. The second set ofexperiments involved not an idealized community, but a great many perturbations of it. In thiscase, the richness estimates averaged 49.5% for the two-step method and 51.7% for the one-stepmethod. The second average seems a bit high, but the 50% target is well within the 8.4% errorinterval, [47.4, 56.0].5.5 The behaviour of error termsAlthough more random communities could be sampled in order to obtain more precise data forplotting error as a function of sample size, the results of the previous section yield a reasonablyclose first approximation. Table 5.9 illustrates how expected errors could be systematicallyderived from the experiments described in this chapter. The table is based on the error curvederived from the experimental data.n6080100120140160180200220240260280error15.913.912.411.410.59.99.48.98.58.17.97.6n300320340360380400420440460480500520error7.37.16.96.86.66.46.36.16.05.95.85.8Table 5.9. Practical table for the assessment of errors in richness estimation17

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