The Middle Devonian brachiopod, Mucrospirifer, was studied over most of its geographical and stratigraphical range in order to test the theory of punctuated equilibria. Punctuated equilibria holds that most evolution is concentrated in rapid speciation events and that the subsequent lifespan of a species is then characterized by approximate morphological stasis. Although many fossil lineages have been studied since the theory of punctuated equilibria was proposed, very few have included broad geographical coverage. To study a species adequately through time, the extent of its morphological variation in space must be known. Specimens of Mucrospirifer were collected from New York, Ontario, Michigan, Pennsylvania, Maryland, and West Virginia from sandstones, siltstones, mudstones, calcareous shales, and limestones spanning 5-7 million years of geological history. Although many species of Mucrospirifer have been proposed, the most recent taxonomic work reduced the number to two and found that the overall shape of the shell and the shape of the fold and sulcus were the best criteria to distinguish species of Mucrospirifer. These same two criteria were applied in this study. Overall shape was examined by Fourier analysis of the outline of each usable adult specimen employing a video digitizing system assembled for this project. Selection of harmonics that contribute most to the shape of Mucrospirifer was aided by stepwise discriminant analysis, and only these harmonics were used in subsequent statistical analyses. Shape differences among adult specimens cannot be attributed to allometry which was not significant when linear regression of log-transformed data for harmonic 0 (size) vs harmonic 2 (shape) was applied. Using cluster analysis, polar ordination, and principal component analysis extensive continuous morphological variation of Mucrospirifer was detected over its geographical range as well as within populations, so that only a single polytypic species, Mucrospirifer mucronatus, could be identified. Although no strong correlation between morphology and lithology was found over the entire study area, using linear regression an east-west trend of increasing roundness was identified in New York state. This trend may be due to an adaptation to water turbulence that decreases from the nearshore in the east to the offshore in the west or to sediment type which becomes finer grained going from east to west. Using principal component analysis and linear regression, no significant directional change in overall shape could be detected. Therefore, morphological stasis characterizes the 5-7 million-year history of Mucrospirifer mucronatus in the study area. These findings lend substantial support to the theory of punctuated equilibria. / Ph. D.