Limits and Possibilities for Sustainable Development in
Northern Birch Forests:
A general landscape-scale model relating mountain
birch forest dynamics to various anthropogenic
influences, herbivory, and climate change
AO Gautestad, FE Wielgolaski*, B Solberg**, I Mysterud*
* Department of Biology, University of Oslo, Norway
** Agricultural University of Norway, Department of Forestry, Ås, Norway
Outline
• Introduction: What can a model do for the
HIBECO project?
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Topoclimatic models for the height gradient in the HIBECO model
20.0
18.0
3-Month Max. Temperature, T
T = 15 +2 / (H/ 20 + 1) - 0.55 * H / 100
16.0
14.0
12.0
T = 13.7 -ABS(H-75)/80 + (1000+15.2*H)/2200
10.0
8.0
0
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He ight above bottom of valley, H
700
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900
1000
• General model structure: Exploring spatiotemporal
birch forest dynamics under influence from forestry
in a homogeneous environment
• Adding realism I: Age-structured forest dynamics
at scale 1 Ha
• Adding realism II: Dynamics in a heterogeneous
landscape
• Adding realism III: Climate change scenarios
• Adding realism IV: Influences from herbivores –
grazing ungulates and leaf-eating insects
Purpose of the model
• An instrument linking various aspects of the HIBECO
project closer together
– HIBECO is an interdiciplinary project
– Proper modeling requires explicit qualitative and quantitative
descriptions of essential variables and parameters and their
dynamic interactions
• Exploring complex interactions in space and time:
Scenarios
– Basic scientific value
– Practical value for management and politics: sustainable use of
birch forest resources and maintenance of the northern birch forest
ecosystem
Sustainable use of mountain birch:
How can modeling make a contribution?
• Birch is a keystone species in many parts of the Northern terrestrial
ecosystems
• Mountain birch forest ranges are expanding due to a warmer climate
and changes in cultural use of the landscape
• Mountain birch may become an increasingly important resource in the
future (forestry etc.)
• Expansion of the forest ranges also means a parallel contraction of the
treeless landscapes (problems related to reindeer herding and grazing
field availability).
• Models may be used to explore long term interactions and
consequences (“landscape behaviour”) under various hypothetical
management regimes in virtual landscapes
Part 1: General Model Structure
Exploring spatiotemporal birch forest
dynamics and disturbances in a
homogeneous environment
12.8 km
100 m
Pattern from intrinsic processes in
a birch / forestry model system
Rules for local cell disturbances (logging events)
• Rule 1:
– At each time increment
randomly choose 5% of the
cells
– Reset all chosen cells
dominated by old-growth
stands to young stands (i.e.,
local logging event at 1 Ha
scale)
• Rule 2:
– At each time increment
randomly choose one of the
arena cells with old-growth
stands
– Perform logging in this cell,
and all connected cells with
old-growth stands (i.e.,
logging with no spatial
scale constraints up to arena
size)
Test: 150-year simulation
Rule 1:
Rule 2:
Time step:
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"Disturbed" cells
"Old growth" cells
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Tim e
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"Disturbed" cells
"Old growth" cells
Time
Time series analysis of rule 2:
Large series (9200 time steps)
4
Fractal spatial pattern...
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2.5
Log(N)
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1.5
y = -0.881x + 3.6973
R2 = 0.9265
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N 3000
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Log(class)
2000
y = 4996x-0.8814
Disturbance size class histogram
R 2 = 0.9266
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0
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Class
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3
Rule 2-pattern
relatively insensitive to
parameter adjustments
2.5
Log(N)
2
Here: relatively small local inter-cell
variation in forest growth rate
1.5
1
P(size class
increment)/step)=0.9
y = -0.8435x + 2.6624
R2 = 0.7964
0.5
n= ca 3700
0
0
0.5
1
1.5
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Log(class)
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3.5
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Rule 2-pattern shows
“mild chaos” on a return
map of order 1
Polynomial:
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y = -0.0003x2 + 2.1987x - 165.03
R2 = 0.0566
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3500
Step T+1
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Comparing cover of old forest at
time T (x-axis) with T+1 (y-axis)
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Statistical mechanics: Selforganized critical state...
