Biology Reference
In-Depth Information
Target shape A shape being compared to the reference shape. See Reference.
Thin-plate spline An interpolation function used to predict the difference in shape between a reference and
another shape over all points on the form, not just at landmarks. This interpolation function minimizes the bend-
ing energy of the deformation, which is equivalent to modeling that deformation as smoothly as possible given
the observed landmarks (thus taking a parsimonious approach to interpolation). Thin-plate spline analysis pro-
duces scores for the non-uniform component of the deformation
scores for the uniform component are produced
by a different analysis (Chapter 5).
Transformation See Map.
Two-point shape coordinates See Bookstein coordinates.
Type I, Type II error Type I error is rejecting a true null hypothesis. Type II error is failing to reject a false null
hypothesis. Most approaches to statistics are careful to state and analyze Type I error, much less attention is paid
to Type II error, and it is typically harder to estimate the rate of Type II errors.
Type 1 landmark A landmark that can be defined in terms of local information, such as a landmark located at
the junction of three bones or two bones and a muscle (i.e. anatomical features that meet at a point). There is no
need to refer to any distant structures or maxima/minima of curvature. The typology of landmarks is based on
Bookstein, 1991. See also Type 2 and Type 3 landmarks (Chapter 2).
Type 2 landmark A landmark defined by a relatively local property, such as the maximum or minimum of curva-
ture of a small bulge or at the endpoint of a structure. These are considered less useful than Type 1 landmarks
because their evidence of homology is at least partly geometric rather than purely histological or osteological. See
also Type 1 and Type 3 landmarks (Chapter 2).
Type 3 landmark A landmark defined in terms of extremal points, such as the landmark on the rostrum
furthest
away from
the foramen magnum. Such landmarks are regarded as deficient because they have one less degree of
freedom than they have coordinates (the other degree of freedom is lost when specifying how to locate the land-
mark). Such landmarks can be used in geometric morphometric studies, but the loss of a degree of freedom must
be taken into account when conducting statistical tests. See also Type 1 and Type 2 landmarks (Chapter 2).
Unbalanced Design An experimental design in which the sample size within each combination of the factors is
not equal. This makes it difficult to partition the variance, and gives rise to a variety of different approaches to
calculating the sums of squares in a MANOVA or MANCOVA (Chapter 9).
Uniform components The components describing the uniform deformation. For two-dimensional configurations,
the uniform deformation is described by two components: compression/dilation and shear. The uniform defor-
mation is sometimes considered the zeroth partial warp (Chapter 5).
Uniform deformation A deformation that is purely uniform (or affine), or the purely uniform component of a
deformation. The uniform deformations include only the uniform transformations that alter shape (compression/
dilation and shear). They do not include transformations that do not alter shape (translation, scaling and rotation).
See also Uniform shape component (Chapter 5).
Uniform component scores Scores locating a specimen, relative to the reference, along the uniform components.
The summed squared scores on the uniform components and partial warps equal the Procrustes distance between
each specimen and the reference. Taken together, the uniform and non-uniform scores fully describe the shape
difference between the reference and that specimen (Chapter 5).
Variation, morphological variation A term used to refer to the general idea of variety, usually within a single
population in contrast to disparity which refers to variation among species. Variation is typically measured as the
sample variance:
P
i
5
1
ð
2
x
i
2
x
Þ
S
2
5
ð
n
1
Þ
2
that is, the mean of the summed squared deviations from the mean. See also Disparity (Chapter 10).
Vector A set of
P
coordinates that specify the location of a point in
P
dimensions.
