Biology Reference
In-Depth Information
METHODS OF DATA ANALYSIS
Replacing traditional morphometric variables with landmark coordinates does not
deprive us of the methods we have long used in statistical analyses of morphological data.
We can ask all the questions that we ever asked about morphology. Such questions often
comprise two parts, the first of which
Bookstein (1991)
termed the “existential question”:
is
there an effect on shape? We answer that by determining the probability that the association
between variables is no greater than could have arisen by chance. The second question,
“
what
is the effect?” calls for description. In the ontogenetic series of piranhas discussed
earlier, we can analyze the relationship between shape and size by computing the centroid
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(A)
(B)
(C)
(D)
FIGURE 1.12
Analyzing the impact of size on shape by multivariate regression. (A) Configurations of land-
marks from which differences in position, scale and orientation have been removed; (B) the covariance between
size and shape depicted by vectors of relative landmark displacements; (C) the covariance between size and shape
depicted by a deformed grid; (D) the covariance between size and shape depicted by a deformed grid plus vectors
of relative landmark displacement.
