Self-Organised .....Soil (??)


Riz Fernando Noronha

Supervised by Kim Sneppen and Kunihiko Kaneko

  • Soil particle-sizes follow a power-law

  • There is a correlation between the fractal dimension and the biodiversity of the soil

  • Hypothesis: Biology contributes to the fractal structure


Tyler and Wheatcraft, 1989

Parameters

  • : Soil filling rate
  • : Death rate of worms
  • : Nutrient generation rate
  • : Reproductive rate of worms

One is a great number!

Algorithm

  • Worm create nutrients in their vicinity

  • Mutual co-existence

  • Can be thought of as a predator-prey, as the worms consume soil in a 2-step process

Mean-Field Equations

Survival in lattice vs Meanfield

Two Species

  • Add a second species, and make it asymmetric in terms of:
    • , nutrient generation rate
    • , reproduction rate

  • is a parasite.

Mean-Field: Parasite Problem


  • Worms don't care who creates the nutrient
  • A slight advantage mean you dominate
  • Competitive Exclusion: Higher always wins

Mean-Field: Higher always wins

Multiple Nutrients


  • Have worms eat all other nutrients, besides their own

    • Worms simply oscillate in phase
    • Similar to single-species model

  • Have worms eat nutrients in a cycle

    • 1 > 2 > 3 > 4 > 1, etc

Literature suggests spiral waves...


Takeuchi and Hogweg, 2012

Why no Spirals?

  • Assume we have a magical wave source.

  • Waves ejected in the right order

  • Soil needed for nutrient generation, and so waves cannot propagate!


After removing soil

Spatial confinement


  • Assuming you're surrounded by soil, how do you propagate into it?

  • All species must be present on the expansion boundary

  • Expansion is hard!

Power Laws

  • For certain parameter values, we do see power-law distributed "particle sizes".

  • Size ~ Cluster size

  • Potentially, oscillations span across the critical point

  • More work is needed!