Allometry is used to describe the morphological evolution of species, and is based on the relation
between an organism's size and the size of any part of the organism.
Allometry is studied during the growth of a single organism; as a comparison between different
organisms of the same species; and between organisms in different species. The allometric
equation is graphed on an XY axis, with the body size on the x-axis and the part size on the yaxis. The scatter produced by the different measurements being compared can then be analyzed
for useful data.
Allometry allows scientists to study biological functions as they increase as a power of body size.
For instance, more energy is consumed by an elephant, but a mouse probably consumes more
energy when that energy is measured as a function of mouse body weight.
The allometric equation is generally stated as
y = mx + b
where y = predicted size of body part; x = observed body weight; m = slope acquired; and b = the
value of y where it intercepts the vertical axis.
Not all allometric comparisons are linear; the allometric equation is frequently modified to
compensate for this. The point is to determine a consistent relationship for the species in
question.
Another allometric equation that compensates for nonlinear functions is:
log(y) = log(b) + m[log(x)]
Allometry is an important method for describing morphological evolution. It is the
relation between the size of an organism and the size of any of its parts: for example,
there is an allometric relation between brain size and body size, such that (in this case)
animals with bigger bodies have bigger brains.
Allometric relations can be studied
• during the growth of a single organism;
• between different organisms within a species;
• between organisms in different species.
A typical allometric graph plots body size on the x-axis and some other character, such as
brain, or eye-stalk, size on the y-axis.
The points on these graphs can be for
• the same individual measured at different ages;
• for different individuals of a species (in which case the scatter will mainly be due to
variation in age);
• for different species in a higher taxon.
What is allometry?
Allometry is all about studying the relative sizes of plant parts. Usually,
relationships
between dbh (diameter at breast height, or 1.37 m up from ground level), tree height, total
biomass, leaf weight, etc., are calculated. For example, what we do here is prepare
equations (regressions) to calculate the total above-ground biomass of a Sassafras tree in
winter (without leaves) as a function of dbh: we are therefore implicitly assuming that
biomass is directly related to tree diameter.
Allometry is useful because it allows the total biomass of a forest or stand to be
estimated, without having to cut down all the trees, take them back to the lab, dry the
pieces in an oven, and then weigh all the pieces. Part of our study at Totoket Mountain
was to estimate the biomass of the entire forest: click here to jump to that page.
How do we do it, anyway?
To calculate the total biomass of our Sassafras trees, we had to calculate


the weight of the bole
the weight of all the branches
In case you want to try this at home, here's what we did to each tree! We did it for
four trees, of different sizes and shapes, so that our results would be more applicable to
"all" sassafras trees.



We cut down the tree with a chainsaw.
We divided the tree into bole and branches.
For the bole:
o We cut the bole into 1 m long sections
o We weighed all the sections in the field
o We cut a 2-3 cm "cookie" off the end of each section
o We took the cookies back to the lab
o We weighed each cookie (wet weight)
o We measured the thickness of each cookie
o We measured the "outside bark" diameter of each cookie
o We stripped the bark off each cookie
o
o
o
o
o
o
o

