• Aucun résultat trouvé

From the biology to the Allometric Equation (AE)

N/A
N/A
Protected

Academic year: 2021

Partager "From the biology to the Allometric Equation (AE)"

Copied!
19
0
0

Texte intégral

(1)

HAL Id: hal-02803588

https://hal.inrae.fr/hal-02803588

Submitted on 5 Jun 2020

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

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�

(2)

From the biology to the

Allometric Equation (AE)

Pham Cuong, Inoguchi Akiko

Hanoi, June 18 - 22

th

2012

Authors : L. Saint-André (CIRAD - INRA), M.

Henry (FAO) and N. Picard (CIRAD)

(3)

Objectives

Context: How can we measure the

volume or the biomass of standing

trees ?

Well……, do we

have a balance to

(4)

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?

(5)

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

(6)

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)

(7)

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

(8)

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)

(9)

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:

(10)

Biological concepts

Genetic

Climate

conditions

Soil fertility

Manageme

nt

Tree growth encompasses primary growth (height) and secondary

growth (cambium activity) : a highly complex process

(11)

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

(12)

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…..)

(13)

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

(14)

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

(15)

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)

(16)

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

(17)

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

(18)

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

2

H)

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

(19)

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

Références

Documents relatifs

Following this line of thought, I argue that this trend could be traced back to the early origin of scientific approaches—the disciplines of general biology that separated from

Proof.. with data which are the sum of an optimal regularity part and a contribution of the singularities. As in theorem 3.4, we compute explicitly the solution

Furthermore, f belongs also to F(py, r, c, h) and so is its unique allocation.. The general case. The same argument applies for x. Extending fair shares to matrices with

Thus, the library loading mechanism is guaranteed to load all symbols correctly as long as the freetype.dll is in the correct path; thus the windows version of the interface, if

the comparative analysis of biomass structure of forest stands on the territory of Eurasia is fulfilled in a new light, the result of which is the additive allometric

However, when the effects of high learning rates and carbon drifts are combined, the option value in the long term learning case seems to be above the corresponding early

With the rise of interest in organizational culture which became one of most important things in organizations, because of its role in improving of

There are then some diseases that we should pity and cure and others that are shameful and fall under the scope of the legislator. So just as moral defect is a kind of disease,