Spatial Memory and Taxis-Driven Pattern Formation in Model Ecosystems

• Author(s) / Creator(s)

  • Jonathan R. Potts
  • Mark A. Lewis

• Mathematical models of spatial population dynamics typically focus on the interplay
  between dispersal events and birth/death processes. However, for many animal communities,
  significant arrangement in space can occur on shorter timescales, where
  births and deaths are negligible. This phenomenon is particularly prevalent in populations
  of larger, vertebrate animals who often reproduce only once per year or less. To
  understand spatial arrangements of animal communities on such timescales, we use a
  class of diffusion–taxis equations for modelling inter-population movement responses
  between N ≥ 2 populations. These systems of equations incorporate the effect on animal movement
  of both the current presence of other populations and the memory of past
  presence encoded either in the environment or in the minds of animals. We give general
  criteria for the spontaneous formation of both stationary and oscillatory patterns,
  via linear pattern formation analysis. For N = 2, we classify completely the pattern
  formation properties using a combination of linear analysis and nonlinear energy
  functionals. In this case, the only patterns that can occur asymptotically in time are
  stationary. However, for N ≥ 3, oscillatory patterns can occur asymptotically, giving
  rise to a sequence of period-doubling bifurcations leading to patterns with no obvious
  regularity, a hallmark of chaos. Our study highlights the importance of understanding
  between-population animal movement for understanding spatial species distributions,
  something that is typically ignored in species distribution modelling, and so develops
  a new paradigm for spatial population dynamics.

• Date created

  2019-06-04

• Subjects / Keywords

  • Taxis
  • Advection–diffusion
  • Chaos
  • Population dynamics
  • Animal movement
  • Movement ecology

• Type of Item

  Article (Draft / Submitted)

• License

  Attribution-NonCommercial 4.0 International