Ordination is a common tool for reconstructing paleoecological gradients for ordering samples and taxa along one or more axes of variation in faunal composition. The primary source of variation, known as the primary gradient, commonly is highly correlated with water depth in marine systems, and elevation or moisture in terrestrial systems. When ordination sample scores are plotted stratigraphically, they commonly reveal long-term patterns of variation related to changes in this primary gradient, and these patterns have proved useful in regional correlation. In addition, ordination scores display high-frequency, high-amplitude patterns of variation unrelated to this primary gradient. The origin of this high-frequency variation has been enigmatic, but recently has been argued to reflect faunal patchiness. Numerical modeling of ordination scores derived from the Upper Ordovician Kope Formation of the Cincinnati, Ohio area is used here to demonstrate that such high-frequency patterns of variation indeed can arise from the presence of faunal patchiness along ecological gradients. The magnitude of this variation is controlled by the peak-abundance distribution of fossil taxa as well as the abundance distribution of a taxon at any given position along the primary gradient. Replicate sampling or moving averages should be employed to control for this high-frequency variation before ordination sample scores can be treated as a suitable proxy for environmental factors such as water depth, elevation, or moisture.

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