A modified bootstrap procedure for cluster sampling variance estimation of species richness

Abstract

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 input parameters to a richness estimator should not be ignored. We propose a modified bootstrap variance estimator that 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 (MC) simulations, the modified bootstrap procedure performed well in terms of tracking the average MC estimates of richness and standard errors. Bootstrap-based estimates of standard errors were as a rule conservative. Extensions to other sampling designs, estimators of species richness and diversity, and estimates of change are possible.

Keywords:

• species covariance
• biodiversity
• tree species
• coverage
• forest vegetation survey
• species occurrence

Acknowledgements

The data for eastern Canada were kindly provided by the Nova Scotia Department of Natural Resources, the Prince Edward Island Department of Agriculture and Forestry, the New Brunswick Department of Natural Resources and Energy, the Québec Ministère des Resources Naturelles, Faune et Parcs, and the Ontario Ministry of Natural Resources. The BCI forest dynamics research project was made possible by National Science Foundation grants to Stephen P. Hubbell: DEB-0640386, DEB-0425651, DEB-0346488, DEB-0129874, DEB-00753102, DEB-9909347, DEB-9615226, DEB-9615226, DEB-9405933, DEB-9221033, DEB-9100058, DEB-8906869, DEB-8605042, DEB-8206992, and DEB-7922197, support from the Center for Tropical Forest Science, the Smithsonian Tropical Research Institute, the John D. and Catherine T. MacArthur Foundation, the Mellon Foundation, the Celera Foundation, and numerous private individuals, and through the hard work of over 100 people from 10 countries over the past two decades. The plot project is part of the Center for Tropical Forest Science, a global network of large-scale demographic tree plots. The MIOMBO data were those used by Kleinn and Vilčko 32 and stem from a project on sustainable bark harvesting in Southern Africa (funded by DFID-R8305-Forest Research Programme). Dr Jenny Wong was the project leader and Dr Frantisek Vilèko kindly prepared the data set. Data of Fushan were kindly provided by the Taiwan Forest Research Institute. The Fushan 25 ha FDP was established by the joint efforts of the Taiwan Forestry Bureau, the Taiwan Forestry Research Institute, and the Institute of Ecology and Evolutionary Biology, National Taiwan University. Data from the USDA Forest Service FIA programme were kindly provided by Dr B. Smith and P. Miles.