, Volume 56, Issue 2–3, pp 234–238 | Cite as

Analyzing insect movement as a correlated random walk

  • P. M. Kareiva
  • N. Shigesada
Original Papers


This paper develops a procedure for quantifying movement sequences in terms of move length and turning angle probability distributions. By assuming that movement is a correlated random walk, we derive a formula that relates expected square displacements to the number of consecutive moves. We show this displacement formula can be used to highlight the consequences of different searching behaviors (i.e. different probability distributions of turning angles or move lengths). Observations of Pieris rapae (cabbage white butterfly) flight and Battus philenor (pipe-vine swallowtail) crawling are analyzed as a correlated random walk. The formula that we derive aptly predicts that net displacements of ovipositing cabbage white butterflies. In other circumstances, however, net displacements are not well-described by our correlated random walk formula; in these examples movement must represent a more complicated process than a simple correlated random walk. We suggest that progress might be made by analyzing these more complicated cases in terms of higher order markov processes.


Probability Distribution Random Walk Markov Process Complicated Process Complicated Case 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Broadbent SR, Kendall DG (1953) The random walk of Trichostrongylus retortaeformis. Biometrics 9:460–466Google Scholar
  2. Crumpacker DW, Williams JS (1973) Density, dispersion, and population structure in Drosophila pseudoobscura. Ecol Mon 43:498–538Google Scholar
  3. Jones R (1977) Movement patterns and egg distribution in cabbage butterflies. J Anim Ecol 46:195–212Google Scholar
  4. Jones R, Gilbert N, Guppy M, Neals V (1980) Long-distance movement of Pieris rapae. J Anim Ecol 49:629–642Google Scholar
  5. Kaiser H (1976) Quantitative description and simulation of stochastic behavior dragonflies (Aeschna cyanea, Odonata). Acta Biotheor 25:163–210Google Scholar
  6. Nossal RJ, Weiss GH (1974) A descriptive theory of cell migration on surfaces. J Theor Biol 47:103–113Google Scholar
  7. Rausher M (1979) Coevolution in a simple plant-herbivore system. Dissertation. Cornell University, Ithaca, New York, USAGoogle Scholar
  8. Root RB, Kareiva PM (1983) The search for resources by cabbage butterflies (Pieris rapae): ecological consequences and adaptive significance of markovian movements in a patchy environment. Ecol Monog (in press)Google Scholar
  9. Saito N (1967) Introduction to Polymer Physics. Syokabo Press, TokyoGoogle Scholar
  10. Siniff D, Jessen C (1969) A simulation model of animal movement patterns. Adv Ecol Res 6:185–219Google Scholar
  11. Skellam JG (1951) Random dispersal in theoretical populations. Biometrika 38:196–218Google Scholar
  12. Smith JNM (1974a) The food searching behavior of two European thrushes. I. Description and analysis of search paths. Behaviour 48:276–302Google Scholar
  13. Smith JNM (1974b) The food searching behavior of two European thrushes. II. The adaptiveness of the search patterns. Behaviour 49:1–61Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • P. M. Kareiva
    • 1
  • N. Shigesada
    • 2
  1. 1.Division of BiologyBrown UniversityProvidenceUSA
  2. 2.Department of BiophysicsKyoto UniversityKyotoJapan

Personalised recommendations