Fast and slow advances toward a deeper integration of theory and empiricism

  • Karen C. AbbottEmail author
  • Fang Ji
  • Christopher R. Stieha
  • Christopher M. Moore
Original Paper


In this article, we present a modern commentary on Ludwig, Jones, and Holling’s classic paper, “Qualitative analysis of insect outbreak systems: the spruce budworm and forest,” published in the Journal of Animal Ecology in 1978. In contrast to papers that become classics for advancing one big idea, Ludwig et al.’s contribution is striking for its breadth of impact. It has become a foundational reference in areas as disparate as insect ecology and management, alternative stable states, the effects of natural enemies, and the separation of time scales between fast- and slow-changing variables. Interestingly, the paper is not generally remembered as an attempt to bridge the divide between theoretical and empirical ecologists, as we will show, even though this is how the authors motivated their work. In this commentary, we examine the expected and unexpected ways Ludwig et al. (J Anim Ecol 47:315–332, 1978) have found a place in modern ecological thought.


Alternative stable states Insect outbreaks Ludwig et al. (1978) Qualitative analysis Separation of timescales Spruce budworm Theory and empiricism 



We thank Sam Catella, Angie Lenard, Brian Lerch, Amy Patterson, Robin Snyder, and Alex Strang for helpful comments and discussion on an earlier draft. Steve Ellner and an anonymous reviewer provided insights and suggestions that improved the final article. The idea to print modern commentaries on classic papers in Theoretical Ecology was devised by Alan Hastings and supported by the editorial board, and we are grateful for the opportunity to contribute. Thank you to the 785 Twitter users who participated in our poll, and to Andrew MacDonald for helping to disseminate the poll.

Funding information

KCA and FJ received partial support from a James S. McDonnell Foundation Complex Systems Scholar Grant during the completion of this work.


