Morphometric analyses are commonly performed on organisms, and are particularly useful in analysing the fossil record. In this use, it is assumed that morphometrics can quantify a trait of evolutionary significance, and by detecting changes in the shape of organisms, deduce something of their or evolutionary relationships.
"Morphometrics", in the broader sense of the term, is also used to precisely locate certain areas of featureless organs such as the brain, and is used in describing the shape of other things.
An object's shape be described in many ways – a defined sequence of measurements can be taken; the position of certain important landmarks can be recorded, or the outline of the object can be defined. Each of these exaggerates a certain aspect of an object. Morphometric analysis begins by obtaining and (usually) digitising one of these suites of descriptors. Since morphometrics is concerned solely with shape, analysis begins by removing confounding factors – size, rotation and location must all be corrected for.
Typically, analysis begins with principal component analysis, which highlights any trends and makes it easy to spot any correlation with other features.
The methodology is useful in cases where linear and angular data are available, and is of great utility in study of growth. However, it can only distinguish changes in length, and cannot be used to map how these changes are accomplished.
Well chosen landmarks reflect homologous points – i.e. points with evolutionary significance. In order for a landmark to be of utility, it must be present on all specimens studied.
The number of landmarks which can provide meaningful data is approximately equal to the number of specimens sampled: if there are more landmarks than specimens, some landmarks are redundant, and results produced may be unsubstantiated.
Outline analysis is often considered an alternative to be used only when landmarks are too difficult to define or observe. This is in part due to the difficulty in collecting 3D outlines, which has restricted the data to a relatively information-empty 2D line drawn round the edge of specimens. However, the increasing availability of 3D mapping techniques, such as laser rangers, is making 3D outline analysis (using semilandmarks on "semilandmark-lines") an increasingly attractive alternative. As this discipline is a rapidly developing field of research, pioneered by Norm MacLeod and others, its techniques have not yet stabilised (and will not be discussed here at present).
The use of outline data is in some ways inferior to geometric analysis, but for many shapes it can be more informative. Both techniques pick up different forms of variation and ideally both should be considered in tandem. The perceived failings of outline morphometrics are that it doesn't compare points of a homologous origin, and that it oversimplifies complex shapes by restricting itself to considering the outline and not internal changes. Also, since it works by approximating the outline by a series of ellipses, it deals poorly with pointed shapes.
Detractors of the technique claim that the loss of information means that unrelated organisms can be mistakenly grouped together – a famous example being that outline analysis struggles to differentiate a scapula from a fortuitously shaped potato chip. However, this stems partly from a misapplication of the technique; and the same criticism can be levelled at geometric morphometrics, which groups (for example) a shark more closely to an ichthyosaur than a swordfish.
In practice, there are a number of ways of quantifying an outline. Older techniques have been superseded by the two main modern approaches: eigenshape analysis,Lohmann, G.P. (1983). "Eigenshape analysis of microfossils: A general morphometric procedure for describing changes in shape". Mathematical Geology 15 (6): 659–672. Retrieved on 2008-03-10.> and elliptical fourier analysis (EFA),Ferson, S.; Rohlf, F.J.; Koehn, R.K. (1985). "Measuring Shape Variation of Two-Dimensional Outlines". Systematic Zoology 34 (1): 59–68. Retrieved on 2008-03-10.> using hand- or computer-traced outlines. The former involves fitting a preset number of semilandmarks at equal intervals around the outline of a shape, recording the deviation of each step from semilandmark to semilandmark from what the angle of that step would be were the object a simple circle. The latter defines the outline as the sum of the minimum number of ellipses required to mimic the shape.
Both methods have their weaknesses; the most dangerous (and easily overcome) is their susceptibility to noise in the outline. Likewise, neither compares homologous points, and global change is always given more weight than local variation (which may have large biological consequences). Eigenshape analysis requires an equivalent starting point to be set for each specimen, which can be a source of error EFA also suffers from redundancy, in that not all variables are independent. On the other hand, it is possible to apply them to complex curves without having to define a centroid; this makes removing the effect of location, size and rotation much simpler. An alternative to eigenshape analysis is to treat the semilandmarks as landmarks – which is of limited value.
Landmark data allows the deviation of an individual specimen from the mean to be visualised via thin plate splines. These visualisations are formed by calculating the mean location of landmarks, and drawing a rectilinear grid over them. This grid is then deformed ("stretched") so as to keep the landmarks in the same grid square, while moving the points themselves to their location in each specimen (see figure [upload imminent]).
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