Collaborative Research: Non-Linear Population Dynamics: Mathematical Models, Biological Experiments and Data Analysis Grant uri icon



  • Dennis
    Understanding the fluctuations in animal numbers is a
    central issue in population biology that has far-reaching impact
    on and implications for problems ranging from food production to
    the conservation of species. Nonlinear dynamics opens the way to
    a new phase of population research in which theory and
    experimentation focus on phenomena such as cycles and
    quasi-periodicity, chaos and strange attractors, multiple
    attractors and complicated basins of attraction, saddle sets and
    their stable manifolds, and so on. This interdisciplinary
    project, in which Robert Costantino, Jim Cushing, Brian Dennis,
    Robert Desharnais, and Shandelle Henson collaborate, covers a
    spectrum of activities essential to testing nonlinear population
    theory: the translation of the biology into the language of
    mathematics and back again, the analysis of deterministic and
    stochastic models, the development and application of statistical
    techniques for the analysis of data, and the design and
    implementation of biological experiments. A series of experiments
    with flour beetles of the genus Tribolium provide rigorous
    experimental tests of nonlinear phenomena. Topics include
    nonlinearity in the context of stochasticity, chaos and
    population control, the impact of periodic environments on animal
    abundance, demographic dynamics and natural selection,
    nonequilibrium species interactions, and statistical questions
    concerning parameterization and validation of models.
    With a sound understanding of the underlying dynamics of
    animal populations, ecologists can anticipate the consequences of
    environmental degradation and learn better ways to manage natural
    populations and control populations of pests. For example, one of
    the experiments suggests that, by taking advantage of the
    "sensitivity to initial conditions" that is the hallmark of a
    chaotic system, managers can dramatically decrease pest
    population numbers without the use of chemical pesticides by
    making small perturbations at critical times. The marriage of
    ecological theory and experiments by the interdisciplinary
    research team leads to new techniques for the application of
    mathematics to ecological problems. The project is supported by
    the Applied Mathematics, Computational Mathematics, and
    Statistics programs in MPS and the Population Biology and Ecology
    programs in BIO.

date/time interval

  • September 1, 1999 - August 31, 2002

total award amount

  • 84,000