NCEAS Project 2264

Complex Population Dynamics

  • William W. Murdoch
  • Peter Turchin


ActivityDatesFurther Information
Graduate Student4th January 1996—30th December 1998Participant List  
Working Group4th—19th January 1996Participant List  
Postdoctoral Fellow1st May 1996—31st October 1998Participant List  
Working Group29th August—9th September 1996Participant List  
Graduate Student1st October—31st December 1996Participant List  
Working Group1st—10th January 1997Participant List  
Working Group15th May—5th June 1997Participant List  
Working Group10th—23rd December 1997Participant List  
Working Group9th—30th June 1998Participant List  
Working Group4th—21st December 1998Participant List  

Abstract

Population cycles and other complex population dynamics occur in a wide range of taxa and environments, including temperate and tropical forest insects, marine and freshwater fish and invertebrates, and boreal mammals. Population cycles show enormous variation in amplitude (from less than one to five orders of magnitude), period (from a single generation to 30-50 generations), and the strength of periodicity (ranging from noisy pseudoperiodic or apparently chaotic oscillations to an almost perfect periodicity). In addition, cycles may involve not only the total population abundance, but also other aspects of dynamics, e.g. oscillations in age structure and complex spatio-temporal behaviors, such as synchronous oscillations or periodic traveling waves.

There are many potential explanations for oscillatory population dynamics (in the general sense), with some focusing on intrinsic factors, but most often invoking some aspect of consumer-resource interactions (we briefly review some theoretical and empirical mechanisms by which population cycles can arise in Section 11). The theoretical literature on population cycles is enormous, but there has been no attempt to systematize it and to relate various postulated mechanisms to the oscillatory patterns observed in real populations.

Our long-term goal is to bring order to what is known theoretically and empirically about population cycles. More specifically, we propose to:

    1. define and classify the range of mechanisms that can induce oscillatory population behavior in theoretical models;
    2. establish correspondences between theoretical mechanisms that could drive cycles and quantitative descriptors of oscillatory population dynamics (these will be defined in Section 111. 1);
    3. apply a combination of modeling and statistical techniques to a number of data sets (Section IV) in an attempt to determine which of the possible theoretical mechanisms may be responsible for population oscillations in each particular case.
    4. attempt to develop general statements about mechanisms that are responsible for cycles in nature, and the conditions under which different mechanisms may operate and different types of oscillatory dynamics may arise.

Previous investigations of population oscillations have utilized primarily two distinct approaches: potential mechanisms have been investigated with mathematical models, while data patterns have been investigated with phenomenological time-series analyses (cycles have also been investigated experimentally, but this approach is not part of our proposal because it falls outside of the scope of the research supported by the Center). We propose to bring together individuals representing both approaches to collaborate on a program in which theoretical model development and statistical analyses of data will be tightly linked. We hope to gain strong synergistic advantages from such a collaboration.

