Supplementary Material
Methods: FBA field measurements
The FBA protocol required the development of a fractal tree model based on the natural form of the tree with
each section or internodes referred to as links. Links were individual sections of wood (stem), branch, or twig
between two branching points. For aboveground, the initial link was the wood (diameter ≤ 7 cm), and the stem
divides into branches (diameter from 2 cm to 6.99 cm) and twigs (diameter ≤ 1.99 cm) to form the crown. These
links allow length–diameter scaling relationships to be determined. Tree stem lengths varied from 2 to 40 cm
from soil surface therefore diameter at breast height (DBH) normally used for developing the tree allometric
equation was replaced with stem base diameter measured at the middle of stem height. Belowground biomass
was determined in much the same manner as for aboveground, except that proximal root measurements were
used. Proximal roots had wood root (diameter ≥ 2 cm), branch roots (diameter from 0.5 cm to 1.99 cm), and
twig roots (diameter < 0.5 cm). FBA simulated only root biomass of one proximal root therefore a summation
was necessary to estimate total proximal root biomass.
Prior to biomass determination, schematic diagrams were prepared for all aboveground branching patterns with
field data measurements for diameter and length links. Accuracy required two measurements for each data point,
the second measure at 90 degrees to the first and at three link points, proximal, middle, and distal. The main
stem is link 0, the next link 1, and subsequent offspring numbered sequentially as link 2 and link 3 until all links
were completed. Data collection included leaf numbers and fruit for each link. To ensure reliable estimates data
were collected for a minimum of 100 branching point for each tree as recommended by van Noordwijk and
Mulia (2002).
To calculate biomass it was necessary to determine the probability distributions of p and q. The scaling factor
for p is a transfer coefficient that denotes a change in total cross-sectional area at branching points. This was
calculated as the ratio between sum of squared diameters before and after branching. The scaling factor for q is
an allocation coefficient that denotes relative size of the largest link at a branching point. This was calculated as
the ratio between the largest squared diameter after branching and sum of squared diameter after branching.
Prior to biomass determination, schematic diagrams were prepared for all belowground branching patterns.
Collection of field data for link diameter and length was in a manner similar to that for aboveground.
Belowground FBA uses proximal root terms that have the same meaning to lateral or horizontal root terms. This
study uses proximal root term when explaining the model and uses lateral root when explaining other
researchers’ findings. Root diameter and length data recording started with the first proximal root and continued
for a minimum of 100 links. Horizontal proximal roots are 0 to 45 degrees angle from soil surface and vertical
proximal root as more than 45 degrees.
Supplementary material
Results
Fig S1 Schematic drawing of an unpruned 4-year-old showing above and belowground architecture following
FBA numbering
16
Shoot
16
14
14
12
12
10
10
p 8
p 8
6
6
4
4
2
2
0
0
0
2
4
6
8
10
12
14
Root
0
16
2
4
6
8
10
12
14
16
Link diameter (cm)
Link diameter (cm)
1.2
Shoot
1.2
1.0
1.0
0.8
0.8
q 0.6
q 0.6
0.4
0.4
0.2
0.2
Root
0.0
0.0
0
2
4
6
8
10
Link diameter (cm)
12
14
16
0
2
4
6
8
10
12
14
16
Link diameter (cm)
Fig S2 Distribution of p (top) and q (bottom) factors as a function of link diameter. The horizontal line in p
represent a conservation of cross sectional area across a branching point (p = 1).The horizontal line in q
represents a perfect fork (q = 0.5)
Twig
120
Branch
180
160
100
Link lenth (cm)
Lingk length (cm)
140
80
60
40
120
100
80
60
40
20
20
0
0
0.0
0.5
1.0
1.5
2.0
2.5
0
2
Link diameter (cm)
4
6
Link diameter (cm)
Wood
45
40
Link length (cm)
35
30
25
20
15
10
5
0
0
5
10
15
20
Link diameter (cm)
Fig S3 Aboveground or shoot link length and diameter relationship for twig, branch, and wood categories
Table S1 Allometric constants and scaling coefficients for taproot of 10 jatropha
Least trimmed squared (LTS)
Taproot
a
0.01802
b
1.33340
R2
0.94000
p
<0.00010
cf
1.55600
cf = correction factor
8