Procrustes Analysis
A technique from geometric morphometrics known as Procrustes analysis was used to examine ontogenetic shape changes in Hiscobeccus capax. In geometric morphometrics and statistics, shape is defined as the spatial information about an object that is preserved when effects of location, scale, and rotation are removed (Kendall, 1989). Procrustes, the namesake of this technique, was a character in Greek mythology who offered travellers a place to rest, but made them fit the shape of his iron bed by stretching or cutting them to the appropriate size! Procrustes analysis and similar morphometric techniques represent objects of interest as a series of landmarks, defined as discrete anatomical points corresponding between taxa, or features that are maintained throughout the life history of a single species (Bookstein, 1991). In Procrustes analysis, configurations of landmarks are relocated to a common point in space by translating the geometric centroid of each landmark constellation to the origin. The scaling procedure is based on resizing all landmark coordinates according to a predefined size metric. For example, centroid size, the metric used in this study, is defined as the summed Euclidean distance between each landmark and the centroid of the entire landmark configuration (Dryden and Mardia, 1998). Rotational differences between landmark constellations are eliminated by orienting each set of landmarks according to a reference form until the sum of squares difference between the two configurations is minimized (Rohlf and Slice, 1990). A rotation procedure based on singular value decomposition of landmark configuration matrices is recommended by Bookstein (1997), and was used in this study. Although several software packages for Procrustes analysis are available, no software exists that can implement this technique based on interlandmark measurement data. For this project, I wrote custom R code that performs Procrustes analysis on three-dimensional landmark coordinates determined based on linear interlandmark measurements (code and documentation available upon request).
After translation, scaling, and rotation, landmark data reflect morphological differences among objects within a dimensionless shape space. The resulting shape coordinate data have great utility for morphometric analysis because they can be treated using a variety of multivariate statistical techniques. For instance, principal component analysis is commonly applied to shape coordinate data in order to determine how external variables contribute to morphological variation between samples, or to determine what landmarks contribute most to shape variation within a species.
After translation, scaling, and rotation, landmark data reflect morphological differences among objects within a dimensionless shape space. The resulting shape coordinate data have great utility for morphometric analysis because they can be treated using a variety of multivariate statistical techniques. For instance, principal component analysis is commonly applied to shape coordinate data in order to determine how external variables contribute to morphological variation between samples, or to determine what landmarks contribute most to shape variation within a species.
Flume Tank Observation
A one-way flume tank was used to examine patterns of passive flow through H. capax (Figure 1). One-way recirculating flume tanks are used to produce unidirectional laminar flows such that fluid phenomena of biological or engineering interest can be studied across a range of different flow velocities. The channel of the flume used in this study measured 3.5 m long by 0.27 m wide, and was filled to a maintained water depth of 0.23 meters during all experiments. A flow-straightener was placed immediately in front of the channel inlet in order to reduce turbulence and maintain laminar flow within the flume.
During every flow experiment, a single model brachiopod was placed in the middle of the flume channel, 1.25 m downstream of the channel inlet. For each experiment, the model was secured to the base of the flume channel with a small amount of plasticine, and positioned in one of several possible life orientations.
Patterns of passive flow through the model brachiopods were visualized by injecting diluted volumes of India ink approximately 5 cm upstream of each model using a pipette connected to a length of aquarium airline hose.
During every flow experiment, a single model brachiopod was placed in the middle of the flume channel, 1.25 m downstream of the channel inlet. For each experiment, the model was secured to the base of the flume channel with a small amount of plasticine, and positioned in one of several possible life orientations.
Patterns of passive flow through the model brachiopods were visualized by injecting diluted volumes of India ink approximately 5 cm upstream of each model using a pipette connected to a length of aquarium airline hose.