A HYBRID CONTINUOUS/DISCRETE-TIME MODEL FOR INVASION DYNAMICS OF ZEBRA MUSSELS IN RIVERS∗

• Author(s) / Creator(s)

  • QIHUA HUANG
  • HAO WANG
  • MARK A. LEWIS

• While some species spread upstream in river environments, not all invasive species
  are successful in spreading upriver. Here the dynamics of unidirectional water flow found in rivers can
  play a role in determining invasion success. We develop a continuous-discrete hybrid benthic-drift
  population model to describe the dynamics of invasive freshwater mussels in rivers. In the model, a
  reaction-advection-diffusion equation coupled to an ordinary differential equation describes the larval
  dispersal in the drift until settling to the benthos, while two difference equations describe the population growth on the benthos. We study the population persistence criteria based on three related
  measures: fundamental niche, source-sink distribution, and net reproductive rate. We calculate the
  critical domain size in a bounded domain by analyzing a next generation operator. We analyze the
  upstream and downstream spreading speeds in an unbounded domain. The model is parameterized by
  available data in the literature. Combining the results of model parameterization and theoretical analysis, we numerically analyze how the interaction between population growth and dispersal, river flow
  rate, and water temperature affects both persistence and the spread of zebra mussels along a river.

• Date created

  2017-01-01

• Subjects / Keywords

  • spreading speed
  • critical domain size
  • zebra mussel
  • persistence
  • river
  • invasion

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/r3-sp13-0972

• License

  Attribution-NonCommercial 4.0 International