Skip to main content
Log in

Scaling law in free walking of mice in circular open fields of various diameters

  • Original Paper
  • Published:
Journal of Biological Physics Aims and scope Submit manuscript

Abstract

Open-field tests are routinely used to study locomotor activity in rodents. I studied the effects of apparatus size on rodent locomotor activity, specifically with respect to how resting and walking periods are interwoven. I explored the open-field behavior of mice utilizing circular open fields of various diameters. When the diameter of the test apparatus was greater than 75 cm, the durations of the resting and moving periods of free walking behavior obeyed bounded power-law distribution functions. I found that the properties of the scaling exponents and model selection became similar for test apparatus diameters greater than 75 cm. These results can provide a guide for the selection of the size of the test apparatus for use in the study of the open-field behavior of rodents.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Gould, T.D., Dao, D.T., Kovacsics, C.E.: The open field test mood and anxiety related phenotypes in mice. Neuromethods 42, 1–20 (2009)

    Article  Google Scholar 

  2. Meyer, J.S., Quenzer, L.F.: Psychopharmacology: Drugs, the Brain, and Behavior. Sinauer Associates, Inc. Publishers, Massachusetts (2005)

  3. Paulus, M.P., Geyer, M.A.: Three independent factors characterize spontaneous rat motor activity. Behav. Brain Res. 53, 11–20 (1991)

    Article  Google Scholar 

  4. Nakamura, T., Takumi, T., Takano, A., Aoyagi, N., Yoshiuchi, K., Struzik, Z.R., Yamamoto, Y.: Of mice and men: Universality and breakdown of behavioral organization. PLoS ONE 3, e2050 (2005)

    Article  ADS  Google Scholar 

  5. Nakamura, T., Takumi, T., Takano, A., Hatanaka, F., Yamamoto, Y.: Characterization and modeling of intermittent locomotor dynamics in clock gene-deficient mice. PLoS ONE 8, e58884 (2013)

    Article  ADS  Google Scholar 

  6. Shoji, H., Nakatomi, Y., Yokoyama, C., Fukui, K., Hanai, K.: New index based on the physical separation of motion into three categories for characterizing the effect of cocaine in mice. J. Theor. Biol. 333, 68–77 (2013)

  7. Benjamini, Y., Lipkind, D., Horev, G., Kafkafi, N., Golani, I.: Ten ways to improve the quality of descriptions of whole-animal movement. Neurosci. Biobehav. Rev. 131, 11014–11026 (2010)

    Google Scholar 

  8. Kafkafi, N., Mayo, C.L., Drai, D., Golani, I., Elmer, G.: Natural segmentation of the locomotor behavior of drug-induced rats in a photobeam cage. J. Neurosci. Meth. 109, 111–121 (2001)

    Article  Google Scholar 

  9. Matthus, F., Mommer, M.S., Curk, T., Dobnikar, J.: On the origin and characteristics of noise-induced Lévy walks of E. coli. PLoS ONE 6, e17623 (2011)

    Article  Google Scholar 

  10. Bak, P.: How Nature Works: The Science of Self-Organized Criticality. Springer, New York (1996)

  11. Brown, J.H., Gupta, V.K., Li, B.L., Milne, B.T., Restrepo, C., West, G.B.: The fractal nature of nature: power laws, ecological complexity and biodiversity. Philos. Trans. R. Soc. B. 357, 619–626 (2002)

    Article  Google Scholar 

  12. Clauset, A., Shalizi, C.R., Newman, M.E.J.: Power-law distributions in empirical data. SIAM Rev. 51, 661–703 (2009)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Newman, M.E.J.: Power laws Pareto distributions and Zipf’s law. Contemp. Phys. 46, 323–351 (2005)

    Article  ADS  Google Scholar 

  14. Barabasi, A.-L.: Origin of bursts and heavy tails in human dynamics. Nature 435, 207–211 (2005)

    Article  ADS  Google Scholar 

  15. Miramontes, O., DeSouza, O., Paiva, L.R., Marins, A., Orozco, S.: Lévy flights and self-similar exploratory behavior of termite workers: beyond model fitting. PLoS ONE 9, e111183 (2014)

    Article  ADS  Google Scholar 

  16. Reynolds, A.M., Smith, A.D., Menzel, R., Greggers, U., Reynolds, D.R., Rilley, J.R.: Displaced honey bees perform optimal scale-free search flights. Ecology 88, 1955–1961 (2007)

    Article  Google Scholar 

  17. Vismanathan, G.M., Buldryrev, S.V., Havlin, S., da Luz, M.G.E., Raposo, E.P., Stanley, H.E.: Optimizing the success of random search. Nature 401, 911–914 (1999)

    Article  ADS  Google Scholar 

  18. Atkinson, R.P.D., Rhodes, C.J., Macdonald, D.W., Anderson, R.M.: Scale-free dynamics in the movement patterns of jackals. Oikos 98, 134–140 (2002)

    Article  Google Scholar 

  19. Humphries, N.E., Queiroz, N., Dyer, J.R.M., Pade, N.G., Musyl, M.K., Schaefer, K.M., Fuller, D.W., Brunnschweiler, J.M., Doyle, T.K., Houghton, J.D.R., Hays, G.C., Jones, C.S., Noble, L.R., Wearmouth, V.J., Southall, E.J., Sims, D.W.: Environmental context explains Lévy and Brownian movement patterns of marine predators. Nature 465, 1066–1069 (2010)

