Skip to main content
SpringerLink
Log in

A Continuous Model for Oscillating Outbreaks of the Population of a Phytophagous Moth, the Tent Caterpillar, Malacosoma disstria (Lepidoptera, Lasiocampidae)

  • COMPLEX SYSTEMS BIOPHYSICS
  • Published:
Biophysics Aims and scope Submit manuscript

Abstract

Outbreaks of individual species populations are important phenomena in many aspects and are not alike in terms of the theory of multispecies community dynamics. Outbreaks of insect populations develop more quickly with long-lasting effects experienced by the forest industry. These events are considered as extreme unbalanced and transient processes. The mechanisms of the development and subsidence of insect outbreaks differ in different taxonomic groups of pests. The duration and occurrence of repeated outbreaks of psyllids and forest moths, which affect deciduous or coniferous forests in the same region, are different. Computational simulation is needed for understanding the dynamics of insect outbreaks. For the mathematical description of the outbreaks of forest tent caterpillar, in addition to the threshold version of the development of the insect outbreak, it is interesting to modify continuous computational models for the analysis of fluctuation dynamics. In this paper, we simulate the dynamics of spontaneously damping oscillations under a specific scenario during a population outbreak using a continuous model with delayed regulation and nonlinear counteraction by the biotic environment. The scenario described by the new phenomenological equation, which consists of a series of maxima of different sizes and final attenuation of peaks near balance, occurs for the pest tent caterpillar, Malacosoma disstria, which affects deciduous forests in North America leading to large-scale defoliation. The new scenario is qualitatively different from our model of the threshold development and subsidence of outbreaks of the psyllid Cardiaspina albitextura in Australia.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.

Similar content being viewed by others

REFERENCES

  1. C. Lee and G. Gelembiuk, Evol. Appl. 1 (3), 427 (2008).

    Article  Google Scholar 

  2. M. Nilssen, Fish. Res. 82 (1), 319 (2006).

    Article  Google Scholar 

  3. A. N. Demidova, Nauka i Zhizn’, No. 10, 58 (2017).

  4. N. Chapman, Ecol. Monogr. 9 (3), 261 (1939).

    Article  Google Scholar 

  5. Q. Jin and L. Valsta, Int. J. For. Res. 6 (3), 12 (2015).

    Google Scholar 

  6. A. N. Frolov and I. V Grushevaya, Vestn. Zashchity Rast. 98 (4), 18 (2018).

    Google Scholar 

  7. D. Ludwig, D. Jones, and S. Holling, J. Anim. Ecol. 47 (1), 315 (1978).

    Article  Google Scholar 

  8. M. A. Rozendaal and R. K. Kobe, PLoS One 11 (11), 167 (2016).

    Article  Google Scholar 

  9. A. S. Isasev, V. G. Sukhovol’skii, and R. G. Khlebopros, Lesovedenie, No. 2, 3 (2010).

  10. V. G. Sukhovol’skii, V. I. Ponomarev, and G. I. So-kolov, Zh. Obshch. Biol. 76 (3), 179 (2015).

    Google Scholar 

  11. A. Y. Perevaryukha, Biophysics (Moscow) 61 (2), 334 (2016).

    Article  Google Scholar 

  12. L. R. Clark, Austral. J. Zool. 12 (3), 362 (1964).

    Article  Google Scholar 

  13. E. P. Odum, Ecology (Rinehart & Winston, New York, 1963).

    Google Scholar 

  14. V. A. Trjapitzin and M. G. Volkovitsh, Entomol. Rev. 91 (5), 670 (2011).

    Article  Google Scholar 

  15. W. C. Allee and E. Bowen, J. Exp. Zool. 61 (2), 185 (1932).

    Article  Google Scholar 

  16. A. A. Hall, Doctor of Philosophy Thesis (Western Sydney University, Sydney, 2016).

  17. A. A. Hall, S. N. Johnson, and J. M. Cook, Insect Sci. 26 (2), 351 (2019).

    Article  Google Scholar 

  18. J. Berry, Biosecurity New Zealand 68 (2), 18 (2006).

    Google Scholar 

  19. H. Myers, Am. Sci. 81 (3), 240 (1993).

    ADS  Google Scholar 

  20. C. Bone and S. Dragicevic, Ecol. Modelling 192 (1–2), 107 (2006).

  21. B. Cooke, S. V. Neali, and J. Regniere, in Plant Disturbance Ecology: The Process and the Response (Elsevier, Burlington, 2007), pp. 487–525.

