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

2. Sand dunes A pattern-forming system Morocco Namibia Kasuy wadi, IsraelMars

3. Distribution of sand dunes - Cover 6% of global surface area - Occur in two distinct habitats: 1.Along coasts of seas and rivers (3%) 2.Deserts and arid regions (97%) After Thomas (1997) Approximated sand dunes map

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

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

6. mean annual precipitation (mm/year) 40100150400 adcb bare sand; active dunes a plants(no crusts); stabilized dunes d plants + crusts; stabilized dunes c plants + crusts; semi-stabilized dunes b Stabilization by biogenic crust and/or vegetation a b c d

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

8. Model assumptions crustvegetation competition Influence index: Positive Negative 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 as simple as possible, yet not too simple…

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

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

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

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

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

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

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

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

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

18. 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 Different ecological consequences: Type 1 - bistability of vegetated dunes and bare dunes Type 2 - bistability of vegetated dunes and crusted dunes Yizhaq et al, PRL 2007

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

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

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

23. Thank you!

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

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