We measured the "inside bark" diameter of each cookie
We weighed separately the bark and the wood of each cookie (wet weight)
We oven dried the bark and cookie samples (at 80 C, until dry)
When everything was dry, we weighed the dry bark and dry wood
From these subsamples of each section, we were able to estimate the ovendry weight of each bole section
By adding up the oven-dry weight of the bole sections, we estimated the
weight of the entire bole (for wood, bark, and total weight)
We then estimated a regression line relating tree dbh to total bole biomass
For the branches:
o We measured the basal diameter and length of all branches on the tree
(step A below)
o We took three "representative" branches from each tree back to the lab
o We put these sample branches in the oven and dried them (at 80 C)
o When the branches were dry, we calculated a regression line relating
branch diameter to branch weight (step B below)
o Based on this relationship, we estimated the dry weight of all the branches
on the tree using the basal diameters we measured in the field
o To this we added the oven-dry weight of the dead branches (we brought
these back to the lab, too)
o This allowed us to estimate the total branch dry weight of each tree (step C
below)
o Then we estimated another regression line, this one relating tree diameter
to total branch dry weight (step D below)
o Note that the bark and wood of branches was not separated
By combining our estimates of bole and branch weights, we calculated the total
above-ground biomass of each tree. We then estimated another regression, this one
relating tree diameter to total above ground biomass.
When we calculated our regression equations, we used a log-log transformation on
the data. Rather than make total above ground biomass a function of dbh, we made log10
(total above ground biomass) a function of log10 (dbh). The relationship between the
transformed variables is a linear one: we can calculate this regression line much more
easily than if we dealt with untransformed data. Another effect that the log
transformation has is that it can make large absolute differences appear relatively small:
for example, although the difference between 600 kg and 1000 kg is 400 kg, log(600) =
2.78, log (1000) = 3, and the difference of the logs, 0.22, is less than 8%!
We arrived at the following equations:
Bole biomass:
log10 (bole biomass, g) = 2.3904 * log10 (dbh, cm) + 1.8632
Individual branch weight:
log10 (branch dry weight, g) = 2.807 * log10 (branch diameter, cm) + 1.4418
Total branch weight:
log10 (total branch biomass, g) = 2.5533 * log10 (dbh, cm) + .9020
Total above-ground biomass
log10 (bole + branch biomass, g) = 2.3836 * log10 (dbh, cm) + 1.9566
Basic Tree Data
As described above, we cut down four sassafras trees on the east slope at Totoket
Mountain, North Branford, CT for analysis. Basic data for these four trees are given
below.
Total height, m
Tree age (at base), years
Avg. annual radial increment, mm, last 5
years
DBH, cm
Diameter at base, cm
Tree Tree Tree Tree
1
2
3
4
9.1 16.4 14.7 17.2
73.0 77.0 77.0
5.0
6.4
2.0
0.6
0.9
23.4
28.1
11.8
13.9
16.7
21.1
Crown width, widest, m
Crown width, narrowest, m
Height to lowest live branch, m
Estimated bole dry weight, OD kg
Estimated total branch dry weight, OD kg
(live + dead)
Weight dead branches, OD kg
Estimated biomass, OD kg
(above ground, no leaves)
Average bark thickness, cm
Bark water content (g H20 / g OD)
Wood water content (g H20 / g OD)
Bark density, g / cc
Wood density, g/cc
Total bark weight in bole, OD kg
Total wood weight in bole, OD kg
2.0
6.3
1.5
5.9
6.8
7.2
4.7 137.3
3.7
3.5
8.0
27.5
2.6
2.0
7.0
71.2
0.6
32.0
3.2
5.6
0.3
4.9
1.2
2.2
5.4 169.3
30.7
76.7
2.1
31%
59%
0.26
0.42
19.4
117.0
1.1
26%
39%
0.30
0.41
4.7
22.8
1.5
30%
45%
0.24
0.41
10.1
61.1
Note: some data not available for tree 1, because no cookies were taken (the entire tree
was brought back to the lab, where the branches and bole were separated and oven-dried).
We estimated height-age curves for Trees 2, 3, and 4 by aging the cookies taken at 1
m intervals. In some cases, rot inside the bole prevented an accurate measurement,
because rings could not be counted all the way back to age 1. Best-fit curves (third order
polynomial equations) suggest that, in the case of Trees 2 and 3, some sort of release has
occurred during the last 20 or so years.
Tree 2
Tree 3
Tree 4
We also used data collected by previous years' FES 519b classes. This and more can
be found in our downloadable data workbook.
Estimating total bole weight
Click here to see the data for this graph.
Estimating bole volume
The bole of a tree can be considered as any of a number of three-dimensional solids.
Usually, the bole volume is estimated as if it were a cone, a paraboloid, or a neolid (a
solid that flares at the base). We found that sassafras is pretty much cone-shaped, as the
following graph illustrates.
Estimating weight of individual live branches
Click here to see the data for this graph.
Estimating weight of all branches, live and dead
Click here to see the data for this graph.
Estimating above-ground biomass of whole tree
Click here to see the data for this graph.
The graph below is the same as the graph above, except that the log-log transformation
has not been carried out. Observe that the best-fit line is no longer linear. Also, note that
even though it fits the data very well, the biomass predicted by the equation is rarely
exactly what we measured in the lab (the deviation between measured and calculated
biomass is greater than 20% for some of the larger diameter trees)!
How fast are these trees growing?
We measured the average radial growth over the last five years (1996-1992: the
1997 ring was usually impossible to read due to the bark having been removed) for each
tree from each cookie (1 m height increments along the bole). Tree 2 appears to have put
on more radial growth high in the bole than low in the bole; for Trees 3 and 4, the radial
growth changes little with height.
By taking the average annual radial growth, multiplying this by five, doubling that (to
get the diameter change over the last five years), and then subtracting this value from the
measured dbh, we estimated the tree's diameter in 1993. We then put this value into our
biomass equation, and approximated the tree's biomass in 1993. The trees appear to have
grown by 25-30% over the last five years, as the following table shows.
1998 Biomass 1993 dbh 1998 dbh 1993 Biomass 1998 Biomass
% Change
(from lab, kg)
(cm)
(cm) (from eq., kg) (from eq., kg)
Tree 2
169.3
21.4
23.4
110.5
136.8
+24%
Tree 3
30.7
10.6
11.8
20.6
26.6
+29%
Tree 4
76.7
14.9
16.7
46.5
61.1
+31%