The effect of directed movement on the strong allee effect

Chris Cosner, Nancy Rodriguez

Research output: Contribution to journalArticlepeer-review


It is well known that movement strategies in ecology and in economics can make the difference between extinction and persistence. We present a unifying model for the dynamics of ecological populations and street vendors, which are an important part of many informal economies. We analyze this model to study the effects of directed movement of populations subject to strong Allee effect. We begin with the study of the existence of equilibrium solutions subject to homogeneous Dirichlet or no-flux boundary conditions. Next, we study the evolution problem and show that if the directed movement effect is small, the solutions behave like those of the classical reaction-diffusion equation with bistable growth pattern. We present numerical simulations, which show that directed movement can help overcome a strong Allee effect and provide some partial analytical results in this direction. We conclude by making a connection to the ideal free distribution and analyze what happens under competition, finding that an ideal free distribution strategy is a local neighborhood invader.

Original languageEnglish (US)
Pages (from-to)407-433
Number of pages27
JournalSIAM Journal on Applied Mathematics
Issue number2
StatePublished - 2021
Externally publishedYes


  • Allee effect
  • Directed movement
  • Ideal free distribution
  • Reaction-diffusion

ASJC Scopus subject areas

  • Applied Mathematics


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