An intriguing phenomenon in the study of evolutionary rates of morphological change measured from fossil lineages has been the dependence of these rates on the inverse of the measurement interval. This effect has been reported across wide ranges of species as well as within single lineages, and has been interpreted as representing a smooth extension of evolutionary rate from generational timescales to paleontological timescales, suggesting that macroevolution may be simply microevolution extended over longer intervals. There has been some debate about whether this inverse dependence is a real feature of evolutionary change, or a mathematical or psychological artifact associated with the interpretation of data.

Our analysis indicates that the strong inverse dependence of rate on interval is an artifact produced by the phenomenon of spurious self-correlation. Spurious self-correlation can appear in any calculation when a ratio is plotted against its denominator, as is done in plotting rate versus interval, and when these two quantities are not well correlated with one another. We demonstrate that the effect of spurious self-correlation appears in seven published data sets of evolutionary rate that range from taxonomically broad compendia to studies of single families. The effect obscures the underlying information about the dependence of evolutionary change on interval that is present in the data sets. In five of the seven data sets examined there is no significant correlation between the extent of evolutionary change and elapsed time. Where such a correlation does exist, the inverse dependence of rate on interval length is weakened. We describe the role played by taxonomic, dynamic, and character inhomogeneity in producing the lack of correlation of change with interval in each of these data sets. This lack of correlation of change with interval, and the accompanying inverse correlation of rate with interval, most likely arises from discontinuous modes of evolutionary change in which a distinct long-term dynamic dominates net change over geological time spans. It is poorly explained by the extrapolationary microevolutionary models that have been said to account for this phenomenon.

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