Biodiversity and Conservation

, Volume 17, Issue 14, pp 3417–3429 | Cite as

Process and measurement errors of population size: their mutual effects on precision and bias of estimates for demographic parameters

Original Paper

Abstract

Knowing the parameters of population growth and regulation is fundamental for answering many ecological questions and the successful implementation of conservation strategies. Moreover, detecting a population trend is often a legal obligation. Yet, inherent process and measurement errors aggravate the ability to estimate these parameters from population time-series. We use numerical simulations to explore how the lengths of the time-series, process and measurement error influence estimates of demographic parameters. We first generate time-series of population sizes with given demographic parameters for density-dependent stochastic population growth, but assume that these population sizes are estimated with measurement errors. We then fit parameters for population growth, habitat capacity, total error and long-term trends to the ‘measured’ time-series data using non-linear regression. The length of the time-series and measurement error introduce a substantial bias in the estimates for population growth rate and to a lesser degree on estimates for habitat capacity, while process error has little effect on parameter bias. The total error term of the statistical model is dominated by process error as long as the latter is larger than the measurement error. A decline in population size is difficult to document as soon as either error becomes moderate, trends are not very pronounced, and time-series are short (<10–15 seasons). Detecting an annual decline of 1% within 6-year reporting periods, as required for the European Union for the species of Community Interest, appears unachievable.

Keywords

Population parameters Time series Temporal trend Statistical testing Policy implications Conservation 

