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For each specimen, a reflected copy of the original configuration of landmarks is produced (e.g. by changing the signs for one of the coordinates of all landmarks).
Because the reflection brings the landmarks from the right side onto the left side and vice versa, the paired landmarks are relabelled by exchanging the labels between left and right paired landmarks of the reflected copy to make them compatible with the paired landmarks of the original configuration.
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The pair of unchanged and reflected copies of each configuration is invariant under reflection because the two transformations that were applied to the original configuration (identity and reflection) constitute the entire symmetry group.
An analysis of anterior-posterior differences among vertebrae would use the left-right symmetric component computed from the averages of the original and reflected copies of each vertebra.
The unchanged and reflected copies of each configuration that are included in the Procrustes fit can therefore be interpreted as a set of copies of each original configuration to which the whole set of symmetry transformations has been applied.
We then partitioned the genome into regions reflecting copy number changes and assigned copy number using two independent classification methods (see Materials and Methods).
A triplication was also observed with a ratio of 1.90, demonstrating that ratio accurately reflects copy number.
A copy number state of 2 per individual is considered normal (one copy per chromosome); lower values reflect copy number loss and higher values a copy number gain.
The first principal component of the ddPCR, PRT, and aCGH values was then calculated to generate a single figure, reflecting copy number, for each sample.
Thus, intervals of genetic heterogeneity may reflect copy number variation or rearrangements that are common features of paralog clusters (reviewed in Żmieńko et al. 2014).
An obvious question to be addressed is whether the observed NAV3 aberrations would just reflect copy number changes in larger areas of chromosome 12.
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