Analysis of spread and persistence for stream insects with winged adult stages

  • Author(s) / Creator(s)
  • Species such as stoneflies have complex life history details, with larval
    stages in the river flow and adult winged stages on or near the river bank. Winged
    adults often bias their dispersal in the upstream direction, and this bias provides a
    possible mechanism for population persistence in the face of unidirectional river flow.
    We use an impulsive reaction–diffusion equation with non-local impulse to describe
    the population dynamics of a stream-dwelling organism with a winged adult stage, such
    as stoneflies. We analyze this model from a variety of perspectives so as to understand
    the effect of upstream dispersal on population persistence. On the infinite domain we
    use the perspective of weak versus local persistence, and connect the concept of local
    persistence to positive up and downstream spreading speeds. These spreading speeds,
    in turn are connected to minimum travelling wave speeds for the linearized operator in
    upstream and downstream directions. We show that the conditions for weak and local
    persistence differ, and describe how weak persistence can give rise to a population
    whose numbers are growing but is being washed out because it cannot maintain a toe
    hold at any given location. On finite domains, we employ the concept of a critical
    domain size and dispersal success approximation to determine the ultimate fate of the
    populations. A simple, explicit formula for a special case allows us to quantify exactly
    the difference between weak and local persistence.

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  • Type of Item
    Article (Draft / Submitted)
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  • License
    Attribution-NonCommercial 4.0 International