Predicting imminent cyanobacterial blooms in lakes using incomplete timely data

• Author(s) / Creator(s)

  • Heggerud, Christopher M.
  • Xu, Jingjing
  • Wang, Hao
  • Lewis, Mark A.
  • Zurawell, Ron W.
  • Loewen, Charlie J. G.
  • Vinebrooke, Rolf D.
  • Ramazi, Pouria

• Abstract
  (description taken from article)
  In this paper, we consider a diffusive-advective predator-prey system in a spatially heterogeneous environment subject to a hostile boundary condition, where the interaction term is governed by a Holling type II functional response. We investigate the existence and global attractivity of both trivial and semi-trivial steady-state solutions and the existence and local stability of coexistence steady-state solutions, depending on the size of a key principal eigenvalue. In addition, we show that the effect of advection on the principal eigenvalue is monotonic for small advection rates, depending on the concavity of the resource distribution. For arbitrary advection rates, we consider two explicit resource distributions for which we can say precisely the behaviour of the principal eigenvalue as it depends on advection, highlighting that advection can either improve or impair a population’s ability to persist, depending on the characteristics of the resource distribution. We present some numerical simulations to demonstrate the outcomes as they depend on the advection rates for the full predator-prey system. These insights highlight the intimate relationship between environmental heterogeneity, directed movement, and the hostile boundary. The methods employed include upper and lower solution techniques, bifurcation theory, spectral analysis, and the comparison principle.

• Date created

  2024-06-09

• Subjects / Keywords

  • Coexistence
  • Environmental heterogeneity
  • Local stability
  • Global stability
  • Bifurcation theory
  • Spectral analysis

• Type of Item

  Article (Published)

• DOI

  https://doi.org/10.7939/r3-8few-xz09

• License

  This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00033-024-02267-y