Describing Morphology

Acknowledgment: Much of the following material is adapted from David Polley's G562 Geometric Morphometrics course material to which serious students are directed.

Verifying Dissonant Statistics by Randy Dudley from The Metropolitan Museum

We have seen the Raup 1966 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 shape. Fundamental to the description of taxa is the need to distinguish them from one another by repeatable means and to describe variation in shape, separate from other characteristics such as size. There are three general approaches to the generation of morphometric data that can be subjected to statistical analyses.

We care because it is only through this means that we can effectively explore theoretical morphospace, addressing issues including:

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.

Possible statistical analyses include:

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: These measurements are indirectly related to shape, but are, in fact measures of distance. Thus, they are useful in examining scaling effects, but in extracting them we disregard direct information on shape. Indeed frequently, the first principal component extracted from such data is usually dominated by differences in size and correlated variables.

D'Arcy Thompson: (1860 - 1948) Was the first pioneer in the investigation of the relationship between growth, evolution, and geometric form. His classic On Growth and Form identifies such famous examples as the relationship between the Fibonaci sequence and spiral patterns in plant growth. In fact, he was preoccupied by the constraints imposed by the interaction of simple transformational processes and specific initial conditions.

Thompson was fond of expressing morphological variation in terms of "transformations" - by which the shape of one species could be transformed into that of another by the application of regular simple transformations, reflected as deformed grids. (E.g. puffer and mola, right.) Although clever and not lacking merit, these reflected a level of subjectivity. Indeed, the technique was pioneered by the Renaissance artist Albrecht Dürer. They pointed out the need for an algorithmic approach to the quantitative analysis of shape, however.

This was ultimately supplied during the 1990s by Fred Bookstein, F. James Rohlf, and colleagues. (See review by Adams et al., 2013.) Here is a synopsis of what has emerged.

A. Traditional morphometrics: size information is preserved but shape is lost.
B. Landmark-based morphometrics: Shape information is preserved.
Landmark-based analysis: Dismisses the measurements of traditional morphometrics and focuses on the distribution of the landmarks - homologous identifiable points in sets of comparable samples. Landmark positions are first recorded as cartesian coordinates, thus preserving information about shape.

A. Ophiacodon, B. Dimetrodon, C. Titanophoneus
Example: For illustration, we show three specimens with different shapes. In practice, a normal data set would contain more. Constraints:

Step 1: Data acquisition. Can be through:

(Schematic only)
Step 2: Procrustes superimposition. A series of steps in which size, positional, and orientation data are removed, leaving only shape.

(Schematic only)
Step 3: Principal Component Analysis. With size and orientation information removed, landmarks can now be treated as variables in PCA. The results map non-correlated sources of variation in shape without respect to size. This can be explored graphically with reference to the original data (right) or through thin-plate spline grids.

Outline-based analysis: An alternate approach involves describing the outline of an object mathematically by the fitting of coefficients of mathematical functions to a regular array of preset semilandmarks around the outline. In this case, there is no expectation that the points represent homologous features.

Schematic for eigenshape analysis.

From Green Tea and Velociraptors
Morphometrics in three dimensions: Most of the techniques discussed here can in principle be adapted for use with three-dimensional objects, although logistics become more complex.

Data acquisition: Depending on the size of the subject:


Finite element analysis of he distribution of bite forces in theropods, from Ichthyosaurs: A Day in the Life...
Finite Element Analysis: From a three dimensional landmark model, it is a sort step to the use of three dimensional models in the actual testing of functional hypotheses through finite element analysis. (Link to video) This method was developed independently by several researchers in North America, Europe, and China during the mid-20th century as a practical approach to problems of civil and mechanical engineering requiring the simultaneous solution of many partial differential equations.

The steps:

Applications of FEA to paleontology:

Consequently, FEA has become a promising technique in functional morphology. Some noteworthy examples include:


Correlation studies: Biologists are fond of performing statistical studies, looking for meaningful correlations between measurable aspects of different parts of animals' anatomies. For instance, one might look at the ratio of the length and depth of birds' beaks vs. the length of their tarsals to see if larger birds have proportionately deeper beaks. Measurements of this sort can be subjected to the full range of statistical analyses. A fundamental assumption of such studies is that all observations be made from independent members of the same underlying population.

However, when samples are being taken from groups of populations nested in a heirarchical phylogeny, this assumption is violated. The example at right shows of how misleading this can be. Imagine a simple phylogeny with two sister clades, one black, the other red. When we make a bivariate plot of data taken from them, there appears to be a strong statistical relationship. But in fact, when we compare values only within each clade, we see very low correlation.

Fortunately, Joe Felsenstein of the University of Washington provided the solution in Felsenstein, 1985: a statistical technique for adjusting data to account for the phylogeny of the taxa sampled, called phylogenetically independent contrasts (PIC). This method is based on the concept that although the taxa may be non-independent, the differences between measured values in them are independent. Statistical correlation techniques are, therefore, applied to pairwise contrasts in measurements from sister taxa. By applying it, meaningful correlation studies can be performed. Without it, they would be meaningless or misleading. Applying this method absolutely requires a known phylogeny. If hypotheses of phylogeny change, the results of correlation studies based on them must be revised, too.

Additional reading: