Thank you Philipp for sharing. I am particularly interested in the modified 
PCA that maximizes shape variation around the symmetric origin rather than 
the sample mean.

May I ask can the following line of R code be implemented for this purpose:

prcomp(x, retx = TRUE, *center = FALSE*, scale. = FALSE, tol = NULL, rank. 
= NULL, …)

where x is a matrix containing asymmetry vectors (shape difference between 
original and relabled reflections) for all specimens with n (number of 
specimens) rows and p*k columns (p landmarks in k dimensions).

Is the above R code correct? If I understand correctly, the center argument 
should be set to F, then what about the scale. argument?

Best regards,
Lv

On Wednesday, 29 April 2020 23:04:45 UTC+8, mitterp3 wrote:
>
> Dear morphometricians,
>
>
> I hope you are all doing well in these difficult times!
>
>
> I would like to draw your attention to some morphometrics-related papers 
> that we published this year.
>
>
> Mitteroecker P, Bartsch S, Erkinger C, Grunstra NDS, Le Maître A, 
> Bookstein FL (2020) Morphometric Variation at Different Spatial Scales: 
> Coordination and Compensation in the Emergence of Organismal Form. 
> Systematic Biology, early view, https://doi.org/10.1093/sysbio/syaa007
>
>
> In this paper we introduce a new approach for studying integration and 
> canalization of size and shape variation (partly derived from Fred's work 
> on self-similar shape distributions). It is based on the idea that if 
> anatomical elements vary independently, then their variation accumulates at 
> larger scales (or for composite structures). Quantifying size or shape 
> variation relative to its spatial scale thus allows for the identification 
> of coordinating or compensating processes during development and evolution.
>
>
> Neubauer S, Gunz P, Scott NA, Hublin J-J, Mitteroecker P (2020) Evolution 
> of brain lateralization: a shared hominid pattern of endocranial asymmetry 
> is much more variable in humans than in great apes. Science Advances 
> 6(7):eaax9935
>
>
> In this paper we present a multivariate analysis of shape asymmetry with a 
> slightly modified version of PCA that maximizes shape variation around the 
> symmetric origin, not the sample mean. 
>
>
> Mitteroecker P (2020) Morphometrics in Evolutionary Developmental Biology. 
> In: Nuno de la Rosa L, Müller G (eds) Evolutionary Developmental Biology. 
> Springer, Cham
>
>
> This is a brief review of geometric morphometrics in evolutionary 
> developmental biology.
>
>
> Best wishes,
>
>
> Philipp 
>
>
> https://www.researchgate.net/profile/Philipp_Mitteroecker
>

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