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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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