Canadian Forest Service Publications
A modified bootstrap procedure for cluster sampling variance estimation of species richness. 2011. Magnussen, S.; McRoberts, R.E. Journal of Applied Statistics 38(6): 1223-1238
Issued by: Pacific Forestry Centre
Catalog ID: 32287
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Variance estimators for probability sample-based predictions of species richness (S) are typically conditional on the sample (expected variance). In practical applications sample sizes are typically small and the variance of the input parameters to a richness estimator should not be ignored. We propose a modified bootstrap variance estimator which attempts to capture the sampling variance by generating B replications of the richness prediction from stochastically resampled data of species incidence. The variance estimator is demonstrated for the observed richness (SO), five richness estimators, and with simulated cluster sampling (without replacement) in 11 finite populations of forest tree species. A key feature of the bootstrap procedure is a probabilistic augmentation of a species incidence matrix by the number of species expected to be ‘lost’ in a conventional bootstrap resampling scheme. In Monte-Carlo simulations the modified bootstrap procedure performed well in terms of tracking the average Monte-Carlo estimates of richness and standard errors. Bootstrap-based estimates of standard error were as a rule conservative. Extensions to other sampling designs, estimators of species richness and diversity, and estimates of change are possible.