Abstract
Understanding the dynamics of spruce budworm population is very important for the protection of spruce and balsam fir trees of North American forests, and a full understanding of the dynamics requires careful consideration of the individual physiological structures that is essential for outbreak control. A model as a delay differential equation is derived from structured population system, and is validated by comparing simulation results with real data from the Green River area of New Brunswick (Canada) and with the periodic outbreaks widely observed. Analysis of the equilibrium stability and examination of the amplitudes and frequencies of periodic oscillations are conducted, and the effect of budworm control strategies such as mature population control, immature population control and predation by birds are assessed. Analysis and simulation results suggest that killing only budworm larvae might not be enough for the long-term control of the budworm population. Since the time required for development during the inactive stage (from egg to second instar caterpillar) causes periodic outbreak, a strategy of reducing budworms in the inactive stage, such as removing egg biomass, should also be implemented for successful control.
Similar content being viewed by others
References
Beretta, E., Kuang, Y., 2002. Geometric stability switch criteria in delay differential systems with delay-dependent parameters. SIAM J. Math. Anal. 33(5), 1144–1165.
Blais, J.R., 1981. Effects of late spring frosts in 1980 on spruce budworm and its host trees in Laurentian Park region of Quebec. Res. Notes Ste. Foy, PQ: Environment Canada, Canada Forestry Service 1(3), 16–17.
Cooke, K., ven den Driessche, P., Zou, X., 1999. Interaction of maturation delay and nonlinear birth in population and epidemic models. J. Math. Biol. 39, 332–352.
Crawford, H.S., Jennings, D.T., 1989. Predation by birds on spruce budworm Choristoneura Fumiferana: functional, numerical and total responses. Ecology 70(1), 152–163.
Dunken, R., 2006. Conifer defoliating insects of British Columbia, Natural Resources Canada, http://www.pfc.cfs.nrcan.gc.ca/entomology/defoliators/index_e.html.
Fleming, R.A., Shoemaker, C.A., 1992. Evaluating models for spruce budworm-forest management: comparing output with regional field data. Ecol. Appl. 2(4), 460–477.
Felling, D.G., Dewey, J.F., 1982. Western spruce budworm. Forest insect and Disease (FID), Leaflet 53, US Department of Agriculture Forest Service, http://www.fs.fed.us/r6/nr/fid/fidls/fidl53.pdf.
Fogal, W.H., Plowman, V.C., 1989. Systemic insecticides for protecting northern spruce and pine seed trees. Information Report PI-X-92, Petawawa National Forestry Institute, Forestry Canada.
Hassell, D.C., Allwright, D.J., Fowler, A.C., 1999. A mathematical analysis of Jone’s site model for spruce budworm infestation. J. Math. Biol. 38, 377–421.
Jones, D.D., 1976. The budworm site model. In: Pest Management, Proceedings of an International Conference, October 25–29, 1976, pp. 91–155. Pergamon Press, Oxford.
Ledder, G., 2007. Forest defoliation scenarios. Math. Biol. Eng. 4(1), 15–28.
Li, J., Kuang, Y., 2007. Analysis of a model of the glucose-insulin regulatory system with two delays. SIAM J. Appl. Math. 67(3), 757–776.
Li, J., Kuang, Y., Mason, C.C., 2006. Modeling the glucose-insuline regulatory system and ultradian insulin secretory oscillations with two explicit time delays. J. Theor. Biol. 242, 722–235.
Ludwig, D., Jones, D.D., Holling, C.S., 1978. Qualitative analysis of insect outbreak systems: the spruce budworm forest. J. Anim. Ecol. 47, 315–332.
Ludwig, D., Aronson, D.G., Weinberger, H.F., 1979. Spatial patterning of the spruce budworm. J. Math. Biol. 8, 217–158.
Magnussen, S., Alfaro, R.I., Boudewyn, P., 2005. Survival-time analysis of white spruce during spruce budworm defoliation. Silva Fenncia 39(2), 177–189.
Murray, J.D., 2002. Mathematical Biology I: An Introduction, 3rd edn. Springer, Berlin.
Raske, A.G., West, R.J., Sundaram, K.M.S., Sundaram, A., 1991. The effectiveness of Bacillus thuringiensis, diflubenzuron and fenitrothion against the homlock looper, Lambdina fiscellaria, in Newfoundland in 1987. Information Report N-X-279, Forestry Canada.
Redak, R.A., Cates, R.G., 1984. Douglas-fir (Pseudotsuga menziesii)-spruce budworm (Choristoneura occidentalis) interactions: the effect of nutrition, chemical defenses, tissue phenology, and tree physical parameters on budworm success. Oecologia (Berlin) 64, 61–67.
Sheehan, K.A., Kemp, W.P., Colbert, J.J., Crookston, N.L., 1989. The western spruce budworm model: structure and content. General Technical Report, PNW-GTR-241, United States Department of Agriculture, Pacific Northwest Research Station, pp. 1–77, http://www.fs.fed.us/pnw/pubs/pnw_gtr241.pdf.
Singh, M., Easton, A., Cui, G., Kozlova, I., 2000. A numerical study of the spruce budworm reaction diffusion equation with hostile boundaries. Nat. Resour. Model. 13(4), 335–549.
Royama, T., 1984. Population dynamics of the spruce budworm Choristoneura Fumiferana. Ecol. Monogr. 54(4), 429–462.
Royama, T., MacKinnon, W.E., Kettela, E.G., Carter, N.E., Hartling, L.K., 2005. Analysis of spruce budworm outbreak cycles in New Brunswick, Canada, since 1952. Ecology 86(5), 1212–1224.
So, J.W., Wu, J., Zou, X., 2001. Structured population on two patches: modeling dispersal and delay. J. Math. Biol. 43, 37–41.
Williums, D.W., Liebhold, A.M., 2000. Spatial synchrony of spruce budworm outbreaks in Eastern North America. Ecology 81(10), 2753–2766.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Vaidya, N.K., Wu, J. Modeling Spruce Budworm Population Revisited: Impact of Physiological Structure on Outbreak Control. Bull. Math. Biol. 70, 769–784 (2008). https://doi.org/10.1007/s11538-007-9278-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-007-9278-x