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From the biology to the Allometric Equation (AE)
Laurent Saint-André, Matieu Henry, Nicolas Picard
To cite this version:
Laurent Saint-André, Matieu Henry, Nicolas Picard. From the biology to the Allometric Equation (AE). Training Material Biology To AE, UN-Reducing Emissions from Deforestation and forest Degra-dation (UN-REDD). Genève, CHE.; Food and Agriculture Organization (FAO). ITA., Jun 2012, Hanoi, Vietnam. 18 p. �hal-02803588�
From the biology to the
Allometric Equation (AE)
Pham Cuong, Inoguchi Akiko
Hanoi, June 18 - 22
th2012
Authors : L. Saint-André (CIRAD - INRA), M.
Henry (FAO) and N. Picard (CIRAD)
Objectives
Context: How can we measure the
volume or the biomass of standing
trees ?
Well……, do we
have a balance to
Objectives
Context: When there can be a
lot of different trees in a given
forest….
I guess we are
lost…., and is it
necessary to fell all
these beautiful trees
to measure their
biomass?
What is Allometry ?
Broad definition : within a given population, there is a statistical relationship
between the size of an organism and the size of any part of it (Gould, 1966)
H
D
CD
For example: between height and diameter; diameter and
crown size; biomass and diameter; etc..
Can be used to predict some
difficult-to-measure tree characteristics from
easily collected data.
Volume prediction
Volume tables
Biomass prediction
Biomass equations
Nutrient content prediction
What is Allometry ?
More restrictive definition : proportionality between the relative
increments of two metrics measured on an organism (Huxley, 1924)
relative
increment in
Biomass
relative
increment in
Diameter
Allometric
coefficient
Which gives by integration
a
D
b
c
B
=
+
x
And by extension
Where a gives the proportionality between the relative increments, b gives
the proportionality between biomass and diameter (given a) and c is the
biomass of the tree when D=0 (if D was measured at a height different from
zero)
What is Allometry ?
The literature on biomass equations dangles between two opposites
sides:
A- The group of West, Brown and Enquist have been developing an appealing theory of biological allometry relying on the fractal properties of branching networks, referred as allometric biomass partitioning theory (APT) by McCarthy and Enquist (2007)s1 accounting for the constraint of biomechanical stability s2 accounting for the minimization of hydrodynamic
resistance through the vascular network. Two main parameters:
From West et al. 1997:
When taking s1=1 to fit the hypothesis of volume filling and uniform biomechanical constraints, the tree mass
is predicted to be related to the tree diameter raised to a power a=8/3≈2.67
But rather stands for an average tree model to explore biomass variations among plant
size orders than being predictive for single species
What is Allometry ?
The literature on biomass equations dangles between two opposites
sides:
B- The very large group of purely statistical equations, with little regard to the
understanding of the biological processes involved. Such models are only reliable within
their domain of validity
Often calibrated on small number of trees, covering a little part of
tree size variations for a given species
Equations of various forms
Catalogues and databases start to be available for all continents
(ex: Zianis for Europe; Navar for south America; Henry for Africa)
What is Allometry ?
A good candidate set of volume or biomass equations should be
simultaneously:
(i)consistent: standardized biomass partition and additivity of tree
compartments
,
(ii) generic: common form of the models whatever the tree species or
the forest structure. Meaningful parameters (ie related to the biology)
.
(iii) robust: system operating correctly across a wide range of
operational conditions with a low sensitivity to the sampling design and the
working hypotheses
(iv) accurate.
Building appropriate volume and biomass equations are then still
challenging scientifically:
Biological concepts
Genetic
Climate
conditions
Soil fertility
Manageme
nt
Tree growth encompasses primary growth (height) and secondary
growth (cambium activity) : a highly complex process
Biological concepts
Tree and stand growth: case of even-aged and monospecific forests
-Wood production
(volume) of a given
tree species at a given
stand mean (or top)
height should be
identical for all site
classes.
- Soil fertility (site
index) determines the
time need to attain this
height and volume.
-A- Stand production
-Eichhorn’s rule
-Assmann’s yield
level theory
-There are some range of variations of
wood production at a given top height
(variations related to the stockability
issue)
From Maguire D, 2011
-Langsaeter
Hypothesis
-Losses in productivity
if the standing stock is
too low
Biological concepts
Tree and stand growth: case of even-aged and monospecific forests
-B- Tree production
function of the overall stand production (see previously) which gives the
potential moderated by two reducers
-an Index of Stand density (global pressure on the tree)
(stand density in itself (Sd), stand basal area (G),
hart-becking spacing factor based on tree growth without
competition, Reinecke density index (Rdi) and stand density
Index (Sdi) based on the self-thinning law, etc…)
- an Index of Social status of the tree (between tree competition)
(h/Ho, d/Do, the relationship between radial increment and
tree diameter, etc…..)