    Article  ADS  Google Scholar 

  20. Sims, D.W., Southall, E.J., Humphries, N.E., Hays, G.C., Bradshaw, C.J.A., Pitchford, J.W., James, A., Ahmed, M.Z., Brierley, A.S., Hindell, M.A., Morritt, D., Musyl, M.K., Righton, D., Shepard, E.L.C., Wearmouth, V.J., Wilson, R.P., Witt, M.J., Metcalfe, J.D.: Scaling laws of marine predator search behaviour. Nature 451, 1098–1102 (2008)

    Article  ADS  Google Scholar 

  21. Mashanova, A., Oliver, T.H., Jansen, V.A.A.: Evidence for intermittency and a truncated power law from highly resolved aphid movement data. J. R. Soc. Interface 6, 199–208 (2010)

    Article  Google Scholar 

  22. Vandercone, R., Premachandra, K., Wijethunga, G.P., Dinadh, C., Ranawana, K., Bahar, S.: Random walk analysis of ranging patterns of sympatric langurs in a complex resource landscape. Am J. Primatol 75, 1209–1219 (2013)

    Google Scholar 

  23. Edwards, A.M.: Overturning conclusions of Lévy flight movement patterns by fishing boats and foraging animals. Ecology 92, 1247–1257 (2011)

    Article  Google Scholar 

  24. Edwards, A.M., Phillips, R.A., Watkins, N.W., Freeman, M.P., Murphy, E.J., Afanasyev, V., Buldyrev, S.B., da Luz, M.G.E., Raposo, E.P., Stanley, H.E., Viswanathan, G.M.: Revisiting Lévy flight search patterns of wandering albatrosses, bumblebees, and deer. Nature 449, 1044–1048 (2007)

    Article  ADS  Google Scholar 

  25. Benhamou, S.: How many animals really do the Lévy walk? Ecology 88, 1962–1969 (2007)

    Article  Google Scholar 

  26. Viswanathan, G.M., Afanasyev, V., Buldyrev, S.V., Murphy, E.J., Price, P.A., Stanley, H.E.: Lévy flight search patterns of wandering albatrosses. Nature 381, 413–415 (1996)

    Article  ADS  Google Scholar 

  27. de Jager, M., Weissing, F.J., Herman, P.M.J., Nolet, B.A., Van de Koppe, J.: Lévy walk evolves through interaction between movement and environmental complexity. Science 332, 1551–1553 (2011)

    Article  ADS  Google Scholar 

  28. Reynolds, A.: Liberating Lévy walk research from the shackles of optimal foraging. Phys. Life Rev. 14, 59–83 (2015)

  29. Hanai, K., Ozaki, M., Yamauchi, D., Nakatomi, Y., Yokoyama, C., Fukui, K.: Scale-free dynamics involved in locomotor activity of ant and mouse. WSEAS Trans. Biol. Biomed. 6, 511–515 (2006)

    Google Scholar 

  30. Drai, D., Benjamini, Y., Golani, I.: Statistical discrimination of natural modes of motion in rat exploratory behavior. J. Neurosci. Meth. 96, 119–131 (2000)

    Article  Google Scholar 

  31. Burnham, K.P., Anderson, D.R.: Model selection and multimodel inference: A practical information-theoretic approach. Springer, New York (2002)

    MATH  Google Scholar 

  32. Reynolds, A.M.: Mussels realized Weierstrassian Lévy walks as composite correlated random walks. Sci. Rep. 4, 4409 (2014)

    Article  ADS  Google Scholar 

  33. Beggs, J.M., Plenz, D.: Neuronal avalanches in neocortical circuits. J. Neurosci. 23, 11167–11172 (2003)

    Google Scholar 

  34. Sims, D.W., Righton, D., Pitchford, J.W.: Minimizing errors in identifying Lévy flight behavior of organisms. J. Anim. Ecol. 76, 222–229 (2007)

    Article  Google Scholar 

  35. White, E.P., Ernest, S.K.M., Kerkhoff, A.J., Enquist, B.J.: Relationships between body size and abundance in ecology. Trends Ecol. Evol. 22, 323–350 (2007)

    Article  Google Scholar 

  36. White, E.P., Enquist, B.J., Green, J.L.: On estimating the exponents of power-law frequency distribution. Ecology 89, 905–912 (2008)

    Article  Google Scholar 

  37. Geyer, M.A.: Approaches to the characterization of drug effects on locomotor activity in rodents. In Adler, M.W., and Cowan, A. (eds.). Modern Methods in Pharmacology Vol. 6 Testing and Evaluation of Drug Abuse, Wiley Liss, 81-100 (1990)

  38. Barnett, S.H.: The rat: A study in behavior. Aldine Publishing Co., Chicago (2007)

    Google Scholar 

  39. Miramontes, O.: Divorcing physics from biology? Optimal foraging and Lévy flights. Comment on Liberating Lévy walk research from the shackles of optimal foraging by A.M. Reynolds. Phys. Life Rev. 14, 108–110 (2015)

Download references

Acknowledgments

I would like to thank K. Hanai for his technical assistance and K. Yoshii for his helpful comments. This research was supported by JSPS KAKENHI Grant Numbers 26800225 and 15H01125.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hiroto Shoji.

Additional information

Submitted to the Journal of Biological Physics on April 21, 2015

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Shoji, H. Scaling law in free walking of mice in circular open fields of various diameters. J Biol Phys 42, 259–270 (2016). https://doi.org/10.1007/s10867-015-9406-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10867-015-9406-z

Keywords

Navigation