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2009, Volume 12, Issue 2: 481-493. Doi: 10.3934/dcdsb.2009.12.481
This issue Previous Article Finite-time perturbations of dynamical systems and applications to tumor therapy Next Article A metapopulation model with local competitions

Daphnia species invasion, competitive exclusion, and chaotic coexistence

  • 1.

    School of Mathematics and School of Biology, Georgia Institute of Technology, Atlanta, GA 30332-0160

  • 2.

    School of Life Sciences, Arizona State University, Tempe, AZ 85287-4501

  • 3.

    Department of Mathematics, Arizona State University, Tempe, AZ 85287-1804

Received:  August 31, 2008
Revised:  March 31, 2009
Published:  August 2009
Abstract Related Papers Cited by
    Abstract
  • The cladoceran Daphnia lumholtzi has invaded many US rivers and lakes. To better understand the ecological factors and consequences associated with D. lumholtzi invasion, we carried out a microcosm experiment evaluating competition of D. lumholtzi with a widespread native daphnid, D. pulex. We applied two light treatments to these two different microcosms and found strong context-dependent competitive exclusion in both treatments. We observed that D. lumholtzi out-competed D. pulex in the high light treatment, while D. pulex out-competed D. lumholtzi in the low light treatment. To better understand these results we developed and tested a mechanistically formulated stoichiometric population interaction model. This model exhibits chaotic coexistence of the competing species of Daphnia. The rich dynamics of this model allow us to suggest some plausible strategies to control the invasive species D. lumholtzi.
    Mathematics Subject Classification: Primary, 92B05, 92D40, 92D25; Secondary, 34A34, 34D05, 34D23, 34D40.

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