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 ∼25% of the total community), the least biased estimator was the second‐order jackknife, followed by the first‐order 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.

What sampling is needed for reliable estimations of genetic diversity in Fraxinus excelsior L. (Oleaceae)?

“…Herein, we define accuracy as the difference between an estimate and the true value of the population, here estimated from the largest sample available, and precision as the variance of the estimates (Hellmann and Fowler, 1999). In consequence, accuracy is measured with a bias estimator, and precision with standard errors and related measures.…”

“…The bias of the estimators was evaluated by joint analysis of the coefficient of variation and the mean square error following Kirst et al (2005). In this framework, the bias is the difference between the expected value of the estimator (the mean of the estimates of all possible samples that can be taken from the population) and the true population value (Hellmann and Fowler, 1999). Hence, we used the formula:…”

Assessment of richness estimation methods on macroinvertebrate communities of mountain ponds in Castilla y León (Spain)

“…4-26.7, 35.6-41.3 and 63.6-66.7% of total samples. In a similar study, Hellmann and Fowler (1999) found that for Jackknife 1, Jackknife 2 and Boot, the sub-sample size needed to estimate richness in the total sample were, respectively, 22. 6-29.1, 36.8-43.9 and 63.1-69.0% of total samples.…”

“…These approaches include measures of bias and accuracy of the estimated richness in relation to the true richness using an a priori chosen sub-sample size. However, the estimated richness is strongly dependent on sample size (Colwell and Coddington, 1994;Melo and Froehlich, 2001;Petersen and Meier, 2003) and different sub-samples sizes will produce different bias and accuracy values (Hellmann and Fowler, 1999). In addition, these approaches require data for maximum species numbers for their calculation, so they cannot be used here.…”

Sample-based Estimation of Regional Forest Tree Species Richness

“…Under these circumstances, few species richness estimators have performed well in Monte Carlo simulations with actual forest inventory data (Magnussen, 2011;Magnussen et al, 2010). Heretofore popular estimators of richness like the Jackknife, the bootstrap, and Chao's coverage-based estimators generally disappoint because they were not designed for sampling with multi-tree quadrants (Hellmann & Fowler, 1999;Hwang & Shen, 2010;Lam & Kleinn, 2008;Palmer, 1991;Schreuder et al, 2000;Schreuder et al, 1999).…”