I

TypeProducts of NCEAS Research
Presentations Boucher, V.; Borer, Elizabeth T.; Burton, Rebecca S.; Cottingham, Kathryn L.; Goldwasser, Lloyd; Gram, Wendy K.; Kendall, Bruce E.; Micheli, Fiorenza; Seabloom, Eric. 1999. Ecology and restoration of California serpentine grasslands. 84th Annual Meeting of the Ecological Society of America. Spokane, WA.
Journal Article Ellner, Stephen P.; Kendall, Bruce E.; Wood, Simon; McCauley, Edward; Briggs, Cheryl J. 1997. Inferring mechanism from time-series data: Delay-differential equations. Physica D-Nonlinear Phenomena. Vol: 110. Pages 182-194.
Journal Article Ellner, Stephen P.; McCauley, Edward; Kendall, Bruce E.; Briggs, Cheryl J.; Hosseini, Parviez R.; Wood, Simon; Janssen, Arne; Sabelis, M.; Turchin, Peter; Nisbet, Roger M.; Murdoch, William W. 2001. Habitat structure and population persistence in an experimental community. Nature. Vol: 412. Pages 538-543.
Journal Article Ellner, Stephen P.; Seifu, Yodit; Smith, Robert H. 2002. Fitting population dynamic models to time-series data by gradient matching. Ecology. Vol: 83. Pages 2256-2270.
Presentations Ellner, Stephen P.; Kendall, Bruce E. 2003. Understanding simple population dynamics: Methods and insects. 88th Annual Meeting of the Ecological Society of America. Savannah, GA.
Presentations Ellner, Stephen P. 2005. The dynamical detective: Using nonlinear models to test ecological hypotheses. SIAM Conference on Applications of Dynamical Systems, 26 May 2005.
Journal Article Gram, Wendy K.; Borer, Elizabeth T.; Cottingham, Kathryn L.; Seabloom, Eric; Boucher, V.; Goldwasser, Lloyd; Micheli, Fiorenza; Kendall, Bruce E.; Burton, Rebecca S. 2004. Distribution of plants in a California serpentine grassland: Are rocky hummocks spatial refuges for native species?. Plant Ecology. Vol: 172. Pages 159-171.
Presentations Harder, L. D.; Barrett, Spencer C. H.; Kendall, Bruce E. 1999. The role of floral design in pollen dispersal by tristylous (Pontederia cordata). Joint Annual Meeting of the Society for the Study of Evolution and the American Society of Naturalists. Madison, WI.
Presentations Kendall, Bruce E. 1996. Inferring causes of population cycles by combining mechanistic models and time-series analysis. Synthesis in Ecology: Applications, Opportunities, and Challenges. NCEAS Symposium. Santa Barbara, CA.
Presentations Kendall, Bruce E. 1996. Spatial structure and population dynamics: Disentangling the effects of environmental heterogeneity and limited dispersal. Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara. Santa Barbara, CA.
Presentations Kendall, Bruce E. 1996. Tests to distinguish environmental and demographic stochasticity in survivorship data. 81st Annual Meeting of the Ecological Society of America. Providence, RI.
Presentations Kendall, Bruce E. 1997. Distinguishing environmental and demographic stochasticity: What causes the variation in survival of Acorn Woodpeckers?. Department of Biological Sciences, University of Calgary. Alberta.
Presentations Kendall, Bruce E. 1997. Inferring causes of population cycles by combining mechanistic models and time-series analysis. Symposium on Research at the National Center for Ecological Analysis and Synthesis. Ecological Society of America Annual Meeting. Albuquerque, NM.
Presentations Kendall, Bruce E. 1998. Describing and understanding population fluctuations: Demographic stochasticity, environmental stochasticity, and population cycles. Department of Biology, College of Staten Island. New York.
Journal Article Kendall, Bruce E. 1998. Estimating the magnitude of environmental stochasticity in survivorship data. Ecological Applications. Vol: 8. Pages 184-193.
Journal Article Kendall, Bruce E.; Fox, Gordon A. 1998. Spatial structure, environmental heterogeneity, and population dynamics: Analysis of the coupled logistic map. Theoretical Population Biology. Vol: 54. Pages 11-37.
Journal Article Kendall, Bruce E.; Prendergast, John; Bjornstad, Ottar N. 1998. The macroecology of population dynamics: Taxonomic and biogeographic patterns in population cycles. Ecology Letters. Vol: 1. Pages 160-164.
Presentations Kendall, Bruce E. 1998. What causes population cycles? Answers from a synthesis of statistical and mechanistic modeling approaches. Symposium on Intersection of Diverse Perspectives: Results from Creative Cross-Disciplinary Collaborations. Ecological Society of America Annual Meeting. Baltimore, MD.
Presentations Kendall, Bruce E. 1998. Why do populations fluctuate, and what can we do about it?. Donald Bren School of Environmental Science and Management, University of California, Santa Barbara. Santa Barbara, CA.
Presentations Kendall, Bruce E. 1999. Density-dependent dispersal can destabilize population dynamics. 84th Annual Meeting of the Ecological Society of America. Spokane, WA.
Presentations Kendall, Bruce E. 1999. Density-dependent dispersal can destabilize population dynamics. Conference on Theory and Mathematics in Biology and Medicine. Amsterdam,The Netherlands.
