90 EPA/600/A-86/104 Adaptive Sampling in Environmental Studies Steven K. Thompson Department of Statistics 326 Classroom Building Pennsylvania State University University Park, PA 16802-2111 Abstract Adaptive sampling refers to designs in which the pro- cedure for selecting units or sites at which to make ob- servations may depend on observations made during the survey. For example, in pollution assessment studies, additional observations may be made in the vicinity of observed hot spots. In surveys of animal and plant popu- lations, sampling intensity may be increased in the vicin- ity of high observed abundance. In this paper, examples of adaptive sampling procedures in survey situations in- volving whales, shrimp, moose, waterfowl, forest birds, fish, hardwood tree species, and environmental restora- tion are described. Introduction Adaptive sampling refers to designs in which the pro- cedure for selecting units or sites on which to make observations may depend on observations made during the survey. Thus, the sampling plan has the flexibility to change during the course of the survey in response to observed patterns in the population. For example, in a survey of a rare, clustered animal population, when- ever unusually high abundance is observed at a sample site, neighboring sites may be added to the sample. In a survey of an environmental pollutant, additional ob- servations may be added in the vicinity of observed hot spots. Descriptions of a variety of adaptive sampling designs are found in Thompson (1992) and Thompson and Seber (1996). Some types of adaptive designs include adaptive clus- ter sampling, adaptive allocation, ordinary sequential designs, and optimal Bayes designs, In adaptive cluster sampling, an initial sample is selected by some conven- tional design such as simple random sampling, strat- ified sampling, unequal probability sampling, system- atic sampling, or conventional cluster sampling. Then, whenever a unit in the sample satisfies a specified condi- tion, such as having a high value, neighboring units are added to the sample. Still more units may then be added because some of the neighboring units also satisfy the condition. With adaptive allocation designs the alloca- tion of sampling effort among strata is determined se- quentially during the survey, usually based on observed sample means or variances (Seber and Thompson 1994, Thompson 1990, 1991a,b, 1993,1994,1996). Examples An example of a situation in which adaptive allocation is used is the annual moose survey conducted by the Alaska Department of Fish and Game in interior Alaska (Gasaway et al. 19S6). Moose are surveyed from air- craft flying over selected sample plots within a large study region. The study region is stratified based on the quality of habitat. At the end of each day during die survey, sample variances are computed for each stratum and the sampling effort for the next day is allocated to approximate the optimal Neyman allocation. Adaptive allocation designs have also been used and investigated for surveys of commercial fish species in- cluding mackerel and orange roughy (Francis 1991), anchovy (lolly 1993, Jolly and Hampton 1990, 1991), and shrimp (Thompson, Ramsey, and Seber 1992). The inherent problem in such surveys is that die mobility of the populations makes the patterns of abundance unpre- dictable prior to the survey so that classical allocation 1 ------- Adaptive Sampling in Environmental Studies 91 formulas are of limited usefulness. In the adaptive ver- sion, the pattern is assessed in the initial part of the survey, for example as the research vessel travels west- ward through the study region, and sampling effort re- allocated for the second part of the survey, as the vessel returns westward in the example. With adaptive alloca- tion the conventional stratified sampling estimator is not in general unbiased. Unbiased estimation is possible, however, through a variety of methods. Adaptive cluster sampling or similar designs have been investigated for ecological populations such as wa- terfowl (Smith, Conroy, and Brakhage 1995), and trees (Roesch, 1993). A related procedure has sometimes been used in whale surveys (Kishino and Kasamatsu 1987, Schweder and 0ien 1993). Other adaptive sam- pling designs have been examined for salmon (Geiger 1994) and for soil