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Dynamics of sand dunes stabilization . Or: What can nonlinear dynamics tell us about ecology?. Shai Kinast. The Negev Physics Fete March 15, 2013. Sand dunes. A pattern-forming system. Namibia. Morocco. Mars. Kasuy wadi , Israel. Distribution of sand dunes.
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Dynamics of sand dunes stabilization Or: What can nonlinear dynamics tell us about ecology? ShaiKinast The Negev Physics Fete March 15, 2013
Sand dunes A pattern-forming system Namibia Morocco Mars Kasuywadi, Israel
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)
Sand dunes stabilization why is it important? stabilized active people live on sand
Sand dunes stabilization psammophilic flora and fauna Change in dune mobility change in biodiversity
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)
Stabilization by biogenic crust Israel Egypt Fixed dunes Active dunes Israel-Egypt Border (NW Negev) annual precipitation ~ 100mm/year
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
Model assumptions Influence index: Positive Negative precipitation crust vegetation growth rates precipitation
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)
Model assumptions Influence index: Positive Negative wind – indirect and direct crust vegetation competition precipitation
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
A. Dune cover vs. precipitation bare sand fraction:
A. Dune cover vs. precipitation compare with field observations (a) p = 40 (b) p = 80 (c) p = 150 (d) p = 400
A. Dune cover vs. precipitation Bistability steady state depends on initial conditions
A. Dune cover vs. precipitation Hysteresis • ecosystem may not recover after drought
B. Dune cover vs. precipitation and wind vegetation crust plants removal cover fraction cover fraction time (yr) time simulation of plants removal
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
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
B. Dune cover vs. precipitation and wind bistability? 100m on-site removal of plants and crusts more than 15 years ago!
C. Desertification vs. rehabilitation (BV) (VB) B = crust-dominated dune V = plants-dominated dune arrows represent possible disturbances
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
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)
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