  1. Abbott KC (2011) A dispersal-induced paradox: synchrony and stability in stochastic metapopulations. Ecol Lett 14:1158–1169PubMedPubMedCentralCrossRefGoogle Scholar
  2. Abbott KC, Karst J, Biederman LA, Borrett SR, Hastings A, Walsh V, Bever JD (2015) Spatial heterogeneity in soil microbes alters outcomes of plant competition. PLoS ONE 10:e0125788PubMedPubMedCentralCrossRefGoogle Scholar
  3. Andrewartha HG, Birch LC (1954) The distribution and abundance of species. University of Chicago PressGoogle Scholar
  4. Bascompte J, Solé R V (1995) Rethinking complexity: modelling spatiotemporal dynamics in ecology. Trends Ecol Evol 10:361–366PubMedCrossRefGoogle Scholar
  5. Beisner BE, Haydon DT, Cuddington KM (2003) Alternative stable states in ecology. Front Ecol Environ 1:376–382CrossRefGoogle Scholar
  6. Boccara N (2010) Modeling complex systems. Springer, BerlinGoogle Scholar
  7. Boersch-Supan PH, Ryan SJ, Johnson LR (2017) deBInfer: Bayesian inference for dynamical models of biological systems in R. Methods Ecol Evol 8:511–518CrossRefGoogle Scholar
  8. Boettiger C, Ross N, Hastings A (2013) Early warning signals: the charted and uncharted territories. Theor Ecol 6:255–264CrossRefGoogle Scholar
  9. Bulte EH (2003) Open access harvesting of wildlife: the poaching pit and conservation of endangered species. Agric Econ 28:27–37CrossRefGoogle Scholar
  10. Carpenter SR, Ludwig D, Brock WA (1999) Management of eutrophication for lakes subject to potentially irreversible change. Ecol Appl 9:751–771CrossRefGoogle Scholar
  11. Caswell H (1988) Theory and models in ecology - a different perspective. Ecol Model 43:33–44CrossRefGoogle Scholar
  12. Chattopadhayay J, Sarkar RR, Mandal S (2002) Toxin-producing plankton may act as a biological control for planktonic blooms—field study and mathematical modelling. J Theor Biol 215:333–344PubMedCrossRefPubMedCentralGoogle Scholar
  13. Crėpin A-S (2006) Using fast and slow processes to manage resources with thresholds. Environ Resour Econ 36:191–213CrossRefGoogle Scholar
  14. DeAngelis DL (2018) Individual-based models and approaches in ecology: populations, communities and ecosystems. CRC Press, Boca RatonGoogle Scholar
  15. Dennis B, Patil GP (1984) The gamma distribution and weighted multimodal gamma distributions as models of population abundance. Math Biosci 68:187–212CrossRefGoogle Scholar
  16. Ding D, Shi J, Wang Y (2017) Bistability in a model of grassland and forest transition. J Math Anal Appl 451:1165–1178CrossRefGoogle Scholar
  17. Dwyer G, Dushoff J, Elkinton JS, Levin SA (2000) Pathogen-driven outbreaks in forest defoliators revisited: building models from experimental data. Amer Nat 156:105–120CrossRefGoogle Scholar
  18. Enns RH (2010) It’s a nonlinear world. Springer, BerlinGoogle Scholar
  19. Eriksson A, Elías-Wolff F, Mehlig B, Manica A (2014) The emergence of the rescue effect from explicit within- and between-patch dynamics in a metapopulation. Proc R Soc B 20133127:281Google Scholar
  20. Fahse L, Wissel C, Grimm V (1998) Reconciling classical and individual-based approaches in theoretical population ecology: a protocol for extracting population parameters from individual-based models. Am Nat 152:838–852PubMedCrossRefPubMedCentralGoogle Scholar
  21. Fawcett TW, Higginson AD (2012) Heavy use of equations impedes communication among biologists. PNAS 109:11735–11739PubMedCrossRefPubMedCentralGoogle Scholar
  22. Fung T, Seymour RM, Johnson CR (2011) Alternative stable states and phase shifts in coral reefs under anthropogenic stress. Ecol 92:967–982CrossRefGoogle Scholar
  23. Fussmann GF, Ellner SP, Hairston NG Jr, Jones LE, Shertzer KW, Yoshida T (2005) Ecological and evolutionary dynamics of experimental plankton communities. Adv Ecol Res 37:221–243CrossRefGoogle Scholar
  24. Getz WM, Marshall CR, Carlson CJ, Giuggioli L, Ryan SJ, Romañach S S, Boettiger C, Chamberlain SD, Larsen L, D’Odorico P, O’Sullivan D (2017) Making ecological models adequate. Ecol Lett 21:153–166PubMedCrossRefPubMedCentralGoogle Scholar
  25. Grimm V, Railsback SF (2005) Individual-based modeling and ecology. Princeton University PressGoogle Scholar
  26. Hairston NG, Smith FE, Slobodkin LB (1960) Community structure, population control, and competition. Am Nat 94:421–425CrossRefGoogle Scholar
  27. Hall SR, Duffy MA, Cȧceres C E (2005) Selective predation and productivity jointly drive complex behavior in host-parasite systems. Am Nat 165:70–81PubMedCrossRefPubMedCentralGoogle Scholar
  28. Harmsen R, Sibbald B (1984) Testing model feasibility and sufficiency through laboratory simulation: a case study. Ecol Model 21:161–174CrossRefGoogle Scholar
  29. Hastings A (2004) Transients: the key to long-term ecological understanding?. Trends Ecol Evol 19:39–45CrossRefGoogle Scholar
  30. Hastings A, Abbott KC, Cuddington K, Francis T, Gellner G, Lai Y-C, Morozov A, Petrovskii S, Scranton K, Zeeman ML (2018) Transient phenomena in ecology. Science 361:eaat6412PubMedCrossRefGoogle Scholar
  31. Huston MA (2014) Disturbance, productivity, and species diversity: empiricism vs. logic in ecological theory. Ecol 95:2382–2396CrossRefGoogle Scholar
  32. Jiang C, Cui C, Zhong W, Li G, Li L, Shao Y (2016) Tumor proliferation and diffusion on percolation clusters. J Biol Phys 42:637–658PubMedPubMedCentralCrossRefGoogle Scholar
  33. Jones DD (1979) The budworm site model. In: Norton C A, Holling C S (eds) Pest management: Proceedings of an International Conference. Oxford University Press, pp 91–155Google Scholar
  34. Kendall BE, Ellner SP, McCauley E, Wood SN, Briggs CJ, Murdoch WW, Turchin P (2005) Population cycles in the pine looper moth: dynamical tests of mechanistic hypotheses. Ecol Monogr 75:259–276CrossRefGoogle Scholar
