GreenLab Course
Production - Expansion
Biomass partitioning
Organ dimension
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Organ weight and sizes
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The sum of all the biomass increments of an organ gives its weight.
In the GreenLab model, the relation relating sizes to fresh biomass is defined from allometries.
Allometric equations take the general form Y = u.Mw, where Y is some biological variable, M is a measurement of body size, u a global scaling factor and w is some scaling exponent.
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Using allometric equations thus makes it possible to evaluate organ dimensions.
On the assumption of an average stable density dorg, and simple organ shapes, the organ dimension can be defined from the allometric general form, where M stands for the volume vorg (i.e. the density that divides the biomass qorg ) and Y a metric or metric relation.
The general organ allometry is thus:
Yorg = u . (qorg / dorg )w = u . vorgw
Usual organ shapes and their dimensions
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Fruits
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For fruits, the basic shape to consider can be the sphere, characterized by its radius r
We thus have: vf = 4/3 . π . r3 giving
r = ( 3 . vf /(4 π) ) 1/3
This approach can be extended to an ellipsoid shape defined by 3 axes r1 = r, r2 = a . r and r3 = b . r
We thus have:
vf = 4/3 . π . r1 . r2 . r3 = 4/3 . π . a . b . r3 giving
r = ( 3 . vf /(4 . a . b . π) ) 1/3
Internodes
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The internode can be represented by a cylinder defined by its height h and its section s.
In the general allometry form, let us consider the allometry between height and section with b as a lengthening scaling factor, and γ as the scaling exponent:
h / s = b . (vi)γ
The cylinder height and section can then be expressed from the volume vi as follows:
for height: h = b1/2 . ( vi )((1+γ)/2) and
for section: s = b-1/2 . ( vi )((1-γ)/2)
Note
If γ = 1 then the section s is constant and height h becomes proportional to the volume.
If γ = -1 then the height h is constant and section s becomes proportional to the volume.
If γ = 2/3 then the ratio height h on diameter is constant.
Leaves
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For leaves, this scaling factor is defined from the Specific Leaf
Weight -SLW- (or the inverse of the Specific Leaf Area, -SLA-).
This variable, noted e, representing leaf (or blade) thickness, is usually considered constant during expansion.
The allometry rules defining organ dimensions from their volume (i.e. from their biomass) is summarised here:
Organ allometry relations in the GreenLab model
Definition
Allometry
Physiology. Allometry, also called biological scaling, in biology, the change in organisms in relation to proportional changes in body size. Allometry is often considered to be one of the few laws in biology. Allometric equations take the general form Y = a.Mb, where Y is some biological variable, M is a measure of body size, and b is some scaling exponent.Definition
SLW (Specific Leaf Weight)
Physiology (abrev.) SLWstands for Specific Leaf Weight and is defined as the ratio of leaf dry weight to area. (See also SLA) Unit: g.m-2.Definition