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Exact(5)
To do so, all individuals are first aligned as a single individual, and their mean shape is calculated.
Finally, the line-circle mean shape is subtracted from specimens.
The mean shape is computed as the mean of these two shapes, which can be calculated as the average between each of the n corresponding coordinates for the line and circle.
Recall that usually the mean shape is chosen as the tangent point [ 49], the point where the tangent space touches Kendall's shape space and which also serves as the origin for the coordinate system in the tangent space; in the present context, this is the completely symmetric consensus.
I generated a second morphospace by instead aligning specimens on the mean shape along the line-circle vector (if a series of lines are drawn between corresponding landmarks on the two shapes, the mean shape is the shape formed of the midpoints of these lines).
Similar(54)
The weakest differentiation in mean shapes was found in Ragnerudsjön Lake (Table 1).
Two mean shapes were defined along each discriminant axes, associated respectively to negative and positive canonical scores, by using multivariate regression of the tangent coordinates upon the canonical score [57].
The extension for the shape data was based on the fact that the Procrustes and Mahalanobis distances of individual observations from the sample mean shapes are measures of deviation that are similar to the absolute value of the deviation from the mean of scalar variables.
Plots of the mean shapes were calculated with R v.3.2.0 [ 70] by using RStudio v.0.97.551 [ 71].
The empirical distribution of population mean shapes was assessed using a principal component (PC) analysis of the resulting shape coordinates.
After applying GPA, residual disparity among configurations depends entirely on shape variation and consensus configurations or mean shapes are obtained.
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Justyna Jupowicz-Kozak
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