research proposal, part 1

In my analysis, I will measure size of the origin and insertion points in the skulls of theropods, compares those to skull strengths and positions of the jaw joint relative to the tooth row, then a phylogenetically independently analyze the results for statistically significant trends in theropods evolution. I intend to use the modern American alligator (Alligator mississippiensis) and various non-migratory birds as morphological analogues. I also intend to identify similar patterns in crocodilian evolution and use them as a control group to test the validity of my results. To do this, I am compiling illustrated reconstructions of theropods skulls from the literature, then measuring the area of all of the fenestrae in the skulls and the total lateral and dorsal area of the skulls using Scion Image software. This will produce a spreadsheet with the absolute and relative areas of the infra and super temporal fenestae, as well as the orbits, anorbital fenestae and nares. I will also measure the area of the antorbital fossa and the narial fossa. Once I have this data, it is simple to find correlations between these areas, which can be fed into phylogenetically independent analysis in order to see if these are true evolutionary trends.
After that, assuming that a line of best fit can be applied to the tooth row, I will plot points on the tooth row in the x/y plane then find then use the arcsin of the slope of that line to find the angle of the tooth row relative to the horizontal axis. I can then use imaging software to rotate the image so that the tooth row is horizontal. From this I can then measure the distance vertically between the jaw joint and the tooth row as well as the inclinations of the major axis of each of the laterally facing fenestae, the angles between the nuchal crest, the squamosal and the jaw joint. In this position, I can also measure the eccentricity of the fenestrae in terms of ellipses with the same area and find the center of each fenesta. I can then find the angle of the inclination from the jaw joint to the center of each fenestra.
In the dorsal view, I can simply make the long axis of the skull horizontal to make these measurements.
following blogs will relay the imporance and the use of each of these measurements.