Why are rare traits unilaterally expressed?: trait frequency and unilateral expression for cranial nonmetric traits...

Based on an analysis of nonmetric trait databases from several large skeletal series in Northern Europe and South America, representing 27 bilateral traits, we report a predictable relationship between the frequency of nonmetric traits and the probability that they are expressed bilaterally. In a wider sampling of traits and populations, this study thus confirms the findings of an earlier study by Ossenberg ([1981] Am. J. Phys. Anthropol. 54:471-479), which reported the same relationship for two mandibular traits. This trend was previously explained by extending the multifactorial threshold model for discontinuous traits to incorporate either separate thresholds for unilateral or bilateral expression, or by a fuzzy threshold in which the probability of bilateral expression increases away from the median threshold value. We show that the trend is produced under the standard multifactorial threshold model for discontinuous traits simply if the within-individual or developmental instability variance remains relatively constant across the range of liability. Under this assumption, the number of individuals in which one side but not the other is pushed over the threshold for trait formation will be a larger proportion of the number of individuals expressing the trait when the trait frequency is low. As trait frequency increases, the significance of within-individual variance as a determinant of trait formation decreases relative to the genetic and among-individual environmental variance. These results have implications for interpreting nonmetric trait data as well as for understanding the prevalence of unilateral vs. bilateral expression of a wide variety of discontinuous traits, including dysmorphologies in humans.