  35. Kendall BE (2015) Some directions in ecological theory. Ecol 96:3117–3125CrossRefGoogle Scholar
  36. Kilpatrick AM, Koelle K, Gross K, Abbott KC (2014) Ecological Society of America Annual Meeting, Ignite 12: theory versus empiricism in the advancement of science. Sacramento, CA.
  37. Levin SA (1992) The problem of pattern and scale in ecology: the Robert H. Macarthur award lecture. Ecol 73:1943–1967CrossRefGoogle Scholar
  38. Ludwig D, Jones DD, Holling CS (1978) Qualitative analysis of insect outbreak systems: the spruce budworm and forest. J Anim Ecol 47:315–332CrossRefGoogle Scholar
  39. May RM (1977) Thresholds and breakpoints in ecosystems with a multiplicity of stable states. Nature 269:471–477CrossRefGoogle Scholar
  40. Morris RF (1963) The dynamics of epidemic spruce budworm populations. Mem Entomol Soc Can 31:1–332CrossRefGoogle Scholar
  41. Muratori S, Rinaldi S (1992) Low- and high-frequency oscillations in three-dimensional food chain systems. SIAM J Appl Math 52:1688–1706CrossRefGoogle Scholar
  42. Navarro L, Morin H, Bergeron Y, Montoro Girona M (2019) Changes in spatiotemporal patterns of 20th century spruce budworm outbreaks in Eastern Canadian boreal forests. Front Plant Sci 9:1905CrossRefGoogle Scholar
  43. Nicholson AJ (1933) The balance of animal populations. J Anim Ecol 2:131–178CrossRefGoogle Scholar
  44. Nisbet RM, Gurney WSC, Pettipher MA (1977) An evaluation of linear models of population fluctuations. J Theor Biol 68:143–160PubMedCrossRefGoogle Scholar
  45. Pascual M, Levin SA (1999) From individuals to population densities: searching for the intermediate scale of nontrivial determinism. Ecol 80:2225–2236CrossRefGoogle Scholar
  46. Přibylová L (2018) Regime shifts caused by adaptive dynamics in prey-predator models and their relationship with intraspecific competition. Ecol Compl 36:48–56CrossRefGoogle Scholar
  47. Pritchard DW, Paterson R, Bovy HC, Barrios-O’Neill D (2017) Frair: an R package for fitting and comparing consumer functional responses. Methods Ecol Evol 8:1528–1534CrossRefGoogle Scholar
  48. Revilla TA (2015) Numerical responses in resource-based mutualisms: a time scale approach. J Theor Biol 378:39–46PubMedCrossRefGoogle Scholar
  49. Rinaldi S, Muratori S (1992) Limit-cycles in slow-fast forest pest models. Theor Popul Biol 41:26–43CrossRefGoogle Scholar
  50. Rinaldi S, Scheffer M (2000) Geometric analysis of ecological models with slow and fast processes. Ecosystems 3:507–521CrossRefGoogle Scholar
  51. Rosenbaum B, Rall BC (2018) Fitting functional responses: Direct parameter estimation by simulating differential equations. Methods Ecol Evol 9:2076–2090CrossRefGoogle Scholar
  52. Royama T, MacKinnon WE, Kettela EG, Carter NE, Hartling LK (2005) Analysis of spruce budworm outbreak cycles in New Brunswick, Canada, since 1952. Ecol 86:1212–1224CrossRefGoogle Scholar
  53. Scheffer M, Carpenter S, Foley JA, Folke C, Walker B (2001) Catastrophic shifts in ecosystems. Nature 413:591–596PubMedPubMedCentralCrossRefGoogle Scholar
  54. Sharma Y, Abbott KC, Dutta PS, Gupta AK (2015) Stochasticity and bistability in insect outbreak dynamics. Theor Ecol 8:163–174CrossRefGoogle Scholar
  55. Snyder RE, Ellner SP (2018) Pluck or luck: does trait variation or chance drive variation in lifetime reproductive success?. Am Nat 191:E91–E107CrossRefGoogle Scholar
  56. Spencer PD, Collie JS (1995) A simple predator–prey model of exploited marine fish populations incorporating alternative prey. ICES J Mar Sci 53:615–628CrossRefGoogle Scholar
  57. Stephens PA, Frey-Roos F, Arnold W, Sutherland WJ (2002) Model complexity and population predictions. The alpine marmot as a case study. J Anim Ecol 71:343–361CrossRefGoogle Scholar
  58. Sturtevant BR, Cooke BJ, Kneeshaw DD, MacLean DA (2015) Modeling insect disturbance across forested landscapes: insights from the spruce budworm. In: Simulation modeling of forest landscape disturbances. Springer, pp 93–134Google Scholar
  59. Turchin P, Wood SN, Ellner SP, Kendall BE, Murdoch WW, Fischlin A, Casas J, McCauley E, Briggs CJ (2003) Dynamical effects of plant quality and parasitism on population cycles of larch budmoth. Ecol 84:1207–1214CrossRefGoogle Scholar
  60. Walker M, Jones TH (2011) Relative roles of top-down and bottom-up forces in terrestrial tritrophic plant–insect herbivore–natural enemy systems. Oikos 93:177–187CrossRefGoogle Scholar
  61. Waxman D, Gavrilets S (2005) 20 Questions on adaptive dynamics. J Evol Biol 18:1139–1154PubMedCrossRefPubMedCentralGoogle Scholar
  62. Wilman EA, Wilman EN (2017) Fast, slow, and adaptive management of habitat modification-invasion interactions: woodland caribou (Rangifer tarandus). Ecosphere 8:e01970CrossRefGoogle Scholar
  63. Zeng J, Zeng C, Xie Q, Guan L, Dong X, Yang F (2016) Different delays-induced regime shifts in a stochastic insect outbreak dynamics. Physica A 462:1273–1285CrossRefGoogle Scholar
  64. Zhao X-Q (2017) Dynamical systems in population biology. Springer, BerlinGoogle Scholar
  65. Ziebarth NL, Abbott KC, Ives AR (2010) Weak population regulation in ecological time series. Ecol Lett 13:21–31PubMedCrossRefPubMedCentralGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  • Karen C. Abbott
    • 1
    Email author
  • Fang Ji
    • 1
  • Christopher R. Stieha
    • 2
  • Christopher M. Moore
    • 3
  1. 1.Department of BiologyCase Western Reserve UniversityClevelandUSA
  2. 2.Department of BiologyMillersville UniversityMillersvilleUSA
  3. 3.Department of BiologyColby CollegeWatervilleUSA

Personalised recommendations