**ABSTRACT:** Given that characters exhibiting macroscopic asymmetry have evolved in a wide variety of taxa, heritable variation for bilateral asymmetry must have arisen at some point in their history, The recognition that heritable variation may underlie some statistical asymmetries not only raises concerns about the incautious use of statistical estimates of FA in studies of developmental stability, but it suggests some intriguing questions about the possible evolutionary origins of macroscopic asymmetries. First, we developed an additive model of bilateral variation based on some simple assumptions about the developmental control of bilateral variation. Second, using a new approach for studying statistical asymmetries, we conducted an analysis of bilateral variation in eight metrical traits of a harpacticoid copepod (*Tigriopus californicus*) to search for novel forms of statistical asymmetries. The model we developed revealed three independent statistical asymmetries of potential evolutionary significance: a) a previously unrecognized form of asymmetry (referred to here as normal covariant asymmetry), b) antisymmetry, and c) directional asymmetry. Because each pattern of variation would seem to require different amounts and kinds of developmental-genetic information (a- only negative feedback between sides (bilateral inhibition), b- both bilateral inhibition and average departure from symmetry (bilateral offset), c- bilateral inhibition, bilateral offset, and a consistent overdevelopment of one side or the other (side-bias Control), those requiring less information would seem more likely to represent earlier stages in the evolution of macroscopic asymmetries. Our analysis of bilateral variation in *Tigriopus* revealed no evidence for any form of statistical asymmetry other than fluctuating asymmetry. However, a significant positive covariation between sides, even after correction for body size variation, suggested that factors influencing relative limb length (whether genetic or environmental) affected both sides equally rather than one side at the expense of the other. Finally, we note that certain statistical asymmetries (directional asymmetry, any form of covariant asymmetry) may render characters unreliable for estimating developmental stability because, unlike pure fluctuating asymmetry, they may signal a genetic component to asymmetry variation.

Developmental-genetic factors presumed to underly different patterns of bilateral variation. Concentric lines correspond to contour- intervals of equal probability for each distribution. L= dimension of left side, R= dimension of right side.

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*(revised Nov. 4, 2002)*