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Biodiversity & Conservation

, Volume 9, Issue 5, pp 655–671 | Cite as

Regression and model-building in conservation biology, biogeography and ecology: The distinction between – and reconciliation of – ‘predictive’ and ‘explanatory’ models

  • Ralph Mac Nally
Article

Abstract

In many large-scale conservation or ecological problems where experiments are intractable or unethical, regression methods are used to attempt to gauge the impact of a set of nominally independent variables (X) upon a dependent variable (Y). Workers often want to assert that a given X has a major influence on Y, and so, by using this indirection to infer a probable causal relationship. There are two difficulties apart from the demonstrability issue itself: (1) multiple regression is plagued by collinear relationships in X; and (2) any regression is designed to produce a function that in some way minimizes the overall difference between the observed and ‘predicted’ Ys, which does not necessarily equate to determining probable influence in a multivariate setting. Problem (1) may be explored by comparing two avenues, one in which a single ‘best’ regression model is sought and the other where all possible regression models are considered contemporaneously. It is suggested that if the two approaches do not agree upon which of the independent variables are likely to be ‘significant’, then the deductions must be subject to doubt.

criteria hierarchical partitioning inference model artefacts model selection multiple regression 

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References

  1. Akaike H (1978) A Bayesian Analysis of the minimum AIC procedure. Annals Institute Statistics Mathematics 30: 9-14Google Scholar
  2. Anderson-Sprecher R (1994) Model comparisons and R2. American Statistician 48: 113-117Google Scholar
  3. Böhning-Gaese K (1997) Determinants of avian species richness at different spatial scales. Journal of Biogeography 24: 49-60Google Scholar
  4. Bolger DT, Alberts AC, Sauvajot RM, Potenza P and McCalvin C (1997a) Response of rodents to habitat fragmentation in coastal southern California. Ecological Applications 7: 552-563Google Scholar
  5. Bolger DT, Scott TA and Rotenberry RT (1997b) Breeding bird abundance in an urbanizing landscape in coastal southern California. Conservation Biology 11: 406-421Google Scholar
  6. Brieman L (1995) Better subset regression using the nonnegative garrote. Technometrics 37: 373-384Google Scholar
  7. Burbidge AA, Williams MR and Abbott I (1997) Mammals of Australian islands: factors influencing species richness. Journal of Biogeography 24: 703-715Google Scholar
  8. Chapin TG, Harrison DJ and Katnik DD (1998) Influence of landscape pattern on habitat use by American marten in an industrial forest. Conservation Biology 12: 1327-1337Google Scholar
  9. Chevan A and Sutherland M (1991) Hierarchical partitioning. The American Statistician 45: 90-96Google Scholar
  10. Christensen R (1992) Comment on Chevan and Sutherland. American Statistician 46: 74Google Scholar
  11. Delisle JM and Savidge JA (1997) Avian use and vegetation characterization of conservation program fields. Journal of Wildlife Management 61: 318-325Google Scholar
  12. Demaynadier PG and Hunter MLJ (1998) Effects of silvicultural edges on the distribution and abundance of amphibians in Maine. Conservation Biology 12: 340-352Google Scholar
  13. Draper NR and Smith H (1966) Applied Regression Analysis. John Wiley & Sons, New YorkGoogle Scholar
  14. Fisher M (1997) Decline in the juniper woodlands of Raydah Reserve in southwestern Saudi Arabia: a response to climate change? Global Ecology and Biogeography Letters 6: 379-386Google Scholar
  15. Fitzgibbon CD (1997) Small mammals in farm woodlands: the effects of habitat, isolation and surrounding land-use patterns. Journal of Applied Ecology 34: 530-539Google Scholar
  16. Flack VF and Chang PC (1987) Frequency of selecting noise variables in subset regression analysis: a simulation study. American Statistician 41: 84-86Google Scholar
  17. Freedman DA (1983) A note on screening regression equations. The American Statistician 37: 152-155Google Scholar
  18. Greenberg R, Bichier P, Cruz Angon A and Reitsma R (1997) Bird populations in shade and sun coffee plantations in central Guatemala. Conservation Biology 11: 448-459Google Scholar
  19. Heikkinen RK and Neuvonen S (1997) Species richness of vascular plants in the subarctic landscape of northern Finland: modelling relationships to the environment. Biodiversity and Conservation 6: 1181-1201Google Scholar
  20. Hocking RR (1976) The anlaysis and selection of variables in linear regression. Biometrics 32: 1-49Google Scholar
