DISCUSSION

The results showed that there was no immediate discernable difference in the average distance and symmetry score data collected for the true shape template and deformed template trials. Also, our results show that these reconstructions would typically show small asymmetry when deviation is averaged over the skull. This strongly indicates that it would be just as easy and convincing to reconstruct the deformed pieces from this experiment into an incorrect shape as it would be to reconstruct them into the true one. As per the questions that we raised earlier, we conclude that: 1) puzzle piecing does not necessarily result in the true skull shape; and 2) the fact that deformed skull pieces could be arranged into symmetrical 'skull' does not justify the assumption that plastic deformation from overburden compaction is absent. We argue that retrodeformation methods that use brittle "puzzle piece" reconstruction requires cautious examination of its assumptions. Most importantly, removal of plastic deformation is of vital importance, given that plastically deformed pieces showed improved fit onto an incorrect template.

The considerable variation in the average distance calculations and symmetry scores for the deformed template reconstructions seems to be directly related to the relation of the deformation scheme and the shape of the template skull. In general, deformation schemes that resembled straight X-axis or skull width compression most closely fit the template skull. As stated earlier, the template skull was compressed to 85% of it original width along the established X-axis. By identifying the areas of the specimens that showed the least fit we hope to provide other scientists an idea of where to look to see if and to what extent their fossil is deformed.

This study is merely a preliminary foray into testing "puzzle piece" retrodeformation methods for correcting plastic deformation. More studies need to be done that can statistically test these methods. Several procedures in the methods used in this study need to be addressed. The reconstruction methods allowed for piece overlap, two pieces occupying the same place. This obviously could not happen in an actual physical reconstruction. In the best-fit trials these overlaps hardly happened, but in the other trials the overlaps should be either eliminated or carefully measured to assure more accurate and meaningful results. Another issue that needs to be addressed is the computerized fitting procedure. The computer measures the distance from each vertex of the piece models to the closest surface of the template model. Such a measurement compiles a huge amount of data that has a standard deviation that is often larger than the average distance measurement itself. We propose to conduct a new experiment that performs reconstructions by minimizing the root mean square distance between a series of pre-established landmarks on the specimen in question. We also wish to use a splitting scheme that more closely resembles those found in the natural world. It is possible that the splitting scheme greatly impacts the outcome of such a trial.

Even given the possible improvements listed above, our study represents the first controlled and quantitative examination of the puzzle piecing method of retrodeformation that is being widely used without being tested. However elaborated the model may become, the fact remains that even eight-piece division, which is the simplest model that gave the poorest symmetry score, resulted in a rather symmetrical model with an average asymmetry of less than 1% of the maximum dimension of the skull. This strongly indicates that the puzzle piecing method cannot be validated using symmetry scores. We conclude that independent criteria, such as the knowledge of approximate skull shape as in one published case, are necessary.