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Dynamics of sand dunes stabilization

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  1. Dynamics of sand dunes stabilization Or: What can nonlinear dynamics tell us about ecology? ShaiKinast The Negev Physics Fete March 15, 2013

  2. Sand dunes A pattern-forming system Namibia Morocco Mars Kasuywadi, Israel

  3. Distribution of sand dunes • Cover 6% of global surface area • Occur in two distinct habitats: • Along coasts of seas and rivers (3%) • Deserts and arid regions (97%) Approximated sand dunes map After Thomas (1997)

  4. Sand dunes stabilization why is it important? stabilized active people live on sand

  5. Sand dunes stabilization psammophilic flora and fauna Change in dune mobility  change in biodiversity

  6. Stabilization by biogenic crust and/or vegetation d c plants + crusts; semi-stabilized dunes bare sand; active dunes b a a b plants + crusts; stabilized dunes plants(no crusts); stabilized dunes a b c d c 40 100 150 d 400 mean annual precipitation (mm/year)

  7. Stabilization by biogenic crust Israel Egypt Fixed dunes Active dunes Israel-Egypt Border (NW Negev) annual precipitation ~ 100mm/year

  8. Model assumptions as simple as possible, yet not too simple… Influence index: Positive Negative crust vegetation competition local competition plants and crust compete for land • non local competition • plants and crust compete through: • distribution of water (“source-sink”) • toxic litter from plants

  9. Model assumptions Influence index: Positive Negative precipitation crust vegetation growth rates precipitation

  10. Model assumptions Influence index: Positive Negative wind – indirect and direct crust vegetation • indirect • through sand transport: • root exposure • burial of crust and plants • direct • increased evapotranspiration • branch cutting Wind shield by vegetation (positive feed back)

  11. Model assumptions Influence index: Positive Negative wind – indirect and direct crust vegetation competition precipitation

  12. Mathematical description non local competition indirect wind effect precipitation direct wind effect local competition precipitation indirect wind effect local competition non local competition where: variables represent cover fraction v = vegetation b = biogenic crust

  13. A. Dune cover vs. precipitation bare sand fraction:

  14. A. Dune cover vs. precipitation compare with field observations (a) p = 40 (b) p = 80 (c) p = 150 (d) p = 400

  15. A. Dune cover vs. precipitation Bistability steady state depends on initial conditions

  16. A. Dune cover vs. precipitation Hysteresis • ecosystem may not recover after drought

  17. B. Dune cover vs. precipitation and wind vegetation crust plants removal cover fraction cover fraction time (yr) time simulation of plants removal

  18. B. Dune cover vs. precipitation and wind Two types of bistability Different mechanisms: Type 1 - wind shield by vegetation Type 2 - competition between crust and vegetation

  19. B. Dune cover vs. precipitation and wind Two types of bistability Yizhaq et al, PRL 2007 Different ecological consequences: Type 1 - bistability of vegetated dunes and baredunes Type 2 - bistability of vegetated dunes and crusted dunes

  20. B. Dune cover vs. precipitation and wind bistability? 100m on-site removal of plants and crusts more than 15 years ago!

  21. C. Desertification vs. rehabilitation (BV) (VB) B = crust-dominated dune V = plants-dominated dune arrows represent possible disturbances

  22. Summary • Dune cover vs. precipitation • Model vs. reality • Dune cover vs. precipitation and wind • Two types of bistability • Desertification vs. rehabilitation Kinast et al, PRE 87 020701

  23. Thank you!

  24. D. Oscillations in dune cover amplitude of limit cycle supercritical Hopf bifurcation g v d=13 d=9 cover fraction cover fraction time (yr) time (yr)

  25. D. Oscillations in dune cover vegetation crust period of oscillations period saturates: d d=15 d=30 d=400 d=100 cover fraction time time time time