The study of shark evolution and relationships has always suffered from the fact that sharks possess cartilaginous skeletons and rarely, if ever, leave behind skeletal remains in the fossil record. Because of this, the evolutionary history of sharks has been cobbled together with the teeth they have left behind. Shark teeth are as common as their skeletal material is rare, and museums maintain great collections of fossil teeth. For many years, comparisons between the teeth of different species have been qualitative but in recent years there has been an increase in the number of qualitative, techniques available to paleontologists for comparing animal morphologies and greater ease of use with the advent of computer technologies. These new techniques have added valuable data to debates on relationships within the family Lamnidae that includes species such as Carcharodon carcharias (the great white) and the extinct Carcharocles megalodon (the mega-toothed shark). In this study, the value of using differences in tooth shape to determine relationships was tested through use of Procrustes Fit for resizing and superposition, and then Principle Coordinate Analysis for statistically comparing shape. A comparison was carried out between two fossil populations of C. carcharias from both the San Diego Natural History Museum and the Los Angeles County Museum of Natural History, and a fossil population of the unrelated species Galeocerdo aduncus (an extinct tiger shark). If tooth shape can be reliably used to compare evolutionary relationships, a PCA of the three groups after superposition should reveal that there is no significant difference between populations of the same species while the unrelated species should show a greater degree of difference. This turns out to be the case with G. aduncus clustering separately from the two C. carcharias populations which overlap to such a degree that they are indistinguishable from each other. This study indicates that the data from studies published in previous years using this technique are valid insofar as the techniques can reliably distinguish evolutionary relationships using tooth shape
