6In the Cambrian and Lower Ordovician, trilobites are abundant and their remains are often the primary components of limestonesOur specimens have been silicified, so that only the limestone is dissolved when exposed to Hydrochloric Acid.CaCO3(s) + 2H+(aq) + [2Cl-(aq)] --> Ca2+(aq) + CO2(g) + H2O(l) + [2Cl-(aq)]
8What are trilobites and how do they grow? (Ontogeny) Protaspid: Disk or globular shape, no true segmentation.Meraspid: Adds thoracic segments with each molt.Holaspid: Gets larger with each molt, adult number of thoracic segments.
9Hypotheses to be tested Shape change during the development of the trilobite Calyptaulax is allometric (Adults are not simply scaled up versions of larger ones).The transition from meraspid to holaspid stage can be seen in the head and trail and is not just dependent on an adult number of thoracic segments.
10Landmark Selection Landmarks are a biological coordinate. Must provide adequate coverage of the formCan be found reliably across specimens in different states of preservation.Consistency of relative positionCoplanarity of landmarks (accounting for orientation)
11Type 1 landmarks are the most useful for defining shape they occur at intersections.Type 2 landmarks are at the end of a line or other feature.Type 3 landmarks are the most unreliable and are only used when they can not be avoided and occur on a curved line.
12These landmarks, A,B, and C work as a axis of symmetry allowing to use partial samples as we can flip the image over the base.ABC
13These landmarks, A,B, and C also act as a baseline to show the direction of shape change vectors.
14Type 2The next three land marks are at the inside edge of furrows S1, S2 and S3
15Type 1The next landmarks are where the same sections (S1 S2 and S3) meet the Axial furrow.
16Type 1Where the occipital and the axial furrows intersect. Where the axial and the palpebral furrow intersect. Where the palpebral and posterior furrow intersect. At the outside most point of the palpebral furrow.
19Landmarks x/y coordinates Semi-landmark coordinates along a curve. LM=11CURVES=1POINTS=50IMAGE=Cran and 0.75cm standard.tifSCALE=Raw DataLandmarks x/y coordinatesSemi-landmark coordinates along a curve.Scaling Factor
20Centroid SizeCentroid size is the square root of the sum of squared distances of a set of landmarks from thier centroid. The centroid is determined by the average of the x,y coordinates.
22Future WorkWe are still collecting data, when we are done we need to apply multivariate statistics to the data.
23Future Work (Procrustes Superimposition) These are trilobite landmark coordinates after they have been superimposed: rotated, scaled by centroid size, and moved so that only shape differences remain.The denominator of the formula for the Procrustes distance between two sets of landmark configurations is the product of their Centroid Sizes.Kim et al. 2002
24Testing the hypothesis of merapsid-holaspid shape change Procustes Distance = shortest distance along an arc between two landmarksHolaspidMeraspidKim et al. 2002
25PCAPrinciple Components Analysis to find out which aspects of shape change explain the most variance as the trilobite grows.
26Thin Plate Spline analysis to show how coordinates deform during different portions of ontogeny and the movement of which coordinates best explains the shape differences.Webster et al. 2011