Biology Reference
In-Depth Information
described by
Bookstein (1991)
, semilandmarks can be “fitted” across the curve or surface by
using one of two different algorithms. One algorithm uses the TPS to map each set of coor-
dinates onto the sample mean such that the
bending energy
is minimized. The other algorithm
seeks to minimize the Procrustes distance across the sets of coordinates. Both methods
require iterations of sample mean computation, sliding of the landmarks along the tangent
vectors so as to meet the optimization criterion, and sliding the semilandmarks back to the
nearest point along the curve or surface (
Gunz et al., 2005; Mitteroecker and Gunz, 2009
).
Once the semilandmarks have been “fitted” by one of the two possible algorithms, they
can be treated as homologous landmarks and subjected to further statistical analyses.
Wil-
liams and Slice (2010)
demonstrate how semilandmarks can be effectively used to identify
variation in facial structures that are not well defined by traditional landmarks. The curva-
ture of the nasal aperture, the orbit, the zygomatic bone and arch, and the maxillary alveolar
process were recorded as semilandmarks and then analyzed for age-related changes. This
study found changes in the shape of these structures associated with age as well as popula-
tion and sex-related variation.
Programs for Data Analysis
There exists a wide range of software packages that perform various geometric morpho-
metric analyses. There are utility programs for post-collection data processing, programs
that conduct specific analyses, and comprehensive programs for both geometric morpho-
metric and standard statistical analyses.
Table 12.3
includes some of the more popular
geometric morphometric programs used in biological anthropology along with their capa-
bilities and access information. The free statistical computation and graphical program R:
A Language and Environment for Statistical Computing (R Development Core Team, 2011,
http://www.r-project.org/
)
is also capable of performing many geometric morphometric
analyses and code for various geometric morphometric procedures is freely available,
both from R and from other sources on the Internet, including the SUNY-Stony Brook
Morphometrics site (
http://life.bio.sunysb.edu/morph/
). For using R for both traditional
and geometric morphometrics, the text
Morphometrics with R
(
Claude, 2008
) is a good
place to start.
CURRENT APPLICATIONS OF GEOMETRIC MORPHOMETRICS
IN SKELETAL BIOLOGY
Skeletal biologists have eagerly adopted the tools of geometric morphometrics and have
applied them to a wide range of research questions. This process has integrated the
approaches to data collection and analysis into biological anthropology, and at times, the
needs of anthropological analyses have helped shape advances within geometric morpho-
metrics (
Slice, 2007
). A survey of current applications of geometric morphometrics to human
skeletal biology is presented below and organized by research area. Since the focus of this text
is human skeletal biology, the review does not include studies involving nonhuman primates
or paleoanthropology, although there is a considerable body of geometric morphometric
