Skip to main content
SpringerLink
Log in
Book cover

Women in Mathematical Biology pp 179–210Cite as

Flying Spiders: Simulating and Modeling the Dynamics of Ballooning

  • Conference paper
  • First Online:

Part of the book series: Association for Women in Mathematics Series ((AWMS,volume 8))

Abstract

Spiders use a type of aerial dispersal called “ballooning” to move from one location to another. In order to balloon, a spider releases a silk dragline from its spinnerets and when the movement of air relative to the dragline generates enough force, the spider takes flight. We have developed and implemented a model for spider ballooning to identify the crucial physical phenomena driving this unique mode of dispersal. Mathematically, the model is described as a fully coupled fluid–structure interaction problem of a flexible dragline moving through a viscous, incompressible fluid. The immersed boundary method has been used to solve this complex multi-scale problem. Specifically, we used an adaptive and distributed-memory parallel implementation of immersed boundary method (IBAMR). Based on the nondimensional numbers characterizing the surrounding flow, we represent the spider as a point mass attached to a massless, flexible dragline. In this paper, we explored three critical stages for ballooning, takeoff, flight, and settling in two dimensions. To explore flight and settling, we numerically simulate the spider in free fall in a quiescent flow. To model takeoff, we initially tether the spider-dragline system and then release it in two types of flows. Based on our simulations, we can conclude that the dynamics of ballooning is significantly influenced by the spider mass and the length of the dragline. Dragline properties such as the bending modulus also play important roles. While the spider-dragline is in flight, the instability of the atmosphere allows the spider to remain airborne for long periods of time. In other words, large dispersal distances are possible with appropriate wind conditions.

The original version of this chapter was revised. An erratum to this chapter can be found at https://doi.org/10.1007/978-3-319-60304-9_13

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Batchelor, G.K.: Introduction to Fluid Mechanics. Cambridge University Press, Cambridge (1999)

    MATH  Google Scholar 

  2. Bell, J.R., Bohan, D.A., Fevre, R.L., Weyman, G.S.: Can simple experimental electronics simulate the dispersal phase of spider ballooners? J. Arachnol.33(2), 523–532 (2005)

    Article  Google Scholar 

  3. Berger, M.J., Colella, P.: Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys.82(1), 64–84 (1989)

    Google Scholar 

  4. Berger, M.J., Oliger, J.: Adaptive mesh refinement for hyperbolic partial-differential equations. J. Comput. Phys.53(3), 484–512 (1984)

    Google Scholar 

  5. Bonte, D., Vandenbroecke, N., Lens, L., Maelfait, J.: Low propensity for aerial dispersal in specialist spiders from fragmented landscapes. Proc. R. Soc. B270(1524), 1601–7 (2003)

    Article  Google Scholar 

  6. Bonte, D., Van Dyck, H., Bullock, J.M., Coulon, A., Delgado, M., Gibbs, M., Lehouck, V., Matthysen, E., Mustin, K., Saastamoinen, M., Schtickzelle, N., Stevens, V.M., Vandewoestijne, S., Baguette, M., Barton, K., Benton, T.G., Chaput-Bardy, A., Clobert, J., Dytham, C., Hovestadt, T., Meier, C.M., Palmer, S.C.F., Turlure, C., Travis, J.M.J.: Costs of dispersal. Biol. Rev.87(2), 290–312 (2012)

    Article  Google Scholar 

  7. Childs, H., Brugger, E., Whitlock, B., Meredith, J., Ahern, S., Pugmire, D., Biagas, K., et al.: VisIt: an end-user tool for visualizing and analyzing very large data (2012).http://www.osti.gov/scitech/servlets/purl/1170761

    Book  Google Scholar 

  8. Coyle, F., Greenstone, M.H., Hultsch, A.-L., Morgan, C.E.: Ballooning mygalomorphs: estimates of the masses of Sphodros and ummidia ballooners. J. Arachnol.13, 291–296 (1985)

