Biology Reference
In-Depth Information
Glossary
Affine transformation (Also called “uniform”). Transformation (or mapping) that leaves parallel lines parallel.
The possible affine transformations include those that do not alter shape (scaling, translation, rotation) and those
that do (shear and contraction/dilation). See also Explicit uniform terms, Implicit uniform terms (Chapter 5).
Allometry Shape change correlated with size change, sometimes more narrowly defined as a change in the size of
a part according to the power law Y
bX k , where Y is the size of the part, X is either the size of another part or
overall body size, and k and b are constants. There are three distinct types of allometry: (1) ontogenetic, an ontoge-
netic change in shape correlated with an ontogenetic increase in size; (2) static, variation in shape correlated with
variation size among individuals at a common developmental stage; and (3) evolutionary, an evolutionary change
in shape correlated with evolutionary changes in size (Chapters 9, 11).
Alpha ( α )
5
(1) The acceptable Type I error rate, typically 5%; (2) a factor multiplying partial warps before comput-
ing principal components of them; if
α 5
0, principal components of partial warps are conventional principal com-
ponents; when
0, the partial warps are differentially weighted. Either those with lower bending energy are
weighted more highly (
α 6¼
α .
0) or those with greater bending energy are weighted more highly (
α ,
0). Typically,
values of
1 are used. See also Relative warps.
ANCOVA Analysis of covariance. A method for testing the hypothesis that samples do not differ in their means
when the effects of a covariate are taken into account. See also ANOVA, MANOVA and MANCOVA (Chapters
8, 9).
Anisotropic Not isotropic, having a preferred direction. In general, anisotropy is a measure of the degree to
which variation in some parameter is a function of its direction relative to some axis. In geometric morphometrics,
anisotropy usually refers to a measure of an affine transformation
1
1or
2
either the ratio between principal strains, or a
ratio of variances along principal axes. See also Isotropic (Chapter 3).
ANOVA Analysis of variance. A method for testing the hypothesis that samples do not differ in their means.
ANOVA differs from MANOVA in that the means are unidimensional scalars. See also ANCOVA, MANOVA
and MANCOVA (Chapter 9).
Balanced Design An experimental design in which the sample size for each combination of factors is equal. This
makes it relatively straightforward to partition the variance (Chapter 9).
Baseline A line joining two landmarks, used in some superimposition methods to register shapes by assigning
fixed values to one or more coordinates of those landmarks. See also Baseline registration, Bookstein coordi-
nates, Sliding baseline registration (Chapters 3, 4).
Baseline registration A method of superimposing landmark configurations by assigning two landmarks fixed
values (the two landmarks are the endpoints of the baseline). The most common method of baseline registration
is the two-point registration developed by Bookstein, in which the ends of the baseline are fixed at (0, 0) and
(1, 0), yielding Bookstein coordinates. Other methods of baseline registration fix the endpoints at different values
(see Dryden and Mardia, 1998) or only fix one coordinate of each baseline point (see Sliding baseline registra-
tion) (Chapters 3, 4).
Basis A set of linearly independent vectors that span the entire vector space, also the smallest necessary set of
vectors that span the space. The basis can serve as a coordinate system for the space because every vector in that
space is a unique linear combination of the basis vectors. However, the basis itself is not unique; any vector space
has infinitely many bases that differ by a rotation. An orthonormal basis is a set of mutually orthogonal axes, all
of unit length. Partial warps and principal components are two common orthonormal bases used in shape analy-
sis. See also Eigenvectors (Chapters 5, 6).
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