Morphometrics

Morphometrics (from Greek μορϕή morphe, "shape, form", and -μετρία metria, "measurement") or morphometry refers to the quantitative analysis of form, a concept that encompasses size and shape. Morphometric analyses are commonly performed on organisms, and are useful in analyzing their fossil record, the impact of mutations on shape, developmental changes in form, covariances between ecological factors and shape, as well for estimating quantitative-genetic parameters of shape. Morphometrics can be used to quantify a trait of evolutionary significance, and by detecting changes in the shape, deduce something of their ontogeny, function or evolutionary relationships. A major objective of morphometrics is to statistically test hypotheses about the factors that affect shape.

"Morphometrics", in the broader sense, is also used to precisely locate certain areas of organs such as the brain, and in describing the shapes of other things.

Three general approaches to form are usually distinguished: traditional morphometrics, landmark-based morphometrics and outline-based morphometrics.

Traditional morphometrics analyzes lengths, widths, masses, angles, ratios and areas. In general, traditional morphometric data are measurements of size. A drawback of using many measurements of size is that most will be highly correlated; as a result, there are few independent variables despite the many measurements. For instance, tibia length will vary with femur length and also with humerus and ulna length and even with measurements of the head. Traditional morphometric data are nonetheless useful when either absolute or relative sizes are of particular interest, such as in studies of growth. These data are also useful when size measurements are of theoretical importance such as body mass and limb cross-sectional area and length in studies of functional morphology. However, these measurements have one important limitation: they contain little information about the spatial distribution of shape changes across the organism. They are also useful when determining the extent to which certain pollutants have affected an individual. these indices include the hepatosomatic index, gonadosomatic index and also the condition factors (shakumbila, 2014).

In landmark-based geometric morphometrics, the spatial information missing from traditional morphometrics is contained in the data, because the data are coordinates of landmarks: discrete anatomical loci that are arguably homologous in all individuals in the analysis (i.e. they can be regarded as the "same" point in each specimens in the study). For example, where two specific sutures intersect is a landmark, as are intersections between veins on an insect wing or leaf, or foramina, small holes through which veins and blood vessels pass. Landmark-based studies have traditionally analyzed 2D data, but with the increasing availability of 3D imaging techniques, 3D analyses are becoming more feasible even for small structures such as teeth. Finding enough landmarks to provide a comprehensive description of shape can be difficult when working with fossils or easily damaged specimens. That is because all landmarks must be present in all specimens, although coordinates of missing landmarks can be estimated. The data for each individual consists of a configuration of landmarks.

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