On the characterization and interpretation of phenotypic ellipse geometry, with examples from Canis and sigmodontine rodents.

Data on the shape of a group of organisms can be conceptualized as forming a point cloud in the multivariate space of measurement. This is literally true for traditional linear measures, while in a geometric morphometric context the cloud resides in Kendalls shape space, tangent to the true shape space. Regardless of the method of construction, the topology of this point cloud, or phenotypic (hyper)ellipse, is a beguiling target for evolutionary analysis. Reordination of the axes will not change the geometry of this phenotypic ellipse, and the notion that its geometry carries a meaningful biological signal is an old idea; but the character of this signal is often elusive. This paper explores the application of the most commonly used parameter designed to summarize differences in phenotypic ellipse geometry (relative eigenvalue variance, or Vrel), and demonstrates that it is incapable of differentiating between several plausible ways in which phenotypic ellipse geometry might differ among species, because it confounds three separate parameters necessary to describe the ellipse. Two example data sets are analyzed to illustrate variability in phenotypic ellipse geometry and draw conclusions about observed differences. The first case compares wolves to domestic dogs, and replicates previous findings of much greater variance yet tighter integration in dogs. This calls into question the simple model of a single peak in the fitness landscape of dogs. The second example comprises geometric morphometric landmarks from the jaws of a clade of sigmodontine rodents, and allows comparison of ellipse geometry in a phylogenetically controlled setting with qualitative ecological categories. Three parameters are found to vary in concert along a grade of most to least ecologically specialized: the phenotypic variance, the effective rank (dimensionality), and the degree of covariance (Vrel and related metrics). Use of all three of these quantities to characterize the geometry of the phenotypic ellipse is advocated, as all are necessary to characterize how variance is distributed in the ellipse in different taxa. The phenotypic ellipse geometries illustrated here appear to reflect something of the geometry of the adaptive peak upon which each taxon sits; or that they represent (aspects of) the mapping function of adaptive peak to phenotypic ellipse, in ways first predicted by Simpson in the twentieth century.