Bias, Precision, and Accuracy of Four Measures of Species Richness

Abstract

Species richness is a widely used surrogate for the more complex concept of biological diversity. Because species richness is often central to ecological study and the establishment of conservation priorities, the biases and merits of richness measurements demand evaluation. The jackknife and bootstrap estimators can be used to compensate for the underestimation associated with simple richness estimation (or the sum of species counted in a sample). Using data from five forest communities, we analyzed the simple measure of richness, the first-and second-order jackknife, and the bootstrap estimators with simulation and resampling methods to examine the effects of sample size on estimator performance. Performance parameters examined were systematic under-or overestimation (bias), ability to estimate consistently (precision), and ability to estimate true species richness (accuracy).For small sample sizes in all studied communities (less than ϳ25% of the total community), the least biased estimator was the second-order jackknife, followed by the firstorder jackknife, the bootstrap, and the simple richness estimator. However, with increases in sample size, the second-order jackknife, followed by the first-order jackknife and the bootstrap, became positively biased. The simple richness estimator was the most precise estimator in all studied communities, but it yielded the largest underestimate of species richness at all sample sizes. The relative precision of the four estimators did not differ across communities, but the magnitude of estimator variance is dependent on the sampled community. Differences in accuracy among the estimators were not independent of community, and accuracy patterns were associated with community species diversity. The results of this study can assist policy makers, researchers, and managers in the selection of appropriate sample sizes and estimators for richness estimation and should facilitate the ongoing assessment of local, and ultimately global, biodiversity.

Performance of nonparametric species richness estimators in a high diversity plant community

“…An approach more comparable to ours was used by Hellmann and Fowler (1999), who recorded the presence of all species in five 0.4 ha plots divided into a series of smaller (5 × 5 m) quadrats within which species presence/absence was recorded. These subplots were then sampled.…”

“…MRE is equivalent to the 'mean deviation' of Palmer (1990) and to the 'bias' of Hellmann and Fowler (1999), except that it is scaled by the true value, being equivalent to the 'bias' used by Walther and Morand (1998). MSRE is equivalent to the 'mean square proportional deviation' of Palmer (1990) and the 'deviation' of Walther and Morand (1998).…”

“…A more complete test of species richness estimator performance might be afforded by applying these estimators to a data set in which the identity and location is known for every individual plant within the reference area and is not limited to a sample of locations (quadrats) only. A test along these lines, using field data, was attempted by Hellmann and Fowler (1999), who sampled five 0.4 ha forest plots with low to moderate species richness in Michigan (from 14 to 56 species), dividing the plots by a grid and enumerating all species within the grid (but without recording the explicit spatial position of each plant). Gimaret-Carpentier et al .…”

Small‐Sample Estimation of Species Richness Applied to Forest Communities

“…The performance of various species richness estimators has been tested using field or simulated datasets with the study taxon being either animal or plant communities; see Table 3 in Walther and Moore (2005) for a list. Our motivation comes from the test results regarding plant communities in Gimaret-Carpentier et al (1998);Hellmann and Fowler (1999); and Chiarucci et al (2003). Based on their investigations, no estimator provides reasonable estimates when the sample proportion is small.…”

An Estimator of Number of Species from Quadrat Sampling

“…H&F's estimator is described as a jackknife and S&vB's as a bootstrap estimator. The performance of these estimators was compared in five real populations by Hellman and Fowler (1999), who found that none is best for all sample sizes and population types. The M&M and Mingoti estimators are based on models for how the individuals of each species are distributed among the quadrats, and the estimation uses empirical Bayes and Bayes methodology, respectively.…”