    Google Scholar 

  9. De Meester, N., Bonte, D.: Information use and density-dependent emigration in an agrobiont spider. Behav. Ecol.21(5), 992–998 (2010)

    Article  Google Scholar 

  10. Glick, P.A.: The distribution of insects, spiders, and mites in the air. Tech. Bull. U.S. Dept. Agric.673, 1–150 (1939)

    Google Scholar 

  11. Gorham, P.W.: Ballooning spiders: the case for electrostatic flight. ArXiv:1309.4731v1 (2013)

    Google Scholar 

  12. Gressitt, J.L.: Biogeography and ecology of land arthropods of Antarctica. In: Mieghem, J., Oye, P. (eds.) Biogeography and Ecology in Antarctica. Monographiae Biologicae, vol. 15, pp. 431–490. Springer, Netherlands/Dordrecht (1965)

    Chapter  Google Scholar 

  13. Griffith, B.: An adaptive and distributed-memory parallel implementation of the immersed boundary (IB) method (IBAMR).https://github.com/IBAMR/IBAMR (2014)

  14. Herschlag, G., Miller, L.A.: Reynolds number limits for jet propulsion: a numerical study of simplified jellyfish. J. Theor. Biol.285(1), 2369–2381 (2011)

    Article  MathSciNet  Google Scholar 

  15. Humphrey, J.A.C.: Fluid mechanic constraints on spider ballooning. Oecologia73, 469–477 (1987)

    Article  Google Scholar 

  16. Kim, Y., Peskin, C.S.: Penalty immersed boundary method for an elastic boundary with mass. Phys. Fluids19, 053103 (18 pages) (2007)

    Google Scholar 

  17. Miller, L.A., Peskin, C.S.: Flexible clap and fling in tiny insect flight. J. Exp. Biol.212, 3076–3090 (2009)

    Article  Google Scholar 

  18. Mittal, R., Iaccarino, G.: Immersed boundary methods. Annu. Rev. Fluid Mech.37, 239–61 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  19. Nathan, R., Schurr, F.M., Spiegel, O., Steinitz, O., Trakhtenbrot, A., Tsoar, A.: Mechanisms of long-distance seed dispersal. Trends Ecol. Evol.23, 638–647 (2008)

    Article  Google Scholar 

  20. Peskin, C.S.: Flow patterns around heart valves: a numerical method. J. Comput. Phys.10, 252–271 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  21. Peskin, C.S.: The immersed boundary method. Acta Numer.11, 479–517 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  22. Reynolds, A.M., Bohan, D.A., Bell, J.R.: Ballooning dispersal in arthropod taxa with convergent behaviours: dynamic properties of ballooning silk in turbulent flows. Biol. Lett.2(3), 371–3 (2006)

    Article  Google Scholar 

  23. Reynolds, A.M., Bohan, D.A., Bell, J.R.: Ballooning dispersal in arthropod taxa: conditions at take-off. Biol. Lett.3(3), 237–40 (2007)

    Article  Google Scholar 

  24. Richter, C.J.: Aerial dispersal in relation to habitat in eight wolf spider species. Oecologia214, 200–214 (1970)

    Article  Google Scholar 

  25. Ronce, O.: How does it feel to be like a rolling stone? ten questions about dispersal evolution. Annu. Rev. Ecol. Evol. Syst.38(1), 231–253 (2007)

    Article  Google Scholar 

  26. Shao, Z., Hu, X.W., Frische, S., Vollrath, F.: Heterogeneous morphology of Nephila edulis spider silk and its significance for mechanical properties. Polymer40(16), 4709–4711 (1999)

    Article  Google Scholar 

  27. Sheldon, K.S., Zhao, L., Chuang, A., Panayotova, I.N., Miller, L.A., Bourouiba, L.: Revisiting the physics of spider ballooning. In: Layton, A.T., Miller, L.A. (eds.) Women in Mathematical Biology. Association for Women in Mathematics Series, vol. 8 (2017). doi:10.1007/978-3-319-60304-9_9, 125–139

  28. Sobey, I.J.: Oscillatory flows at intermediate Strouhal number in asymmetric channels. J. Fluid Mech.125, 359–373 (1982)

