Advance of Trees and Krummholz Into
Alpine Tundra
Malanson GP1, Zeng Y1, Butler DR2, Resler LM3
1 University of Iowa
2 Texas State University
3 Virginia Tech
What does a seed
experience?
What does it
need in tundra?
Pluses and minuses of solifluction:
Stony surface vs. Dense vegetation
Concentrated fines in turf exfoliation -
Differential success:
Roles for birds, mammals
Needed: Model of geomorphic process
ICE
+
SLOPE
+
TURF
EXFOLIATION
+
PRESSURE
(SATURATION)
TURF DEPTH
What does a seedling experience?
What does it need in tundra?
vegetation pattern
≠
soil pattern
Wind, and effects,
altered by trees
Average Wind Speed
(m/s)
Average Wind Speed, Tree & Tundra
7
6
5
4
3
2
1
0
1715
815
2315 1415
515
2015 1115
215
1715
815
2315 1415
515
2015
Time of Day
Displacement Air Boundary Layer, Tree &
Tundra
Boundary Layer
(mm)
1.2
1.1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
1715 815 2315 1415 515 2015 1115 215 1715 815 2315 1415 515 2015
Time of Day
Ditto for
snow
+ Feedbacks
Microclimate
lower albedo
warmer temperatures
less wind
snow accumulation
reduced PET
less light (UV?)
Soil
trapping of fine sediment
input of organic matter, nutrients
- Feedbacks
Microclimate
less wind
snow accumulation
shorter growing season
less light
lower soil temperatures
Soil
indurated duff, ?hydrophobic
Feedbacks depend on patterns
of which there are many
Can a simple CA produce many patterns?
What are the general dynamics?
P ro b a b ility
Tree Establishment Probability
1.2
1
0.8
0.6
0.4
0.2
0
Probability=
0
0.2
0.4
0.6
α
−γ (
1+ β e
0.8
1
2
x −x )
1.2
Average size index
- feedback cancels + feedback next to tree
The model shows fractal dynamics
linking the rate of advance and spatial
pattern
Advance & Fractal D
160
1.5
140
1.45
100
1.4
80
1.35
60
1.3
Fractal D
40
Advance
20
1.25
0
1
101
201
301
Iteration
401
501
New Trees
Fractal D
120
Self-organized complexity in the
dynamics
- not necessarily seen in any random
snapshot
Time Series of the Power Law Slope
1
101
201
301
0
Slope
-0.5
-1
-1.5
-2
-2.5
Iteration
401
501
Same general results obtain when the surface is
more variable – either randomly or fractally
With a rapid climate amelioration in the middle
of the time series, the rate of advance briefly
increases but then returns to a self-organized
fractal dynamics
250
Advance Potential
200
150
100
50
0
1
101
201
301
401
501
601
701
801
Iterations
901 1001 1101 1201 1301
Although multiple climatic and soil influences
affect treeline dynamics, the spatial
feedbacks create self-organization in which
effects cross scales
1. Trees: simple, nonlinear effects of trees in
neighborhood
2. Patches: negative feedback reduces the effect of
positive feedback
3. Landscape: synchronized coalescence of patches
triggers a second-order phase transition between
high and low fractal states
Geomorphic processes and
micro-landforms are important
sieves for seeds and germination
from a plant’s-eye-view
While many factors may affect
survival and growth, nonlinearity
will produce complexity even if
only a few dominate