Sample size for analyzing treatment
effects in high elevation forests
Thomas Ledermann & Markus Neumann
Department of Forest Growth and Silviculture
IUFRO workshop 2009
Zermatt, Switzerland
Workshop, Zermatt 2009
Our approach
• Defining the problems of such forests
• How can we reduce the problems?
• Which treatments are adequate?
• Simulation of stand development
• Selection of powerful indicators
• Development of a sampling design
• Testing the results
• Conclusions
Workshop, Zermatt 2009
What’s the problem?
In Austria high elevation forests are often
limited in their protective function due to …
• even-sized, over-matured stands
• diminishing vertical & horizontal structure
• growing stock too high
• diameters too large & too few trees
• increasing senescence
• missing regeneration
Workshop, Zermatt 2009
What are our goals?
Maintaining the protective functionality by…
• enlarging the diameter variation
• initiating regeneration
• increasing diverse structure
• increasing species diversity
• .....?
Workshop, Zermatt 2009
Which treatments?
Workshop, Zermatt 2009
Applied treatments
• Clearcut of stripes
• Cutting of gaps
• Harvest of target diameter
• Control
Workshop, Zermatt 2009
Simulating stand development
PROGNAUS: A distance-independent individual-tree
growth model
Sub-models: • Basal area increment model (BAI-model)
• Height increment model (HI-model)
• Mortality model
• Ingrowth model (DBH > 5 cm)
• Crown ratio model
All the sub-models are independent of age and
provide direct estimates of the target variables
Workshop, Zermatt 2009
Simulating stand development
PROGNAUS: A distance-independent individual-tree
growth model
Calibration • Bitterlich samples from the Austrian
National Forest Inventory (ANFI)
data:
Validity:
• All Austrian sites with MAI100 < 15 [m³/ha]
• Even- and uneven-aged, mixed forest stands of
common Austrian tree species with all types of
commercial and pre-commercial thinnings and
harvesting strategies as represented in the ANFI
• Min. DBH = 5 cm
• Max. DBH as represented in the ANFI
Workshop, Zermatt 2009
Simulating stand development
PROGNAUS-DI/DD: A distance-dependent individualtree growth model
Semi-distance-independent competition variables from
Bitterlich plots such as
• CCF (Krajicek et al., 1961)
• BAL (Wykoff, 1990)
can be calculated as distance-dependent competition
measures (Stage and Ledermann, 2008):
⎛ aij
E[CI j ] = c jj ∑ cij ⎜
⎜a
i =1
⎝ j
m
⎞
⎟
⎟
⎠
Workshop, Zermatt 2009
Simulating stand development
PROGNAUS-DI/DD: A distance-dependent individualtree growth model
⎛ aij
E[CI j ] = c jj ∑ cij ⎜
⎜a
i =1
⎝ j
m
⎞
⎟
⎟
⎠
CIj … competition index for tree j
cij … the marginal contribution of competitor i
to CIj
in case of CCF:
CPAi ⋅ EFi
cij =
100
ri
ai
i
rj
β
α
aij
j
aj
CPAj … crown projection area of competitor i
(crown width from open grown trees)
EFi … per hectare expansion factor of competitor I
dij
Workshop, Zermatt 2009
Simulating stand development
PROGNAUS-DI/DD: A distance-dependent individualtree growth model
Ingrowth model:
•
Ingrowth is estimated on patches of 21m² size.
•
Stand characteristics for each patch are estimated by
means of a Bitterlich sample (BAF = 4 m²/ha) that is
located in the center of the patch.
•
Ingrowth trees are randomly distributed within the
respective patch.
Workshop, Zermatt 2009
before treatment
after treatment
30 years later
Stripes
Gaps
Targetdiameter
harvest
Workshop, Zermatt 2009
Selection of powerful indicators
• mean tree diameter
• Clark & Evans-Index (micro-structure)
• Cox-Index (meso-structure)
• sum of tree diameters
• .....
Powerful for what ?
Workshop, Zermatt 2009
Index of aggregation (Clark & Evans, 1954)
CE = 1
n
r ∗2
∑
n
i
ρ
i
where
ri is the distance from one tree to his next
neighbour and ρ is density of tree per square meter
Workshop, Zermatt 2009
Clumping index (Strand, 1953; Cox, 1971)
s
Cox =
x
2
x
where
s x2
x
is the variance and
is the mean stem number on sub-plots
calculated for sub-plot areas of 100 m²
Workshop, Zermatt 2009
Sampling design
• Large sampling plots (5 with 1 ha)
• Medium sampling plots (10 with 0,5 ha)
• Small sampling plots (20 with 0,25 ha)
• Very small sampling plots (50 with 0,1 ha)
Total sampling area is 5 ha in all cases
Workshop, Zermatt 2009
Sampling design
Workshop, Zermatt 2009
Testing the results: Tukey
Cox – Index vs. treatment in 2015
5*1 ha
10*0.5 ha
20*0.25 ha
50*0.1 ha
Gaps
Stripes
Target
Control
Workshop, Zermatt 2009
Testing the results: Tukey
Clark & Evans – Index vs. treatment in 2015
5*1 ha
10*0.5 ha
20*0.25 ha
50*0.1 ha
Gaps
Stripes
Target
Control
Workshop, Zermatt 2009
Testing the results: Tukey
Mean diameter vs. treatment in 2015
5*1 ha
10*0.5 ha
20*0.25 ha
50*0.1 ha
Gaps
Stripes
Target
Control
Workshop, Zermatt 2009
Conclusions
• the hierarchy of goals – treatment - indicators – methods
has to be observed;
• for assessing spatial structure of forests larger plots are
needed than for other purposes, orientation may be
essential;
• the effectiveness of sampling depends on time needed and
the variation of the indicator(s) to be assessed;
• following our simulation results the treatments show quite
different effects.
Workshop, Zermatt 2009