Abstract
Sampling of a population is frequently required to understand trends and patterns in natural resource management because financial and time constraints preclude a complete census. A rigorous probability-based survey design specifies where to sample so that inferences from the sample apply to the entire population. Probability survey designs should be used in natural resource and environmental management situations because they provide the mathematical foundation for statistical inference. Development of long-term monitoring designs demand survey designs that achieve statistical rigor and are efficient but remain flexible to inevitable logistical or practical constraints during field data collection. Here we describe an approach to probability-based survey design, called the Reversed Randomized Quadrant-Recursive Raster, based on the concept of spatially balanced sampling and implemented in a geographic information system. This provides environmental managers a practical tool to generate flexible and efficient survey designs for natural resource applications. Factors commonly used to modify sampling intensity, such as categories, gradients, or accessibility, can be readily incorporated into the spatially balanced sample design.
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References
Baker WL, Cai Y (1992) The r.le programs for multiscale analysis of landscape structure using the GRASS geographical information system. Landscape Ecology 7:291–302
Cochran WG (1977) Sampling techniques. 3rd ed. Wiley, New York
Courbois PJY, Urquhart NS (2004) Comparison of survey estimates of the finite population variance. Journal of Agricultural, Biological, and Environmental Statistics 9(2):236–251
Di Zio S, Fontanella L, Ippoliti L (2004) Optimal spatial sampling schemes for environmental surveys. Environmental and Ecological Statistics 11(4):397–411
Flores LA, Martinez LI, Ferrer CM (2003) Systematic sample design for estimation of spatial means. Environmetrics 14:45–61
Gilbert RO (1987) Statistical methods for environmental pollution monitoring. Van Nostrand Reinhold, New York
Goodchild MF, Grandfield AW (1983) Optimizing raster storage: an examination of four alternatives. Proceedings of the AutoCarto 6, Ottawa, Canada, pp. 400–407
Griffith D (2005) Effective geographic sample size in the presence of spatial autocorrelation. Annals of the Association of American Geographers 95(4):740–760
Hall RK, Olsen A, Stevens D, Rosenbaum B, Husby P, Wolinsky GA, Heggem DT (2000) EMAP design and river reach file 3 (RF3) as a sample frame in the Central Valley, California. Environmental Monitoring and Assessment 64:69–80
Hansen MH, Madow WG, Tepping BJ (1983) An evaluation of model-dependent and probability sampling inferences in sample surveys. Journal of the American Statistical Association 78:776–760
Herlihy AT, Larsen DP, Paulsen SG, Urquhart NS, Rosenbaum BJ (2000) Designing a spatially balanced, randomized site selection process for regional stream surveys: the EMAP mid-Atlantic pilot study. Environmental Monitoring and Assessment 63:92–113
Huber B (2000) Sample: Designing random sampling programs with ArcView 3.2. Quantitative Decisions, Inc. Available from http://www.quantdec.com/sample/index.htm (accessed 3 March 2004)
Jenness J (2001) Random point generator, v1.1. Jenness Enterprises. Flagstaff, AZ
Lesser VM (2001) Applying survey research methods to account for denied access to research sites on private property. Wetlands 21(4):639–647
Mark DM (1990) Neighbor-based properties of some orderings of two-dimensional space. Geographical Analysis 2:145–157
Oakley KL, Thomas LP, Fancy SG (2003) Guidelines for long-term monitoring protocols. Wildlife Society Bulletin 31(4):1000–1003
Olsen AR (2006) Software for R: psurvey.analysis (2.9). Available from http://www.epa.gov/nheerl/arm
Overton WS (1993) Probability sampling and population inference in monitoring programs. In: Goodchild MF, Parks BO, Stayert LT (eds) Environmental modeling with GIS. Oxford University Press, New York, pp 470–480
Pebesma EJ, Wesseling CG (1998) Gstat, a program for geostatistical modeling, prediction and simulation. Computers and Geosciences 24(1):17–31
Peterson SA, Urquhart NS, Welch EB (1999) Sample representativeness: A must for reliable regional lake condition estimates. Environmental Science and Technology 33:1559–1565
Saalfeld A (1998) Sorting spatial data for sampling and other geographic applications. GeoInformatica 2:37–57
Särndal C (1978) Design-based and model-based inference for survey sampling. Scandinavian Journal of Statistics 5:27–52
Seaber PR, Kapinos FP, Knapp GL (1987) Hydrologic unit maps. US Geological Survey, Denver, Colorado. Water Supply Paper 2294
Smith TH (1976) The foundations of survey sampling: a review. Journal of the Royal Statistics Society A 139:183–204
Stehman SV (1999) Basic probability sampling designs for thematic map accuracy assessments. International Journal of Remote Sensing 20(12):2423–2441
Stehman SV, (2001) Statistical rigor and practical utility in thematic map accuracy assessment. Photogrammetric Engineering and Remote Sensing 67(6):727–734
Stehman SV, Overton WS (1996) Spatial sampling. In: Arlinghaus S (ed) Practical handbook of spatial statistics. CRC Press, Boca Raton, FL, pp. 31–63
Stevens DL Jr. (1997) Variable density grid-based sampling designs for continuous spatial populations. Environmetrics 8:164–195
Stevens DL Jr. (2002) Sample design and statistical analysis methods for the integrated biological and physical monitoring of Oregon streams. Oregon Department of Fish and Wildlife, Report Number OPSW-ODFW-2002-07
Stevens DL Jr, Olsen AR (2000) Spatially restricted random sampling designs for design-based and model-based estimation. In: Accuracy 2000: Proceedings of the 4th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences. Eds: GBM Heuveliuk and MJP Lemmens Delft University Press, Delft pp 609–616
Stevens DL Jr., Olsen AR (2003) Variance estimation for spatially balanced samples of environmental resources. Environmetrics 14:593–610
Stevens DL Jr., Olsen AR (2004) Spatially balanced sampling of natural resources. Journal of the American Statistical Association 99(465):262–278
Theobald DM (2003) GIS concepts and ArcGIS methods. Conservation Planning Technologies, Fort Collins, CO
Theobald DM, Norman JB (2006) Spatially-balanced sampling using the Reversed Randomized Quadrant-Recursive Raster algorithm: A user’s guide for the RRQRR ArcGIS v9 tool. Available from http://www.nrel.colostate.edu/projects/starmap
Tobler W (1970) A computer model of simulating urban growth in the Detroit region. Economic Geography 46:234–240
Thompson SK (2002) Sampling, 2nd ed. Wiley, New York
Thompson WL (ed) (2004) Sampling rare or elusive species. Island Press, Washington, DC
Acknowledgments
We thank N. Peterson for field assistance with this research and M. Farnsworth, J. Gross, B. Noon, and E. Peterson for helpful comments on previous drafts. This research was supported by funding from the STAR Research Assistance Agreements CR-829095 and CR-829096 awarded by the US Environmental Protection Agency. This article was subjected to Agency review and approved for publication. The conclusions and opinions are solely those of the authors and are not necessarily the views of the Agency. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.
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Theobald, D.M., Stevens, D.L., White, D. et al. Using GIS to Generate Spatially Balanced Random Survey Designs for Natural Resource Applications. Environmental Management 40, 134–146 (2007). https://doi.org/10.1007/s00267-005-0199-x
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DOI: https://doi.org/10.1007/s00267-005-0199-x