, Volume 95, Issue 4, pp 581–591 | Cite as

Density dependence tests, are they?

  • Henk Wolda
  • Brian Dennis
Original Papers


A large number of time series of abundances of insects and birds from a variety of data sets were submitted to a new density dependence test. The results varied enormously between data sets, but the relation between the frequency of statistically significant density dependence (SSDD) and the length of the series was similar to that of the power curve of the test, making the results consistent with the hypothesis of the density-dependent model being universally applicable throughout the data used. Pest and non-pest species did not differ in the incidence of SSDD. The more sampling error present in the data, the higher the percentages of SSDD. This was expected given that the power of the test increases with increasing sampling error in the data. Many of the data used here, as well as in the literature, clearly violate the basic assumption of the test that the organism concerned should be univoltine and semelparous. Yet the incidence of SSDD was the same in univoltine as in bi/polyvoltine species and the same in semelparous organisms as in birds that are reproductively active in more than one year. The seasonal migrant Autographa gamma in Britain and Czechoslovakia and even rainfall data were found to have SSDD. Statistical significance, however, does not automatically lead to the conclusion of density-dependent regulation. Any series of random variables which are in a stochastic equilibrium, such as a series of independent, identically distributed, random variables, is typically described better by the alternative (density-dependent) model than by the null (density-independent) model. Significant test results were often obtained with sloppy data, with data that clearly violate the basic assumptions of the test and with other data where an interpretation of the results in terms of densitydependent regulation was absurd. Given the fact that other explanations have to be found for significant test results for all these cases, mechanisms other than regulation may very well be applicable too where the data are entirely appropriate for the test. The test is simply a data-based choice between a model without and one with a stochastic equilibrium. A time series as such does not contain any information about the causes of the fluctuation pattern, so that one cannot expect statistics to produce such information from that time series. A significant test result using suitable data is entirely consistent with the hypothesis of density-dependent regulation, but also with any other suitable hypotheses. Because the test results were generally consistent with the hypothesis of a universal applicability of the density-dependence model, a negative test result may only mean that the time series was not long enough for the density dependence that was present to become statistically significant. Positive results are difficult to interpret, but so are negative results. A final decision needs to be based not so much on the test result as on much detailed information about the population concerned. Because the “density-dependence test” does not test for the presence of the mechanism of density-dependent regulation and because of the loaded, multiple meanings of the term “density-dependence”, calling the test a “test of statistical density dependence” may be preferable.