References

  1. Akcakaya HR, Radeloff VC, Mlandenoff DJ, He HS (2004) Integrating landscape and metapopulation modeling approaches: Viability of the sharp-tailed grouse in a dynamic landscape. Conserv Biol 18:526–537. doi:10.1111/j.1523-1739.2004.00520.x CrossRefGoogle Scholar
  2. Baguette M, Schtickzelle N (2003) Local population dynamics are important to the conservation of metapopulations in highly fragmented landscapes. J Appl Ecol 40:404–412Google Scholar
  3. Balmford A et al (2005) The convention on biological diversity’s 2010 target. Science 307:212–213. doi:10.1126/science.1106281 PubMedCrossRefGoogle Scholar
  4. Bellows TS (1981) The descriptive properties of some models for density dependence. J Anim Ecol 50:139–156. doi:10.2307/4037 CrossRefGoogle Scholar
  5. Bull J, Pickup N, Pickett B, Hassell M, Bonsall M (2007) Metapopulation extinction risk is increased by environmental stochasticity and assemblage complexity. Proc R Soc B: Biol Sci 274:87–96CrossRefGoogle Scholar
  6. Buonaccorsi JP, Staudenmayer J, Carreras M (2006) Modeling observation error and its effects in a random walk/extinction model. Theor Popul Biol 70:322–335. doi:10.1016/j.tpb.2006.02.002 PubMedCrossRefGoogle Scholar
  7. Calder C, Lavine M, Müller P, Clark JS (2003) Incorporating multiple sources of stochasticity into dynamic population models. Ecology 84:1395–1402. doi:10.1890/0012-9658(2003)084[1395:IMSOSI]2.0.CO;2 CrossRefGoogle Scholar
  8. Clark JS, Bjornstad CN (2004) Population time series: process variability, observation errors, missing values, lags, and hidden states. Ecology 85:3140–3150. doi:10.1890/03-0520 CrossRefGoogle Scholar
  9. De Valpine P (2003) Better inferences from population-dynamics experiments using Monte Carlo state-space likelihood methods. Ecology 84:3064–3077. doi:10.1890/02-0039 CrossRefGoogle Scholar
  10. De Valpine P, Hastings A (2002) Fitting population models incorporating process noise and observation error. Ecol Monogr 72:57–76Google Scholar
  11. Dennis B, Ponciano JM, Lele SR, Taper ML, Staples DF (2006) Estimating density dependence, process noise, and observation error. Ecol Monogr 76:323–341. doi:10.1890/0012-9615(2006)76[323:EDDPNA]2.0.CO;2 CrossRefGoogle Scholar
  12. European Commission (1979) Council Directive 79/409/EEC of 2 April 1979 on the conservation of wild birds. Official Journal of the European Union—Legislation 103:1Google Scholar
  13. European Commission (1992) Council Directive 92/43/EEC of 21 May 1992 on the conservation of natural habitats and of wild fauna and flora. Official Journal of the European Union—Legislation 206:7Google Scholar
  14. European Commission (2005) Assessment, monitoring and reporting of conservation status-Preparing the 2001–2007 report under Article 17 of the Habitats Directive. DG Env. B2/AR D rev3. Brussels, http://forum.europa.eu.int/Public/irc/env/monnat/library?l=/reporting_framework
  15. Fewster RM, Buckland ST, Siriwardena GM, Baillie SR, Wilson JD (2000) Analysis of population trends for farmland birds using generalized additive models. Ecology 81:1970–1984Google Scholar
  16. Freckleton RP, Watkinson AR, Green RE, Sutherland WJ (2006) Census error and the detection of density dependence. J Anim Ecol 75:837–851. doi:10.1111/j.1365-2656.2006.01121.x PubMedCrossRefGoogle Scholar
  17. Greenwood JJD, Baillie SR (1991) Effects of density-dependence and weather on population changes of English passerines using a nonexperimental paradigm. Ibis 133:121–133. doi:10.1111/j.1474-919X.1991.tb07675.x CrossRefGoogle Scholar
  18. Gregory RD, Vorisek P, Noble DG, van Strien AJ, Pazserová A, Eaton ME, et al. The generation and use of bird population indicators in Europe. Bird Conserv Int (in press)Google Scholar
  19. Henry P-Y, Lengvel S, Nowicki P, Julliard R, Clobert J, Celik T, et al (2008) Integrating ongoing biodiversity monitoring: potential benefits and methods. Biodivers Conserv. doi:10.1007/s10531-008-9417-1 Google Scholar
  20. Hilborn R, Mangel M (1997) The ecological detective. Confronting models with data. Princeton University Press, Princeton, NJGoogle Scholar
  21. Holmes EE (2001) Estimating risks in declining populations with poor data. Proc Natl Acad Sci USA 98:5072–5077. doi:10.1073/pnas.081055898 PubMedCrossRefGoogle Scholar
  22. Holmes EE, Fagan WF (2002) Validating population viability analysis for corrupted data sets. Ecology 83:2379–2386Google Scholar
  23. Hwang WH, Huang YH (2007) Measurement errors in continuous-time capture-recapture models. J Statist Plann Inference 137:1888–1899. doi:10.1016/j.jspi.2006.04.010 CrossRefGoogle Scholar
  24. Link WA, Sauer JR (1997a) Estimation of population trajectories from count data. Biometrics 53:488–497. doi:10.2307/2533952 CrossRefGoogle Scholar
  25. Link WA, Sauer JR (1997b) New approaches to the analysis of population trends in land birds. Ecology 78:2632–2634 CommentGoogle Scholar
  26. Link WA, Sauer JR (1998) Estimating population change from count data: application to the North American breeding bird survey. Ecol Appl 8:258–268. doi:10.1890/1051-0761(1998)008[0258:EPCFCD]2.0.CO;2 CrossRefGoogle Scholar
  27. McCallum H (2000) Population parameters. Estimation for ecological models. Blackwell Science, Oxford, UKGoogle Scholar
  28. McNamara JM, Harding KC (2004) Measurement error and estimates of population extinction risk. Ecol Lett 7:16–20. doi:10.1046/j.1461-0248.2003.00550.x CrossRefGoogle Scholar
  29. Meir E, Fagan WF (2000) Will observation error and biases ruin the use of simple extinction models? Conserv Biol 14:148–154. doi:10.1046/j.1523-1739.2000.98502.x CrossRefGoogle Scholar
  30. Nowicki P, Richter A, Glinka U, Holzschuh A, Toelke U, Henle K et al (2005) Less input same output: simplified approach for population size assessment in Lepidoptera. Popul Ecol 47:203–212. doi:10.1007/s10144-005-0223-2 CrossRefGoogle Scholar
  31. Pollard E, Moss D, Yates TJ (1995) Population trends of common Birtish butterflies at monitored sites. J Appl Ecol 32:9–16. doi:10.2307/2404411 CrossRefGoogle Scholar
  32. R Development Core Team (2007) R: a language and environment for statistical computing Vers. 2.5.0. R Foundation for Statistical Computing, ViennaGoogle Scholar
  33. Rothery P, Newton I, Dale L, Wesolowski T (1997) Testing for density dependence allowing for weather effects. Oecologia 112:518–523. doi:10.1007/s004420050340 CrossRefGoogle Scholar
  34. Schwager M, Johst K, Jeltsch F (2006) Does red noise increase or decrease extinction risk? Single extreme events versus series of unfavorable conditions. Am Nat 167:879–888. doi:10.1086/503609 CrossRefGoogle Scholar
  35. Schwarz CJ, Seber GAF (1999) Estimating animal abundance. Stat Sci 14:427–456. doi:10.1214/ss/1009212521 Review IIICrossRefGoogle Scholar
  36. Seber GAF (1982) The estimation of animal abundance and related parameters. MacMillan Press, New York, USAGoogle Scholar
  37. Sibly RM, Barker D, Denham MC, Hone J, Pagel M (2005) On the regulation of populations of mammals, birds, fish, and insects. Science 309:607–610. doi:10.1126/science.1110760 PubMedCrossRefGoogle Scholar
  38. Solow AR (1998) On fitting a population model in the presence of observation error. Ecology 79:1463–1466CrossRefGoogle Scholar
  39. Soulé ME (ed) (1987) Viable populations for conservation. Cambridge University Press, Cambridge, UKGoogle Scholar
  40. Staples DF, Taper ML, Dennis B (2004) Estimating population trend and process variation for pva in the presence of sampling error. Ecology 85:923–929. doi:10.1890/03-3101 CrossRefGoogle Scholar
  41. Sutherland WJ (ed) (1996) Ecological census techniques. A handbook. Cambridge University Press, Cambridge UKGoogle Scholar
  42. Thomas JA (2005) Monitoring change in the abundance and distribution of insects using butterflies and other indicator groups. Philos Trans R Soc B-Biological Sci 360:339–357. doi:10.1098/rstb.2004.1585 CrossRefGoogle Scholar
  43. Thomas L (1996) Monitoring long-term population change: why are there so many analysis methods? Ecology 77:49–58. doi:10.2307/2265653 CrossRefGoogle Scholar
  44. Turchin P (2003) Complex population dynamics. Princeton University Press, Princeton NJGoogle Scholar
  45. van Swaay CAM, Nowicki P, Settele J, van Strien AJ (2008) Butterfly monitoring in Europe—methods, applications and perspectives. Biodivers Conserv. doi:10.1007/s10531-008-9440-2 Google Scholar
  46. Williams BK, Nichols JD, Conroy MJ (2002) Analysis and management of animal populations. Academic Press, San Diego, CAGoogle Scholar
  47. Wilmers CC, Post E, Hastings A (2007) A perfect storm: the combined effects on population fluctuations of autocorrelated environmental noise, age structure, and density dependence. Am Nat 169:673–683. doi:10.1086/513484 PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Field Station FabrikschleichachUniversity of WürzburgRauhenebrachGermany
  2. 2.Institute of Environmental SciencesJagiellonian UniversityKrakowPoland

Personalised recommendations