Presentations Kendall, Bruce E. 1999. Estimating the magnitude of environmental stochasticity in demographic processes. Conference on Population Viability Analysis: Assessing Models for Recovering Endangered Species. San Diego, CA.
Presentations Kendall, Bruce E. 1999. The ups and down of life: Predicting the fates of small populations in an uncertain, stochastic, and variable world. Department of Environmental Studies, University of California, Santa Cruz. Santa Cruz, CA.
Journal Article Kendall, Bruce E.; Briggs, Cheryl J.; Murdoch, William W.; Turchin, Peter; Ellner, Stephen P.; McCauley, Edward; Nisbet, Roger M.; Wood, Simon. 1999. Why do populations cycle? A synthesis of statistical and mechanistic modeling approaches. Ecology. Vol: 80. Pages 1789-1805.
Journal Article Kendall, Bruce E.; Ellner, Stephen P.; McCauley, Edward; Wood, Simon; Briggs, Cheryl J.; Murdoch, William W.; Turchin, Peter. 2005. Population cycles in the pine looper moth: Dynamical tests of mechanistic hypotheses. Ecological Monographs. Vol: 75(2). Pages 259-276.
Journal Article McCauley, Edward; Kendall, Bruce E.; Janssen, Arne; Wood, Simon; Murdoch, William W.; Hosseini, Parviez R.; Briggs, Cheryl J.; Ellner, Stephen P.; Nisbet, Roger M.; Sabelis, M.; Turchin, Peter. 2000. Inferring colonization processes from population dynamics in spatially structured predator-prey systems. Ecology. Vol: 81. Pages 3350-3361.
Report or White Paper Murdoch, William W. 1998. Complex Population Dynamics Working Group. (Online version)
Journal Article Murdoch, William W.; Kendall, Bruce E.; Nisbet, Roger M.; Briggs, Cheryl J.; McCauley, Edward; Bolser, Robin. 2002. Single-species models for many-species food webs. Nature. Vol: 417. Pages 541-543.
Journal Article Murdoch, William W.; Briggs, Cheryl J.; Nisbet, Roger M.; Kendall, Bruce E.; McCauley, Edward. 2003. Natural enemy specialization and the period of population cycles: Reply. Ecology Letters. Vol: 6. Pages 384-387.
Data Set Prendergast, John. 1999. Global population dynamics database. NERC Centre for Population Biology, Imperial College. (Online version)
Data Set Prendergast, John; Anderson, Robert P.; Bazeley-White, Ellen. 2004. The global population dynamics database. (Online version)
Journal Article Seabloom, Eric; Borer, Elizabeth T.; Boucher, V.; Burton, Rebecca S.; Cottingham, Kathryn L.; Goldwasser, Lloyd; Gram, Wendy K.; Kendall, Bruce E.; Micheli, Fiorenza. 2003. Competition, seed limitation, disturbance, and reestablishment of California native annual forbs. Ecological Applications. Vol: 13(3). Pages 575-592.
Presentations Tuda, Midori; Dennis, Brian. 1998. Detecting evolution in a host-parasitoid laboratory system with a nonlinear time-series model. INTECOL. Florence, Italy.
Journal Article Tuda, Midori. 1998. Evolutionary character changes and population responses in an insect host-parasitoid experimental system. Researches on Population Ecology. Vol: 40. Pages 293-299.
Journal Article Tuda, Midori; Iwasa, Y. 1998. Evolution of contest competition and its effect on host-parasitoid dynamics. Evolutionary Ecology. Vol: 12. Pages 855-870.
Presentations Tuda, Midori. 1998. Evolution of contest competition in a host-parasitoid experimental system: Tests on model predictions. Fukuoka International Symposium of Population Genetics. Fukuoka, Japan.
Journal Article Tuda, Midori; Bonsall, Michael B. 1999. Evolutionary and population dynamics of host-parasitoid interactions. Researches on Population Ecology. Vol: 41. Pages 81-91.
Journal Article Tuda, Midori; Shimada, Masakazu. 2005. Complexity, evolution, and persistence in host-parasitoid experimental systems with Callosobruchus beetles as the host. Advances in Ecological Research. Vol: 37. Pages 37-75.
Journal Article Turchin, Peter. 1999. Population regulation: A synthetic view. Oikos. Vol: 84. Pages 153-159.
Journal Article Turchin, Peter; Ellner, Stephen P. 2000. Living on the edge of chaos: Population dynamics of fennoscandian voles. Ecology. Vol: 81. Pages 3099-3116.
Book Chapter Turchin, Peter; Ellner, Stephen P. 2000. Modeling time-series data. Edited by Perry, J. N.; Smith R. H.; Woiwod, I. P.; Morse, D. R.. Chaos in Real Data: Analysis of Non-Linear Dynamics from Short Ecological Time Series (Population And Community Biology Series). Vol: 27. Kluwer. London. Pages 33-48.
Book Chapter Turchin, Peter; Briggs, Cheryl J.; Ellner, Stephen P.; Fischlin, A.; Kendall, Bruce E.; McCauley, Edward; Murdoch, William W.; Wood, Simon. 2002. Population cycles of the larch budmoth in Switzerland. Edited by Berryman, A. A.. Population Cycles: The Case for Trophic Interactions. Oxford University Press. New York. Pages 130-141.
Journal Article Turchin, Peter; Wood, Simon; Ellner, Stephen P.; Kendall, Bruce E.; Murdoch, William W.; Fischlin, A.; Casas, Jerome; McCauley, Edward; Briggs, Cheryl J. 2003. Dynamical effects of plant quality and parasitism on population cycles of larch budmoth. Ecology. Vol: 84(5). Pages 1207-1214.
Journal Article Wood, Simon; Thomas, Matthew B. 1999. Super-sensitivity to structure in biological models. Proceedings of the Royal Society B-Biological Sciences. Vol: 266. Pages 565-570.