stabilization Or What can nonlinear dynamics tell us about ecology Shai Kinast The Negev Physics Fete March 15 2013 Sand dunes A patternforming system Morocco Namibia Kasuy wadi ID: 253175
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Slide1
Dynamics of sand dunes stabilization
Or: What can nonlinear dynamics tell us about ecology?
Shai Kinast
The Negev Physics FeteMarch 15, 2013Slide2
Sand dunes
A pattern-forming system
Morocco
Namibia
Kasuy
wadi
, Israel
MarsSlide3
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%)
After Thomas (1997)
Approximated sand dunes mapSlide4
Sand dunes stabilization
active
stabilized
why is it important?
people live on sandSlide5
Sand dunes stabilization
p
sammophilic flora and fauna
Change in dune mobility
change in biodiversitySlide6
mean annual precipitation (mm/year)
40
100
150
400
a
d
c
b
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
dSlide7
Israel
Egypt
Fixed
dunes
Active
dunes
Israel-Egypt Border (NW Negev
)
annual precipitation ~ 100mm/year
Stabilization by
biogenic crustSlide8
Model assumptions
crust
vegetation
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…Slide9
Model assumptions
crust
vegetation
precipitation
Influence index
:
Positive
Negative
precipitation
growth ratesSlide10
Model assumptions
crust
vegetation
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)Slide11
Model assumptions
crust
vegetation
precipitation
Influence index
:
Positive
Negative
wind
–
indirect
and
direct
competitionSlide12
v
= vegetation
b = biogenic crust
variables represent cover fraction
precipitation
precipitation
local competition
local competition
non local competition
non local competition
direct wind effect
indirect wind effect
indirect wind effect
Mathematical description
where:Slide13
A. Dune cover vs. precipitation
bare sand fraction:Slide14
compare with field observations
(a) p = 40
(b) p = 80
(d) p = 400
(c) p = 150
A. Dune cover vs. precipitationSlide15
steady state depends on initial conditions
Bistability
A. Dune cover vs. precipitationSlide16
ecosystem may not recover after drought
Hysteresis
A. Dune cover vs. precipitationSlide17
cover fraction
time
simulation of plants removal
time (yr)
cover fraction
vegetation
crust
plants removal
B. Dune cover vs. precipitation and windSlide18
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 vegetationSlide19
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 2007Slide20
on-site removal of plants and crusts more than 15 years ago!
100m
bistability?
B. Dune cover vs. precipitation and windSlide21
C. Desertification vs. rehabilitation
B = crust-dominated duneV = plants-dominated dune
arrows represent possible disturbances
(B
V)
(V
B)Slide22
Summary
Dune cover vs. precipitationModel vs. reality
Dune cover vs. precipitation and windTwo types of bistabilityDesertification vs. rehabilitation
Kinast
et al, PRE
87
020701Slide23
Thank you!Slide24
amplitude of limit cycle
supercritical
Hopf
bifurcation
time (
yr
)
time (
yr
)
cover fraction
cover fraction
d=9
d=13
D. Oscillations in dune cover
v
gSlide25
cover fraction
vegetation
crust
d=15
d
period of oscillations
time
time
time
time
d=30
d=100
d=400
period saturates:
D. Oscillations in dune cover