Biological concepts
Tree and stand growth: case of even-aged and monospecific forests
-C- Biomass partitioning in the tree
-Ring area increases linearly from
the top of the tree to the crown
basis and remains constant below
the crown
-Pressler’s law
Ring area (cm2) D is ta nc e fr om t h e to p o f th e tr ee ( m ) Ring width(cm)- From the pith to the bark and
along the tree bole. A three
dimension map !
-Wood density variations
Trunk shape tends to become more cylindrical with time.
E.urophylla*pellita de 19 ans 0,30 0,40 0,50 0,60 0,70 0,80 0,90 -200 -100 0 100 200 distance à la moelle (mm) in fr a d e n si té ( g /c m 3) A B C
Biological concepts
Site fertility evaluation (constant in time)
1. Growth
Module
Inventory at A + 1 month
Inventory at A + 1 month
Stand inventory, real or virtual, at an age A
Stand inventory, real or virtual, at an age A
Individual tree growth in
Height
Stand growth
in
dominant H
dominant H
Stand growth in
basal area
basal area
Individual tree growth
in
basal area
basal area
Biological concepts
with an unexpected effect
of stand density on the
dominant height growth
dho/dt = f(site, ho, DENSITY)
o ho h dt dG dt dG dt dho dt dho 2500 t/ha < 600 t/ha dt dg dt dg c α γ 1 2 3 4 c h 2500 t/ha < 600 t/ha
Stand basal area growth
Individual tree height
Inventory (t+1)
Dominant height growth
o ho h dt dG dt dG dt dho dt dho 2500 t/ha < 600 t/ha dt dg dt dg c 1 2 3 4 c h 2500 t/ha < 600 t/ha tt
Individual tree basal area growth
α andγ = f(density, age)
Site Index
Inventory (t)
Biological concepts
2. Wood
Properties
Module
Set of biomass equations
for each part of the tree
Volume for
each tree
0 5 10 15 20 25 30 35 0 2 4 6 8 10 Dominant 0 2 4 6 8 10 Co-dominant 0 2 4 6 8 10 Suppressed H ei gh t( m ) Radius (cm) 0 5 10 15 20 25 30 35 0 2 4 6 8 10 Dominant 0 2 4 6 8 10 0 2 4 6 8 10 Co-dominant 0 2 4 6 8 10 Suppressed H ei gh t( m ) Radius (cm)Stem taper equation
Ring accumulation
Biomass
• by tree compartment
• by ring
Biological concepts
3.
Biogeo-chemical
Module
N P K concentrations
in each ring
Model for nutrients
evolution in rings
0 5 10 15 20 25 0 2 4 6 8 Radius (cm) Hauteur (cm) 0 5 10 15 20 25 0 2 4 6 8 Radius (cm) Hauteur (cm)Set of nutrient content equations
Nutrient content N, P, K, Ca, Mg
Biological concepts
From biology to allometric equations
D2H = surrogate of tree volume
(=treeVol * formFactor)
and biomass = volume * wood density
D2H is therefore well
correlated to the tree biomass and nutrient content
Biom = b*(D
2H)
c
+a
This parameter
encompasses the form factor and the wood density;
it gives the proportionality between the cumulative values of biomass and volume
This parameter gives the tree biomass just before it reaches 1m30 height
This parameter gives the proportionality between biomass increments and volume increments
and nutrient content = biomass * nutrient concentration
Biological concepts
Stem wood d²h (m3/tree) B io m as s (k g /t re e)Crown (leaves or branches)
Age d²h (m3/tree) B io m as s (k g /t re e) Age Ontogenic effect Social status effect a ) b )
From Saint-Andre et al. (2005) MacCarthy and Enquist 2007, and Genet et al. 2010, we drew the following patterns:
1- both internal (changes in wood properties with ontogeny APT ) and external factors (e.g., growing conditions, social status of the tree OPT) are of importance concerning tree biomass relationship – The main consist in identifying the proportion between APT and OPT
2- The observed pattern may vary strongly from one species to another, but our hypothesis is that
species of similar traits (e.g., crown architecture, wood structure) would exhibit similar to identical biomass models