    Article  Google Scholar 

  29. Stauffer, S.L., Coguill, S.L., Lewis, R.V.: Comparison of physical properties of three silks from Nephila clavipes and Araneus gemmoides. J. Arachnol.22(1), 5–11 (1994)

    Google Scholar 

  30. Suter, R.B.: Ballooning in spiders: results of wind tunnel experiments. Ethol. Ecol. Evol.3(1), 13–25 (1991)

    Article  Google Scholar 

  31. Suter, R.B.: Ballooning: data from spiders in freefall indicate the importance of posture. J. Arachnol.20, 107–113 (1992)

    Google Scholar 

  32. Thomas, C.F.G., Hol, E.H.A., Everts, J.W.: Modelling the diffusion component of dispersal during recovery of a population of linyphiid spiders from exposure to an insecticide. Funct. Ecol.4(3), 357–368 (1990)

    Article  Google Scholar 

  33. Thomas, C.F.G., Brain, P., Jepson, P.C.: Aerial activity of linyphiid spiders: modelling dispersal distances from meteorology and behaviour. J. Appl. Ecol.40(5), 912–927 (2003)

    Article  Google Scholar 

  34. Tytell, E.D., Hsu, C.-Y., Fauci, L.J.: The role of mechanical resonance in the neural control of swimming in fishes. Zoology117(1), 48–56 (2014)

    Article  Google Scholar 

  35. Weyman, G.S.: Laboratory studies of the factors stimulating ballooning behavior by linyphiid spiders (Araneae, Linyphiidae). J. Arachnol.23(25), 75–84 (1995)

    Google Scholar 

Download references

Acknowledgements

We are grateful to the National Institute for Mathematical and Biological Synthesis (NIMBioS), which is sponsored by the National Science Foundation (NSF: award DBI-1300426) and The University of Tennessee, Knoxville, for hosting our working group as part of the Research Collaboration Workshop for Women in Mathematical Biology. We especially thank Dr. Anita Layton for organizing the NIMBioS workshop. Additional funding was provided by NSF to KSS (Postdoctoral Research Fellowship 1306883), LAM (CBET 1511427), AC (Graduate Research Fellowship 201315897), and LB (Reeds and Edgerton Funds).

Author information

Authors and Affiliations

  1. Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH, 44106, USA

    Longhua Zhao

  2. Department of Mathematics, Christopher Newport University, Newport News, VA, 23606, USA

    Iordanka N. Panayotova

  3. Department of Ecology and Evolutionary Biology, University of Tennessee, Knoxville, TN, 37996, USA

    Angela Chuang & Kimberly S. Sheldon

  4. The Fluid Dynamics of Disease Transmission Laboratory, Massachusetts Institute of Technology, Cambridge, MA, 02130, USA

    Lydia Bourouiba

  5. Departments of Mathematics and Biology, University of North Carolina, Chapel Hill, NC, 27599, USA

    Laura A. Miller

Authors
  1. Longhua Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Iordanka N. Panayotova
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Angela Chuang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kimberly S. Sheldon
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lydia Bourouiba
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Laura A. Miller
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Longhua Zhao .

Editor information

Editors and Affiliations

  1. Department of Mathematics, Duke University, Durham, North Carolina, USA

    Anita T. Layton

  2. Departments of Mathematics and Biology, University of North Carolina, Chapel Hill, North Carolina, USA

    Laura A. Miller

Rights and permissions

Reprints and permissions

Copyright information

© 2017 The Author(s) and the Association for Women in Mathematics

About this paper

Cite this paper

Zhao, L., Panayotova, I.N., Chuang, A., Sheldon, K.S., Bourouiba, L., Miller, L.A. (2017). Flying Spiders: Simulating and Modeling the Dynamics of Ballooning. In: Layton, A., Miller, L. (eds) Women in Mathematical Biology. Association for Women in Mathematics Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-60304-9_10

Download citation

Publish with us

Policies and ethics

Search

Navigation