  21. Hurvich CM and Tsai CL (1990) The impact of model selection on inference in linear regression. American Statistician 44: 214-217Google Scholar
  22. James FC, Hess CA and Kufrin D (1997) Species-centered environment analysis: indirect effects of fire history on red-cockaded woodpeckers. Ecological Applications 7: 118-129Google Scholar
  23. Laurance WF (1991) Edge effects in tropical forest fragmentation: application of a model for the design of nature reserves. Biological Conservation 51: 205-219Google Scholar
  24. Linhart H and Zucchini W (1986) Model Selection. John Wiley & Sons, New YorkGoogle Scholar
  25. Loyn RH (1987) Effects of patch area and habitat on bird abundances, species numbers and tree health in fragmented Victorian forests. In: Saunders DA, Arnold GW, Burbidge AA and Hopkins AJM (eds) Nature Conservation: The Role of Remnants of Native Vegetation, pp 65-77. Surrey Beatty and Sons, Chipping Norton, AustraliaGoogle Scholar
  26. Mac Nally R and Horrocks G (2000) Landscape-scale conservation of an endangered migrant: The swift parrot Lathamus discolor in its winter range. Biological Conservation (in press)Google Scholar
  27. McCall R, Nee S and Harvey PH (1996) Determining the influence of continental species-richness, island availability and vicariance in the formation of island-endemic bird species. Biodiversity Letters 3: 137-150Google Scholar
  28. McCullagh P and Nelder JA (1989) Generalized Linear Models, 2nd edn. Chapman & Hall, LondonGoogle Scholar
  29. Morse SF and Robinson SK (1999) Nesting success of a neotropical migrant in a multiple-use, forested landscape. Conservation Biology 13: 327-337Google Scholar
  30. Munger JC, Gerber M, Madrid K, Carroll MA, Petersen W and Herberger L (1998) US National Wetland Inventory classification of the occurrence if Columbian spotted frogs (Rana luteiventris) and Pacific treefrogs (Hyla regilla). Conservation Biology 12: 320-330Google Scholar
  31. Naughton-Treves L (1998) Predicting patterns of crop damage by wildlife around Kibale National Park, Kenya. Conservation Biology 12: 156-168Google Scholar
  32. Neter J, Wasserman W and Kutner MH (1990) Applied Linear Statistical Models. Irwin, Homewood, New JerseyGoogle Scholar
  33. Panzer R and Schwartz MW (1998) Effectiveness of vegetation-based approach to insect conservation. Conservation Biology 12: 693-702Google Scholar
  34. Pearman PB (1997) Correlates of amphibian diversity in an altered landscape of Amazonian Ecuador. Conservation Biology 11: 1211-1225Google Scholar
  35. Rencher AC and Pun FC (1980) Inflation of R2 in best subset regression. Technometrics 22: 49-53Google Scholar
  36. Ripple WJ, Lattin PD, Hershey KT, Wagner FF and Meslow EC (1997) Landscape composition and pattern around northern spotted owl nest sites in southwest Oregon. Journal of Wildlife Management 61: 151-158Google Scholar
  37. Sætersdal M and Birks HJB (1997) A comparative ecological study of Norwegian mountain plants in relation to possible future climate change. Journal of Biogeography 24: 127-152Google Scholar
  38. Sakamoto Y, Ishiguro M and Kitagawa G (1986) Akaike Information Criterion Statistics. KTK Scientific Publishers, TokyoGoogle Scholar
  39. Schwarz G (1978) Estimating the dimension of a model. Annals of Statistics 6: 461-464Google Scholar
  40. Snodgrass JW (1997) Temporal and spatial dynamics of beaver-created patches as influenced by management practices in a south-eastern North American landscape. Journal of Applied Ecology 34: 1043-1056Google Scholar
  41. SPSS I (1997) SYSTAT 7.0: The System for Statistics. SPSS Inc., Evanston, USAGoogle Scholar
  42. Thompson ML (1978a) Selection of variables in multiple regression: Part I. A review and evaluation. International Statistical Review 46: 1-19Google Scholar
  43. Thompson ML (1978b) Selection of variables in multiple regression: Part II. Chosen procedures, computations and examples. International Statistical Review 46: 129-146Google Scholar
  44. Toner M and Keddy P (1997) River hydrology and riparian wetlands: a predictive model for ecological assembly. Ecological Applications 7: 236-246Google Scholar
  45. Watson DM, Mac Nally R and Bennett AF (2000) The avifauna of severely fragmented, Buloke Allocasuarina luehmanni woodland in western Victoria, Australia. Pacific Conservation Biology (in press)Google Scholar
  46. Wohlgemuth T (1998) Modelling floristic species richness on a regional scale: a case study in Switzerland. Biodiversity and Conservation 7: 159-177Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Ralph Mac Nally
    • 1
  1. 1.Section of Ecology, Department of Biological SciencesMonash University, ClaytonVictoriaAustralia (fax

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