remediation (Englund and Herari 1995). The populations of interest tend to be rare and unevenly distributed spatially, with aggregation or so- cial linkage tendencies. By adding neighboring units whenever high or interesting values are observed in the sample, the sample total of the variable of interest may be substantially increase—increasing for example the number of animals of the species that are observed— so that unbiased estimation needs to take the adaptive selection procedure into account. The possibilities with adaptive designs are very wide. Much work is needed to determine effective designs for specific populations to compare the efficiency of adaptive designs with conventional designs and to de- termine which type of design will be most effective for the population of interest. For rare, clustered popula- tions, adaptive cluster sampling can produce substantial gains in efficiency relative to conventional designs of equivalent sample size or cost. Factors influencing the relative efficiency include within-network variation, rar- ity within the study region, and cost issues. Adaptive allocation designs have also been shown to give gains in efficiency for unpredictably distributed populations including schooling species of fish and shrimp. Nonsampling errors such as imperfect detection of animals, variable catchability of nets for fish, and in- correct self reporting of drug use must be taken into account with adaptive as well as with conventional de- signs. Generally, it is straightforward to adjust estimates for imperfect detectability by dividing observed values by detection probabilities. Imperfect detectability also adds components to the variance which must be esti- mated (Thompson and Seber 1994). Conclusions Motivation for adaptive sampling is provided both by real world situations such as those described above and by results in sampling theory showing that the optimal sampling strategy in many cases will be an adaptive one. The practical motivations for using adaptive sam- pling procedures for rare, clustered populations, from whales to rare plant species, have led field researchers to suggest adaptive procedures or to use them on an im- provised basis. The theoretically optimal strategies tend to be too complex or require too much prior knowledge for practical implementation. Even so the theoretical results are suggestive of practical adaptive procedures with die potential to improve efficiency in surveys of real populations. Consideration of adaptive along with conventional sampling procedures greatly increases the possibilities in survey sampling. References Brown, J.A. (1994). The application of adaptive cluster sampling to ecological studies. In D J. Fletcher and B .FJ. Manly (Eds), Statistics in Ecology and Environ- mental Monitoring, pp. 86-97. Otago Conference Series No. 2. Dunedin, New Zealand: University of Otago Press. Englund, EX, and Herari, N. (1995). Phased sampling for soil remediation. Environmental and Ecological Statistics, to appear. Francis, RI.C.C. (1984). An adaptive strategy for strat- ified random trawl surveys. New Zealand Journal of Marine and Freshwater Research 18,59-71. Francis, R.I.C.C. (1991). Statistical properties of two- phase surveys: comment. Canadian Journal of Fish~ eries and Aquatic Sciences 48,1228. Gasaway, W.C., DuBois, S.D., Reed, DJ., and Harbo, SJ. (1986). Estimating Moose Population Parame- ters from Aerial Surveys. Biological Papers of the University of Alaska (Institute of Arctic Biology) Number 22. Fairbanks: University of Alaska. ------- 92 S. K. Thompson Geiger, H J. (1994). A Bayesian approach for estimating hatchery contribution in a series of salmon fisheries. Alaska Fishery Research Bulletin 1, 66-75. Jolly, G.M. (1993). Bias in two-phase stratified ran- dom sampling for optimum allocation. Unpublished manuscript. Jolly, G.M., and Hampton, I. (1990). A stratified random transect design for acoustic surveys of fish stocks. Canadian Journal of Fisheries and Aquatic Science 47, 1282-1291. Jolly, G.M., and Hampton, I. (1991). Reply to comment by R.I.C.C. Francis. Canadian Journal of Fisheries and Aquatic Science 48, 1228-1229. Kishino, H., and Kasamatsu, F. (1987). Comparison of the closing and passing mode procedures used in sighting surveys. Report of the International Whaling Commission 37, 