A framework for adapting survey design through time for wildlife population assessment

Abstract

Sampling strategies for monitoring the status and trends in wildlife populations are often determined before the first survey is undertaken. However, there may be little information about the distribution of the population and so the sample design may be inefficient. Through time, as data are collected, more information about the distribution of animals in the survey region is obtained but it can be difficult to incorporate this information in the survey design. This paper introduces a framework for monitoring motile wildlife populations within which the design of future surveys can be adapted using data from past surveys whilst ensuring consistency in design-based estimates of status and trends through time. In each survey, part of the sample is selected from the previous survey sample using simple random sampling. The rest is selected with inclusion probability proportional to predicted abundance. Abundance is predicted using a model constructed from previous survey data and covariates for the whole survey region. Unbiased design-based estimators of status and trends and their variances are derived from two-phase sampling theory. Simulations over the short and long-term indicate that in general more precise estimates of status and trends are obtained using this mixed strategy than a strategy in which all of the sample is retained or all selected with probability proportional to predicted abundance. Furthermore the mixed strategy is robust to poor predictions of abundance. Estimates of status are more precise than those obtained from a rotating panel design.

This is a preview of subscription content, log in to check access.

References

  1. Binder DA, Hidiroglou MA (1988) Sampling in time. In: Handbook of Statistics, vol 6. Elsevier Science Publishers, North Holland, pp 187–211

  2. Brewer KRW, Hanif M (1982) Sampling with unequal probabilities. Lecture notes in statistics, vol 15. Springer, New York

    Google Scholar 

  3. Brown JA, Salehi MM, Moradi M, Bell G, Smith DR (2008) . Popul Ecol 50: 239–245

    Article  Google Scholar 

  4. Buckland ST, Elston DA (1993) Empirical models for the spatial distribution of wildlife. J Appl Ecol 30: 478–495

    Article  Google Scholar 

  5. Chao MT (1982) A general purpose unequal probability sampling plan. Biometrika 69(3): 653–656

    Article  Google Scholar 

  6. Dufour J, Gambino J, Kennedy B, Lindeyer J, Singh MP (1998) Methodology of the Canadian labour force survey. Tech. rep. 71-526-XPB, Statistics Canada

  7. Duncan GJ, Kalton G (1987) Issues of design and analysis of surveys. Int Stat Rev 55(1): 97–117

    Article  Google Scholar 

  8. Haines DE, Pollock KH (1998) Estimating the number of active and successful bald eagle nests: an application of the dual frame method. Environ Ecol Stat 5: 245–256

    Article  Google Scholar 

  9. Hansen MH, Madow WG, Tepping BJ (1983) An evaluation of model-dependent and probability-sampling inferences in sample surveys. J Am Stat Assoc 78(384): 776–793

    Article  Google Scholar 

  10. Holmes DJ, Skinner CJ (2000) Variance estimation for labour force survey estimates of level and change. UK Government Statistical Service Methodology Series No. 21

  11. Horvitz D, Thompson DJ (1952) A generalization of sampling without replacement from a finite universe. J Am Stat Assoc 47: 663–685

    Article  Google Scholar 

  12. Jessen RJ (1942) Statistical investigation of a farm survey for obtaining farm facts. Iowa Agric Stn Res Bull 304: 54–59

    Google Scholar 

  13. Jolly GM, Hampton I (1990) A stratified random transect design for acoustic surveys of fish stocks. Can J Fish Aquat Sci 47: 1282–1291

    Article  Google Scholar 

  14. Khaemba WM, Stein A (2000) Use of GIS for a spatial and temporal analysis of Kenyan wildlife with generalised linear modelling. Int J Geograph Inform Sci 14(8): 833–853

    Article  Google Scholar 

  15. McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Chapman and Hall, London

    Google Scholar 

  16. Opsomer JD, Botts C, Kim JY (2003) Small area estimation in a watershed erosion assessment survey. J Agric Biol Environ Stat 8(2): 139–152

    Article  Google Scholar 

  17. Overton WS, Stehman SV (1996) Desirable design characteristics for long-term monitoring of ecological variables. Environ Ecol Stat 3: 349–361

    Article  Google Scholar 

  18. Overton WS, White D, Stevens DL Jr (1990) Design report for EMAP. Environmental monitoring and assessment program. EPA/600/3-91/053, US Environmental Protection Agency

  19. Särndal CE, Swennsson B, Wretman J (1992) Model assisted survey sampling. Springer, New York

    Google Scholar 

  20. Sen AR (1973) Theory and applications of sampling on repeated occasions with several auxiliary variables. Biometrics 29(2):381–385

    Google Scholar 

  21. Skalski JR (1990) A design for long-term status and trends monitoring. J Environ Manag 30: 139–144

    Article  Google Scholar 

  22. Sunter A (1977) List sequential sampling with equal or unequal probabilities without replacement. Appl Stat 26: 261–268

    Article  Google Scholar 

  23. Sunter A (1977) Response burden, sample rotation, and classification renewal in economic surveys. Int Stat Rev 45: 209–222

    Article  Google Scholar 

  24. Thompson SK, Seber GAF (1996) Adaptive sampling. Wiley, New York

    Google Scholar 

  25. Tillé Y (2006) Sampling algorithms. Springer series in statistics. Springer, New York

    Google Scholar 

  26. Venables W, Ripley B (2002) Modern applied statistics with S, 4th edn. Springer, London

    Google Scholar 

  27. Wood SN (2006) Generalized additive models: an introduction with R. Chapman and Hall/CRC

  28. Yates F, Grundy PM (1953) Selection without replacement from within strata with probability proportional to size. J Royal Stat Soc B 15: 235–261

    Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Fiona M. Underwood.

Electronic Supplementary Material

The Below is the Electronic Supplementary Material.

ESM 1 (PDF 51 kb)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Underwood, F.M. A framework for adapting survey design through time for wildlife population assessment. Environ Ecol Stat 19, 413–436 (2012). https://doi.org/10.1007/s10651-012-0193-4

Download citation

Keywords

  • Adaptive sampling
  • Design-based estimation
  • Monitoring strategies
  • Wildlife population assessment