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0
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Step T
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Landscape ecology:
Shifting mosaic
Disturbance rules vs. landscape element connectivity
Rule 1 (scale-specific)
Rule 2, less synchronized
Rule 2, relatively synchronized
•Stop series at a random point where overall cover of old-growth cells is
approximately 6500 cells
•For the next time step, set disturbance intensity to 0.05 (every 20th cell expected
to be perturbed), and let all local disturbances spread to all connected oldgrowth cells (Rule 2)
•Result: Fractal patterns show better overall connectivity between similar
growth phase elements, both for young and old age classes.
Disturbance rules vs. landscape element connectivity
Rule 1 (scale-specific)
Rule 2, less synchronized
Rule 2, relatively synchronized
All three landscape patterns above offer the same overall logging output in the
long run.
Parameter-sensitive connectivity pattern, in particular “Rule 1”-based
management
Local management areas define
upper scale range for age class
pattern even for “scale-free”
logging rules
12.8 km
768 km
Extent: 9 * 16,384 Ha = 147,456 Ha
Grain: 1 Ha
Extent: 128*128 = 16,384 Ha
Extent: 400 * 147,456 Ha = 58,982,400 Ha
Part 2
Adding realism I: Age-structured forest
dynamics at scale 1 Ha
Time
Intense
computation:
For each time
increment,
update more
than 100 year
classes for
each of the
arena’s 16384
1 Ha pixels
(cells)…
Example from
a “Rule 2” type
of logging
regime
Time series for arena: Old growth forest cover (upper line) and logging intensity (bars)
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2500
Number of 1 Ha cells
2000
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8 0 0
7 0 0
6 0 0
Time series for one
particular cell:
5 0 0
4 0 0
3 0 0
2 0 0
1 0 0
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Number of old trees
Time (years)
Intra-cell dynamics
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BasalNumber
stem area
of trees
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S1
163
145
136
136
127
118
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S10
S9
Ageclass
class
Age
S7
S5
S4
154
Logging
Logging
109
109
Time
Time
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S21
S19
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S13
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Logging
Logging
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Model behaviour needs careful validation
Example: Time series for oldest age class (>=100
years) in a given 1 Ha cell
Time series for oldest age class >100 years
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S1
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Logging
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Tim e
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Logging
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Number of trees
500
Part 3
Adding realism II: Dynamics in a
heterogeneous landscape
Adding GIS
layers for local
abiotic
conditions
Relative growth
rate smaller
close to tree line:
A function of
altitudal summer
temperature
gradient
Frequency histogram template for potential or actual birch forest substrate at 1 Ha scale from index 0 (no
potential for birch) to 5 (full cover)
60
50
Percent
40
30
20
10
0
1
2
3
4
Index
5
100 m
Part 4
Adding realism III: Climate change
scenarios
Topoclimatic models for the height gradient in the HIBECO model
20.0
18.0
3-Month Max. Temperature, T
T = 15 +2 / (H/ 20 + 1) - 0.55 * H / 100
16.0
14.0
12.0
T = 13.7 -ABS(H-75)/80 + (1000+15.2*H)/2200
10.0
8.0
0
100
200
300
400
500
600
Height above bottom of valley, H
700
800
900
1000
Climate change scenarios:
+ 2.4 °C over the next 120 years
(scenarios – not prognoses!)
Series 1: No disturbances
Series 2: “Rule 1”-disturbances
Series 3: “Rule 2”-disturbances
Part 5:
Adding realism IV: Influences from
herbivores – grazing ungulates and leafeating insects
Grazing ungulates (sheep, reindeer) and forest structure
“Rule 1”-generated pattern
“Rule 2”-generated patterns
Sustainable pluralistic utilization of birch forest:
Logging rules (“policy”) can significantly influence the overall quality and availability of forest
elements for other uses, like grazing habitat for sheep and reindeer, hiking/tourism, etc.
Leaf-eating moth outbreaks (Epirrita, Operopthera etc.)
Outbreak
constraints:
Lower limit: 100
m above bottom
of valley
(Winter
inversion)
Upper limit:
13.5 ºC isotherm
for 3-month max
summer
temperature
In this preliminary and
hypothetical 120-year
scenario insects have
tree-killing
preudoperiodic
outbreaks every 8-12
years
http://www.hibeco.org