Biology Reference
In-Depth Information
of the independent variable. The term is also used for the coordinates obtained by a Procrustes superimposition,
the Procrustes residuals, which are deviations between individual specimens and the reference.
Resistant-fit superimposition A superimposition method that uses medians or repeated medians (rather than a
least squares error criterion) to superimpose forms. The method is intended to be resistant to large localized
shape differences, such as those produced by the Pinocchio effect. RFTRA is an example of this type of method.
See also Repeated medians, RFTRA (Chapter 4).
RFTRA (Resistant-fit theta-rho analysis) A resistant-fit superimposition method using the method of repeated
medians to determine the scaling factor and rotational angle. See also Resistant fit and Repeated median
(Chapter 4).
Rigid rotation A rotation of an entire vector or matrix by a single angle. Rigid rotations do not alter the size,
shape or location of the object. Rotations are often represented by square matrices. The rotation matrix:
cos
θ
2
sin
θ
R
5
sin
θ
cos
θ
rotates a 2
N
matrix through an angle
θ
. When different vectors are multiplied by different angles, the rotation
3
is oblique, not rigid.
RMS scatter The square root of the mean of the summed squared distances of specimens about their mean (root
mean square, RMS). It is thus the square root of the variance as measured using Procrustes distances, and a linear
measure of the variability of a group (Chapter 14).
Row vector A vector with coefficients in a row. Contrast to a Column vector.
Sample The collection of observed individuals representing members of a population. An individual observation
is the smallest sampling unit in the study, which might be an individual organism or one of its parts, or a collec-
tion of organisms such as a species or a bacterial colony (Chapter 8).
Scalar A real or complex number.
Scale (1) Noun
size of an object (given some definition of size); (2) verb
to change the size of an object (equiva-
lent to rescale).
Scaling factor A constant which is used to change the scale or size of a matrix or vector. This is done by multiply-
ing or dividing the matrix or vector by the constant.
Score In morphometrics, a coefficient locating a specimen along a vector, calculated by projecting the specimen
onto an axis. Usually, scores locate the position of a specimen relative to the axes of a coordinate system. They
are calculated by taking the dot product between an axis of the coordinate system and the data of a specimen.
The scores are linear combinations of the original variables. Partial warp scores locate the position of an individ-
ual specimen relative to the coordinate system provided by the partial warps. Similarly, principal component
scores locate the position of an individual specimen relative to the coordinate system provided by the principal
components. Scores can be calculated relative to any basis of a vector space because each basis provides a coordi-
nate system for that space. See Dot product.
Semilandmark A point on a geometric feature (curve, edge or surface) defined in terms of its position on that fea-
ture (e.g. at 10% of the length of the curve from one end). Semilandmarks are used to incorporate information
about curvature in a geometric shape analysis. Because semilandmarks are defined in terms of other features,
they contain less information (fewer degrees of freedom) than landmarks (Chapter 2).
Shape In geometric morphometrics, following Kendall, shape is all the geometric information remaining
in an landmark configuration after differences in location, scale and rotational effects are removed (Chapters 1,
2, 3).
Shape coordinates Within geometric morphometrics, coordinates of landmarks after superimposition (Chapters
3, 4)
Shape space Within geometric morphometrics, Kendall's shape space. The term is more general, however, as
it can apply to any space defined by a particular mathematical definition of shape. There are shape spaces for
outline measurements, for example. There are also shape spaces based on different definitions of size. The charac-
teristics of these various shape spaces are not necessarily the same as those of Kendall's (Chapter 4).
