----- Forwarded message from Dean Adams <[email protected]> ----- Date: Fri, 17 May 2013 10:23:48 -0400 From: Dean Adams <[email protected]> Reply-To: Dean Adams <[email protected]> Subject: Re: test for antisymmetry To: [email protected]
Adrien, As far as I am aware, antisymmetry has only been applied to univariate data. Typically, antisymmetry is identified by taking the differences between the R and L measures (R-L) and plotting these for a set of specimens as a histogram. When this histogram is bimodal about the origin, antisymmetry is inferred. This is often accompanied by additional statistical tests of the properties of this distribution. For GM shape data, since shape is multi-dimensional, the analogous procedure is not at all straightforward. One reason is that differences in shape between R and L objects are represented as distances, not difference scores (because there is more than one dimension to shape space). Thus, the distribution of R vs. L shapes will only have positive values, rendering the standard statistical approaches to antisymmetry not informative. A second reason the concept of antisymmetry is not easily generalized to multivariate data is that it requires some a priori axis upon which deviations can be defined as 'positive' or 'negative'. For univariate traits, this is easy: by using (R-L), negative values mean L is bigger than R, and the converse for positive values. But how does this extend to multivariate shape data? I'm not sure that it does. Think of the following example. If antisymmetry is present in GM data, one possibility is that there are two 'clusters' of shapes in shape space, where for each object, its R & L shapes are found in different clusters, but where across objects some R shapes are found in cluster 1 while other R shapes are found in cluster 2. In other words, the 'deviations' between R & L are always present, but go in different directions when comparing among specimens. I believe this would represent antisymmetry in a multivariate context, but identifying this pattern is rather ad-hoc and descriptive (i.e., one must look for clusters, and then see whether they correspond to R & L shapes, etc.). Of course, since GM shape space is highly dimensional, there must be other ways that the concept of antisymmetry could be satisfied. That brings us back to the a priori axis. If one could identify some directional axis in shape space upon which R vs. L differences could be projected to identify '+' and '-' values, it is possible that one could infer antisymmetry from this, in a manner analogous to that used for univariate data. However, I know of no mathematical or biological theory that could be leveraged to identify this axis, so that the univariate concept of antisymmetry could be extended to multivariate data (though admittedly I've not thought long and hard about this issue). If others are aware of any GM implementations of antisymmetry I would very much like to know of them. Hope this is helpful. Dean -- Dr. Dean C. Adams Professor Department of Ecology, Evolution, and Organismal Biology Department of Statistics Iowa State University Ames, Iowa 50011 www.public.iastate.edu/~dcadams/ phone: 515-294-3834 On 5/17/2013 1:27 AM, [email protected] wrote: > ----- Forwarded message from [email protected] ----- > > Date: Thu, 16 May 2013 08:42:42 -0400 > From: [email protected] > Reply-To: [email protected] > Subject: test for antisymmetry > To: [email protected] > > dear morphometricians, > > would you know how could I test my data for the presence of antisymmetry > using morphoJ and R? > I have already places 32 landmarks on all my skulls and performed procrustes > fit followed by a procrustes anova. > > I know that I'm supposed to test my data for skewness and kurtosis but I > can't figure out how to concretely do that... > > I was thinking of exporting my asymmetric components from morphoJ and use the > "moments" package from R which contains skewness and kurtosis functions. > But I'm not sure this is a valid method. > > Thank you very much for your advices > > Adrien, (a young morphometrician in progress) > > ************************************************************ > *///////////////////// Ph.D. Student //////////////////////* > ************************************************************ > *////////////////// Université de Liège ///////////////////* > *//Bâtiment B22; Laboratoire de génétique des populations /* > *////////// boulevard du Rectorat 27; 4000 Liège //////////* > *//////////////////////// Belgique ////////////////////////* > *//////////////// Tél. ULg : +32 4 3662130 ////////////////* > ************************************************************ > *///////////////////// McGill University //////////////////* > */ Department of Biology; W3/19 Stewart Biology Building //* > *// 1205 Ave Docteur Penfield; Montreal, H3A 1B1 Canada ///* > *////////////// Office: +1 514 398 5965 ///////////////////* > ************************************************************ > > ----- End forwarded message ----- > > ----- End forwarded message -----
