Dynamics of sand dunes stabilization Or:

What can nonlinear dynamics tell us about ecology?

Shai KinastThe Negev Physics Fete

March 15, 2013

Sand dunesA pattern-forming system

MoroccoNamibia

Kasuy wadi, Israel Mars

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

Sand dunes stabilization

active stabilized

why is it important?

people live on sand

Sand dunes stabilizationpsammophilic flora and fauna

Change in dune mobility change in biodiversity

mean annual precipitation (mm/year)40 100 150 400

a dcb

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

Israel Egypt

Fixed dunes Active dunes

Israel-Egypt Border (NW Negev)annual precipitation ~ 100mm/year

Stabilization by biogenic crust

Model assumptions

crust vegetationcompetition

Influence index:

Positive

Negative

local competitionplants and crust compete for land

non local competitionplants and crust compete through:- distribution of water (“source-sink”)- toxic litter from plants

as simple as possible, yet not too simple…

Model assumptions

crust vegetation

precipitationInfluence index:

Positive

Negative

precipitation

grow

th ra

tes

Model assumptions

crust vegetation

wind – indirect and directInfluence index:

Positive

Negative

direct• increased evapotranspiration• branch cutting

indirectthrough sand transport:• root exposure• burial of crust and plants

Wind shield by vegetation (positive feed back)

Model assumptions

crust vegetation

precipitation

Influence index:

Positive

Negative

wind – indirect and direct

competition

vbvDPsvvvDPgsvpdtdv

vcvvv 3/2),())((

bvsbvvDPgsbpdtdb

bcbbb ),())((

10 bvv = vegetationb = 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

2/)1)(tanh()( cvvdvgwhere:

bvs 1

bvs 1

A. Dune cover vs. precipitation

bare sand fraction:

compare with field observations

(a) p = 40 (b) p = 80

(d) p = 400(c) p = 150

A. Dune cover vs. precipitation

steady state depends on initial conditionsBistability

A. Dune cover vs. precipitation

ecosystem may not recover after droughtHysteresis

A. Dune cover vs. precipitation

cove

r fra

ctio

n

time

simulation of plants removaltime (yr)

cove

r fra

ctio

n

vegetation

crust

plants removal

B. Dune cover vs. precipitation and wind

B. Dune cover vs. precipitation and windTwo types of bistability

Different mechanisms:

Type 1 - wind shield by vegetation

Type 2 - competition between crust and vegetation

B. Dune cover vs. precipitation and windTwo 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

on-site removal of plants and crusts more than 15 years ago!

100m

bistability?

B. Dune cover vs. precipitation and wind

C. Desertification vs. rehabilitation

B = crust-dominated duneV = plants-dominated dune

arrows represent possible disturbances

(BV) (VB)

SummaryA. 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

Thank you!

amplitude of limit cycle

supercritical Hopf bifurcation

time (yr) time (yr)

cove

r fra

ctio

n

cove

r fra

ctio

n

d=9 d=13

D. Oscillations in dune cover

v

g

cove

r fra

ctio

n

vegetation

crust

d=15

d

perio

d of

osc

illat

ions

time time time time

d=30 d=100 d=400

period saturates:yrTd 27.381

D. Oscillations in dune cover