Key words

Density dependence tests Time series Insects Birds Regulation of numbers 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andrewartha HG, Birch LC (1954) The distribution and abundance of animals. University of Chicago Press, ChicagoGoogle Scholar
  2. Andrewartha HG, Birch LC (1984) The ecological web, University of Chicago Press. Chicago LondonGoogle Scholar
  3. Baars MA (1979) Catches in pitfall traps in relation with mean densities of carabid beetles. Oecologia 41:25–46Google Scholar
  4. Berryman AA (1991) Stabilization or regulation: what it all means! Oecologia 86:140–143Google Scholar
  5. Croin Michielsen N, Van der Meijden E, Otten JJM (1974) Vogelpopulaties, Centraal Nestkast Onderzoek, Vogelringstation. Meijendel Meded 3:1–88Google Scholar
  6. Darsie RF, MacCreary D, Stearn LA (1953) Proc 40th Ann Meeting new Jersey Mosquito Exterm Assoc 1953:169–190Google Scholar
  7. Den Boer PJ (1986) Density dependence and the stabilization of animal numbers. 1. The winter moth. Oecologia 69:507–512Google Scholar
  8. Den Boer PJ (1987) Density dependence and the stabilization of animal numbers. 2. The pine looper. Neth J Zool 37:220–237Google Scholar
  9. Den Boer PJ (1990) On the stabilization of animal numbers. Problems of testing. 3. What do we conclude from significant test results? Oecologia 83:38–46Google Scholar
  10. Den Boer PJ (1991) Seeing the trees for the wood: random walks or bounded fluctuations of population size? Oecologia 86:484–491Google Scholar
  11. Den Boer PJ, Reddingius J (1989) On the stabilization of animal numbers. Problems of testing. 2. Confrontation with data from the field. Oecologia 79:143–149Google Scholar
  12. Dennis B, Taper M (1993) Density dependence in time series observations of natural populations: estimation and testing. Ecology (in press)Google Scholar
  13. Dolnik VR, Paevskii VA (1980) Dynamics of numbers in Baltic bird populations in 1960–76. Sov J Ecol 10:316–325Google Scholar
  14. Hanski I (1990) Density dependence, regulation and variability in animal populations. Philos Trans R Soc London B 330:141–150Google Scholar
  15. Hanski I, Woiwod IP (1991) Delayed density-dependence. Nature 350:28Google Scholar
  16. Hassell MP, Latto J, May RM (1989) Seeing the wood for the trees: Detecting density dependence from existing life-table studies. J Anim Ecol 58:883–892Google Scholar
  17. Holyoak M, Lawton JH (1992) Detection of density dependence from annual censuses of bracken-feeding insects. Oecologia 91:425–430Google Scholar
  18. Kendeigh SC (1979) Invertebrate populations of the deciduous forest: fluctuations and relations to weather (Ill Biol Monogr 50). University of Illinois Press. UrbanaGoogle Scholar
  19. Kendeigh SC (1982) Bird populations in east central Illinois: fluctuations, variations and development over half a century (Ill Biol Monogr 52). University of Illinois Press, UrbanaGoogle Scholar
  20. Nicholson AJ (1933) The balance of animal populations. J Anim Ecol 2:132–178Google Scholar
  21. Nicholson AJ, Bailey VA (1935) The balance of animal populations. Part 1. Proc Zool Soc London 1935:551–598Google Scholar
  22. Novak I (1983) An efficient light-trap for catching insects. Acta Entomol Bohemoslov 80:29–34Google Scholar
  23. Novak I, Severa F (1981) Thieme's vlindergids. WJ Thieme, ZutphenGoogle Scholar
  24. Osterlof S, Stolt B-O (1982) Population trends indicated by birds ringed in Sweden. Ornis Scand 13:135–140Google Scholar
  25. Ôtake A (1966a) Analytical studies of light trap records in the Hokuriku district. I. The rice stem borer, Chilo suppressalis Walker (Lepidoptera: Pyralidae). Appl Entomol Zool 1:177–188Google Scholar
  26. Ôtake A (1966b) Analytical studies of light trap records in the Hokuriku district. II. The green rice leafhopper, Nephotettix cincticeps. Res Popul Ecol 8:62–68Google Scholar
  27. Ôtake A (1978) Population characteristics of the brown planthopper, Nilaparvata lugens (Hemiptera: Delphacidae), with special reference to differences in Japan and the tropics. J Appl Ecol 15:385–394Google Scholar
  28. Ôtake A, Kono T (1970) Regional characteristics in population trends of the smaller brown planthopper, Laodelphax striatellus (Fallén) (Hemiptera: Delphacidae), a vector of rice stripe disease: an analytical study of light trap records. Bull Shikoku Agric Exp Stat 21:127–147Google Scholar
  29. Pankratz A (1983) Forecasting with unvariate Box-Jenkins models. Wiley, New YorkGoogle Scholar
  30. Pollard E, Lakhani KH, Rothery P (1987) The detection of density-dependence from a series of annual censuses. Ecology 68:2046–2055Google Scholar
  31. Reddingius J (1971) Gambling for existence. A discussion of some theoretical problems in animal population ecology. Acta Biotheor 20:1–208Google Scholar
  32. Reddingius J (1990) Models for testing. A secondary note. Oecologia 83:50–52Google Scholar
  33. Reddingius J, Den Boer PJ (1989) On the stabilization of animal numbers. Problems of testing. 1. Power estimates and estimation errors. Oecologia 78:1–8Google Scholar
  34. Regensburg BA, Wanders EAJ (1978) Vogelpopulatieonderzoek-Rapport 1975. Meijendel Meded 6:1–43Google Scholar
  35. Rejmánek M, Spitzer K (1982) Bionomic strategies and long-term fluctuations in abundance of Noctuidae (Lepidoptera). Acta Entomol Bohemoslov 79:81–96Google Scholar
  36. Royama T (1977) Population persistence and density dependence. Ecol Monogr 47:1–35Google Scholar
  37. Royama T (1981) Fundamental concepts and methodology for the analysis of animal population dynamics, with particular reference to univoltine species. Ecol Monogr 51:473–493Google Scholar
  38. Solow AR (1990) Testing for density dependence. A cautionary note. Oecologia 83:47–49Google Scholar
  39. Solow AR (1991) Response, Oecologia 86:146Google Scholar
  40. Solow AR, Steele JH (1990) On sample size, statistical power and the detection of density dependence. J Anim Ecol 59:1073–1076Google Scholar
  41. Stubbs M (1977) Density dependence in the life-cycles of animals and its importance in K- and r-strategies. J Anim Ecol 46:677–688Google Scholar
  42. Van Dongen H, Ros JH (1973) Vogelpopulaties and Vogelringstation. Rapport 1972. Meijendel Meded 2:1–65Google Scholar
  43. Vickery WL, Nudds TD (1991) Testing for density-dependent effects in sequential censuses. Oecologia 85:419–423Google Scholar
  44. Volterra V (1931) Leçons sur la théorie mathématique de la lutte pour la vie, Gauthier-Villars, ParisGoogle Scholar
  45. Williams CB (1971) Insect migration (New Naturalist 36). Collins, LondonGoogle Scholar
  46. Windsor DM (1990) Climate and moisture variability in a tropical forest: Long-term records from Barro Colorado Island, Panama. Smithsonian Contrib Earth Sci 29:1–145Google Scholar
  47. Woiwod IP, Hanski I (1992) Patterns of density dependence in moths and aphids. J Anim Ecol 61:619–629Google Scholar
  48. Wolda H (1987) Altitude, habitat and tropical insect diversity. Biol J Linn Soc London 30:313–323Google Scholar
  49. Wolda H, Broadhead E (1985) The seasonality of Psocoptera in two tropical forests in Panama. J Anim Ecol 54:519–530Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Henk Wolda
    • 1
  • Brian Dennis
    • 2
  1. 1.Smithsonian Tropical Research Institute, Unit 0948APO AAUSA
  2. 2.Dept. Fish and Wildlife ResourcesUniversity of IdahoMoscowUSA

Personalised recommendations