GEOL 331/BSCI 333 Morphometrics, Functional Morphology & Biomechanics

GEOL 331/BSCI 333 Principles of Paleontology

Fall Semester 2020

Morphometrics, Functional Morphology & Biomechanics

Landmarks on the skull of the Late Cretaceous turtle Bauruemys elegans, from Mariani and Romano (2017) doi: 10.7717/peerj.2890

Key Points:

•Morphometrics is the quantitative study of form. There are many available morphometrics to study form and its change with ontogeny, evolution, taphonomy, etc.

•Principal Components Analysis (and its close cousing Principal Coordinates Analysis) are the real workhorse methods in morphometrics, summarizing multiple variables at once.

•Morphospaces are the expression of quantified shape into graphical form. There are both theoretical (mathematical) morphospaces, determined by a priori selection of the axis variables; and empirical morphospaces, derived directly from the morphometric analysis results.

•Our ability to reconstruct the function of extinct forms comes through multiple lines of evidence: analogies with the function in extant animals with similar forms; phylogenetic inferences such as the extant phylogenetic bracket method; biomechanics and other cases of modeling; trace fossil analyses; and correlations between phenomena.

•That said, not all form is functional. Some features at least start as "spandrels": the byproduct of the constructional development of the organism rather than actively-selected traits.

"If you want to inspire confidence, give plenty of statistics. It does not matter that they should be accurate, or even intelligible, as long as there is enough of them." -- La poétique de l'espace, Gaston Bachelard (1958)

MORPHOMETRICS: INTRODUCATION TO THE ANALYSIS OF SHAPE<br>We encourage everyone interested in this subject to examine the excellent "PalaeoMath" series of articles by Norm MacLeod. Furthermore, for those interested in exploring these techniques directly, please check out the following software packages:

Wolfram's Mathematica<br>PAST: Paleontological Statistics<br>R (and see the instructions "R for Palaeontologists" by Mark Bell.)

Note that these notes are by no means comprehensive: you can take (literally) entirely courses on morphometrics, statistical analyses, and functional morphology.

Verifying Dissonant Statistics by Randy Dudley from The Metropolitan Museum

We have seen the Raupian attempt to reduce morphological variation to a small number of parameters. In all but the simplest systems, such a method greatly oversimplifies morphology. Nevertheless, the need to describe morphology with quantitative rigor is fundamental to descriptive paleontology, and to the testing of hypotheses of functional morphology. In this lecture we consider morphology and function separately.

Morphometrics : The quantitative study of form, including both size and shape. Fundamental to the description of individual specimens and collections of specimens in order to: recognize the degree of distinctiveness of different morphs (which might be age stages, sexes, taxa, etc.); trace changes due to evolution, ontogeny, etc.; and to remove the disruptive effects of taphonomy by retrodeformation back to the original shape.

Traditional morphometrics : Measurements that have become standardized for the description of morphology through tradition, usually owing to their lack of ambiguity. Naturalists have been using calipers to obtain quantitative information about morphology for centuries. That information has been fed into multivariate statistical analyses for a full century. These begin to enable us to describe distributions of morphological variation.

The key here is to develop and recognize landmarks : points on a body (often where bones or other body parts join together) which can be compared from one specimen to another.

But what do the data actually mean? In traditional morphometrics, data are measurements of the distances between points on a specimen. These points may be:

Landmarks : Discrete points marked by homologous features (right - red) like:

Foramina<br>Intersections of sutures in bones<br>Branching points of veins<br>Other similar points

Semilandmarks : Arbitrary points on the exterior margin describe shape but may be non-homologous (right - blue) like:

points of maximum width<br>the tips of snouts<br>etc.

These measurements are indirectly related to shape, but are, in fact measures of distance. We might plot these onto a standard Cartesian coordiate system (with some spot arbitrarily chosen as the origin), or by a self-generated coordinate system resulting from all distances between all points.

One of the most standard of all statistical analyses is:

From Wikipedia

Least-squares linear regression : A cluster of bivariate data points are reduced to a line that minimizes the residuals - distances from the line to the data points - on the Y variable on the the square root of the sum of their squares. The regression line represents an...