    Google Scholar 

  22. T. Royama, Ecol. Monogr. 54 (4), 429 (1984).

    Article  Google Scholar 

  23. B. J. Cooke, F. Lorenzetti, and G. Roland, J. Entomol. Soc. Ontario 140, 3 (2009).

    Google Scholar 

  24. ESTR Secretariat, Atlantic Maritime Ecozone Evidence for Key Findings Summary (Canadian Biodiversity: Ecosystem Status and Trends, 2010), Report No. 3 (Canadian Councils of Resource Ministers, Ottawa, 2014).

  25. X. Zhang, Ecol. Evol. 4 (12), 2384 (2014).

    Article  Google Scholar 

  26. R. Louis-Etienne, R. Brian, and J. Cooke, Ecography 41 (9), 1556 (2018).

    Article  Google Scholar 

  27. T. Hlasny and J. Trombik, J. Pest Sci. 89 (2), 413 (2016).

    Article  Google Scholar 

  28. C. Loehle, Ecol. Modelling 49 (2), 125 (1989).

    Article  Google Scholar 

  29. Z. S. Ma and E. J. Bechinski, Entomol. Res. 39 (3), 175 (2009).

    Article  Google Scholar 

  30. D. R. Brillinger, J. Time Series Anal. 33 (5), 718 (2012).

    Article  MathSciNet  Google Scholar 

  31. G. Hutchinson, Ann. N. Y. Acad. Sci. 50 (4), 221 (1948).

    Article  ADS  Google Scholar 

  32. B. D. Hassard, N. D. Kazarinoff, and Y.-H. Wan, Theory and Applications of the Hopf Bifurcation (Cambridge Univ. Press, Canbridge, 1981; Mir, Moscow, 1985).

  33. G. K. Kamenev, D. A. Sarancha, and V. O. Polya-novsky, Biophysics (Moscow) 63 (4), 596 (2018).

    Article  Google Scholar 

  34. T. L. Sabatulina, Russ. Math. 54 (11), 44 (2010).

    Article  MathSciNet  Google Scholar 

  35. E. V. Troshkina, Izv. Samarsk. Gos. Univ., Ser. Estestv. Nauki 9 (2) 215 (2013).

    Google Scholar 

  36. K. Gopalsamy, M. Kulenovic, and G. Ladas, Appl Anal. 31 (3), 225 (1988).

    Article  MathSciNet  Google Scholar 

  37. G. E. Kolosov and M. M. Sharov, Avtomat. Telemekh. 53 (6), 146 (1992).

    Google Scholar 

  38. J. Grieshop, W. Flinn, and R. Nechols, J. Insect Sci. 10 (1), 99 (2010).

    Article  Google Scholar 

  39. A. V. Epifanov and V. G. Tsybulin, Biophysics (Moscow) 61 (4), 696 (2016).

    Article  Google Scholar 

  40. V. G. Sukhovol’skii, Biophysics (Moscow) 48 (2), 319 (2003).

    Google Scholar 

  41. A. Roohi and Z. Yasin, Mar. Ecol. 29 (4), 421 (2008).

    Article  ADS  Google Scholar 

Download references

Funding

This study was supported by the Russian Foundation for Basic Research (project headed by A.Yu. Perevaryukha) with partial support by the budgetary subject SPIIRAS AAAA-A16-116051250009-8.

Author information

Authors and Affiliations

  1. St. Petersburg Institute for Informatics and Automation, Russian Academy of Sciences, 199178, St. Petersburg, Russia

    A. Yu. Perevaryukha

Authors
  1. A. Yu. Perevaryukha
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Yu. Perevaryukha.

Ethics declarations

The author declares no conflict of interest. This article does not contain any studies involving animals or human participants performed by the author.

Additional information

Translated by M. Batrukova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Perevaryukha, A.Y. A Continuous Model for Oscillating Outbreaks of the Population of a Phytophagous Moth, the Tent Caterpillar, Malacosoma disstria (Lepidoptera, Lasiocampidae). BIOPHYSICS 65, 118–130 (2020). https://doi.org/10.1134/S0006350920010169

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0006350920010169

Keywords:

Search

Navigation