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form matrices, one for sample
A
at time 1 and the other for sample
A

at time 2:

The growth matrix for samples representing population
B
is esti-

mated similarly using the estimated form matrices for the

appropriately aged samples:

We now have two growth matrices, each representing an estimate

of the growth pattern for a population. The comparison of two growth

matrices, one for growth of
A
1
into
A
2
and one for growth of
B
1
into
B
2
,

define the differences in relative growth. Growth difference matrix

analysis (
GDMA
) enables comparison of these growth patterns on a

linear distance-by-linear distance basis. The results of
GDMA
report

how change in a linear distance in one sample compares to the change

experienced by the same linear distance in another sample over com-

parable growth intervals.
GDMA
does this for all linear distances.

GDMA
uses the two
GMs
from the samples under study to estimate a

growth difference matrix (
GDM
):

In this notation, two organisms, or samples of organisms have the

same relative growth if and only if the
GDM
consists exclusively of

ratios equal to 1.

5.9 Analysis of example data sets:

differences in facial growth

To demonstrate these various techniques for studying growth and dif-

ferences in growth patterns, we use the data sets introduced in

Chapter 1
. We provide an analysis of facial growth for a species of New

World monkey,
Cebus apella,
and a species of Old World monkey,

Macaca fascicularis
. Individuals from both species were aged accord-

ing to tooth eruption patterns so that we are comparing equivalent

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