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This paper centers on the macroevolutionary problem surrounding the concept of the vertebrate genus. We have been fascinated by the apparent tendency of members of a genus to have the same shape in contrast to the great differences in shape among genera at the family level. If this is true, genera would be considered shape conservative groups. Our initial view of this contrast in shape variation within and among genera leads us to question whether the same evolutionary processes that produce genera can simply be extended to produce families. To approach this question two things need to be done. First, the morphology of genera must be quantified to yield a more exact idea of how the morphological variation of a family is partitioned into genera. And second, evolutionary models need to be built that make different assumptions about how evolution proceeds. Our quantification of the morphology of genera will involve looking at size and shape variation at the familial and generic levels with multivariate methods. The evolutionary models will be used to make predictions of size and shape variation in families and genera under different evolutionary assumptions. As will be presented below, our models make clearly different predictions of how species will come to fill morphological space. Based on a comparison with real data we can reject some types of evolutionary models as incompatible with real data.