Biology Reference

In-Depth Information

Although this analysis was developed specifically for the comparison

of growth patterns, it can be used to study related problems in biology.

For example, Lague and Jungers (1999) used
GDMA
to study differences

in patterns of sexual dimorphism in joint surface morphology among

hominoid species. Other problems that require a quantitative method for

comparing comparisons may also be studied using the method.

5.8 Growth difference matrix analysis: comparing

patterns of growth using growth matrices

“Great as are the differences between the rates of growth in different parts

of a complex organism, the marvel is that the ratios between them are so

nicely balanced as they are, and so capable of keeping the form of the

growing organism all but unchanged for long periods of time, or of slow-

ly changing it in its own harmonious way. There is the nicest possible

balance of forces and resistances in every part of the complex body; and

when this normal equilibrium is disturbed, then we get abnormal growth,

in the shape of tumours and exostoses, and other malformations and

deformities of every kind.”

D'Arcy Thompson (1992)

Our interest may be less in defining a single growth pattern as in

understanding how the growth pattern for one group differs from that

of another. For example, an abnormal growth pattern needs to be com-

pared to a normal growth pattern to be understood. The comparison of

growth patterns can only be done in a coordinate system-free method of

measurement. Our presentation of a coordinate system-free system for

the comparison of growth patterns follows methods previously present-

ed by Richtsmeier and Lele (1993).

To compare growth patterns of two populations, four samples are

used in analysis. Each sample must contain data for the exact same

landmarks. Let us say that we have collected sample data from indi-

viduals of population
A
from two age groups, 1 and 2. We refer to these

samples as
A
1
and
A
2
. We have also collected sample data from corre-

sponding age groups in population
B
. We refer to these samples as
B
1

and
B
2
. In this example, we assume that the populations have been

aged correctly, according to comparable aging criteria.

The first step is to calculate the growth pattern for the samples that

represent population
A
. The growth matrix is estimated using two

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