253-258. Munholland, P.L., and Borkowski, J.J. (1993b). Adap- tive Latin square sampling + 1 designs. Technical Report No. 3-23-93, Department of Mathematical Sciences, Montana State University, Bozeman. Roesch, F.A. Jr. (1993). Adaptive cluster sampling for forest inventories. Forest Science 39, 655-669. Schweder, T., 0ien, N., and Host, G. (1993). Estimates of abundance of northeastern Atlantic minke whales in 1989. Report of the International Whaling Com- mission 43,323-331. Seber, G.A.F., and Thompson, S.K. (1994). Environ- mental adaptive sampling. In G.R Patil and C.R. Rao (Eds), Handbook of Statistics, Vol. 12 (Environ- mental Sampling), pp. 201-220. New York: North Holland/Elsevier Science Publishers. Smith, D.R., Conroy, M.J., and Brakhage, D.H. (1995). Efficiency of adaptive cluster sampling for estimat- ing density of wintering waterfowl. Biometrics, to appear. Thompson, S.K. (1990). Adaptive cluster sampling. Journal of the American Statistical Association 85, 1050-1059. Thompson, S.K. (1991a). Adaptive cluster sampling: Designs with primary and secondary units. Biometrics 47, 1103- 1115. Thompson, S.K. (1991b). Stratified adaptive cluster sampling. Biometrika 78, 389-397. Thompson, S.K. (1993). Multivariate aspects of adap- tive cluster sampling. In G.P. Patil and C.R. Rao (Eds), Multivariate Environmental Statistics, pp.561- 572. New York: North Holland/Elsevier Science Publishers. Thompson, S.K. (1994). Factors influencing the effi- ciency of adaptive cluster sampling. Technical Report 94-0301, Center for Statistical Ecology and Environ- mental Statistics, Department of Statistics, Pennsyl- vania State University, University Park. Thompson, S.K. (1996). Adaptive cluster sampling based on order statistics. Environmetrics 7 123-133. Thompson, S.K., Ramsey, F.L., and Seber, G.A.F. (1992). An adaptive procedure for sampling animal populations. Biometrics 48, 1195-11. Thompson, S.K., and Seber, G.A.F. (1994). Detectabil- ity in conventional and adaptive sampling. Biometrics 50, 712-724. Thompson, S.K., and Seber, G.A.F. (1996). Adaptive Sampling. New York: Wiley. In press. ------- Computing Science and Statistics Volume 27 Statistics and Manufacturing with Subthemes in Environmental Statistics, Graphics and Imaging Proceedings of the 27th Symposium on the Interface Pittsburgh, PA, June 21-24, 1995 Editors Michael M. Meyer James L. Rosenberger INTERFACE FOUNDATION OF NORTH AMERICA ------- NHEERL-COR-2051A TECHNICAL REPORT DATA (Please read instructions on the reverse before com'' 1. REPORT NO. EPA/600/A-96/104 2. 4. TITLE AND SUBTITLE Adaptive sampling in environmental studies 5. REPORT DATE 6. PERFORMING ORGANIZATION CODE 7. AUTHOR(S| S.K. Thompson 8. PERFORMING ORGANIZATION REPORT NO. 9. PERFORMING ORGANIZATION NAME AND ADDRESS Department of Statistics 326 Classroom Building Pennsylvania State University University Park, PA 16802-2111 10. PROGRAM ELEMENT NO. 11. CONTRACT/GRANT NO. 12. SPONSORING AGENCY NAME AND ADDRESS US EPA ENVIRONMENTAL RESEARCH LABORATORY 200 SW 35th Street Corvallis, OR 97333 13. TYPE OF REPORT AND PERIOD COVERED Symposium paper 14. SPONSORING AGENCY CODE EPA/600/02 16. SUPPLEMENTARY NOTES 1995. Proceedings of the 27th Symposium on the Interface. Computer Science and Statistics, Statistics & Manufacturing with Subthemes in Environmental Statistics, Graphics, and Imaging, Pittsburgh, Pa, June 21-24, 1995. 16. ABSTRACT Adaptive sampling refers to designs in which the procedure for selecting units or sites at which the procedure for selecting units or sites at which to make observations may depend on observations made during the survey. For example, in pollution assessment studies, additinal observatioons may be made in the viciniity of observed hot spots. In surveys of animal and plant populations, sampling intensity may be increased in the vicinitiy of observed abundance. In this paper, examples of adaptive sampling procedures in survey situations involving whales, shrimp, moose, waterfowl, forest birds, fish, hardwood tree species, and environmental restoration are described. 17. KEY WORDS AND DOCUMENT ANALYSIS a. DESCRIPTORS b. IDENTIFIERS/OPEN ENDED TERMS c. COSATI Field/Group Adaptive sampling, environmental statistics. 18. DISTRIBUTION STATEMENT 19. SECURITY CLASS {This Report! 21. NO. OF PAGES 4 20, SECURITY CLASS {This page! 22. PRICE ------- |