Biology Reference
In-Depth Information
landmarks do not correspond to “traits” and landmarks are rarely meaningful as
individual points.
In geometric morphometrics, a configuration, not a landmark, is a datum. What we
measure on individuals is their configuration of landmarks. The “trait” might be the
impact of a mutation on the average configuration, or the impact of some experimentally
manipulated factor on the average configuration. Analyses of configurations are necessar-
ily multivariate, but it may be more useful to think of a configuration as a multidimen-
sional datum rather than as a collection of multiple variables. One reason for stressing the
point is that individual landmarks are not expected to be individually meaningful biologi-
cally; their function is to delimit where changes occur. It is the response of the configura-
tion to some factor that conveys biological meaning. Thus, when designing a measurement
scheme, what we are after is a configuration that allows us to delimit where those
responses occur. Landmarks should therefore provide a sufficiently comprehensive sam-
pling of morphology that the features of biological significance can be discovered. If you
are interested in the biomechanics of lever arms, then you should locate landmarks at the
endpoints of those lever arms else you will not have the data required to analyze them.
However, you will not lose or dilute biomechanical information by including other land-
marks of unknown relevance
if they are not functionally relevant, they will not covary
with measures of performance. However, if your only question is “What is the mechanical
advantage of this jaw compared to that one?”, then there is no reason to do a shape
analysis
the question you are asking is about mechanical advantage, not shape. As
Bookstein (1996)
pointed out, geometric methods might be “overkill” in such purely bio-
mechanical studies. When you want to place those lever arms in a broader morphological
context, geometric morphometrics helps to provide one.
CRITERIA FOR CHOOSING LANDMARKS
Ideally, landmarks are (1) homologous anatomical loci that (2) provide adequate cover-
age of the morphology, and (3) can be found repeatedly and reliably. Two other criteria
may also be important under some conditions, that landmarks (4) do not switch positions
relative to each other and (5), in the case of two-dimensional (2D) landmarks, lie within
the same plane. That last criterion is the only one specific to two-dimensional data, and
information that is either lost by restricting landmarks to one plane or made difficult to
interpret when landmarks are not coplanar, is what makes three-dimensional data so
useful.
Homology
In the context of landmarks, the criterion of homology means that the points on one
specimen correspond (as the “same” point) to that point on all individuals. For example,
a landmark located in the middle of the mental foramen of the mandible of one individual
is homologous to a landmark located in the middle of the mental foramen of another
individual. Similarly, a landmark located in the middle of the mandibular foramen of the
