Function calculates the degree of phylogenetic signal across dimensions of shape space from Procrustes shape variables
physignal.eigen(
Y,
phy = NULL,
Cov = NULL,
Blomberg = FALSE,
unit.tree = TRUE,
lambda = 1,
test = TRUE,
iter = 999,
seed = NULL,
tol = 0.001
)Function returns a list with the following components:
The K-components from an eigenanalysis of the phylogenetic signal matrix, K.
The observed eigenvalues of the phylogenetic signal matrix, K.
The set of eigenvalues from the permuted datasets.
The observed traceK statistic.
The set of traceK statistics from the permuted datasets.
The p-value of traceK from permutation.
The effect size of traceK.
The observed detK statistic.
The set of detK statistics from the permuted datasets.
The p-value of detK from permutation.
The effect size of detK.
The observed Kmult statistic.
The set of Kmult statistics from the permuted datasets.
The p-value of multK from permutation.
The effect size of Kmult.
The number of random permutations used in the resampling procedure.
The matched call
A matrix (n x [p x k]) or 3D array (p x k x n) containing Procrustes shape variables for a set of specimens (it is assumed that the data have been subjected to a Generalized Procrustes Analysis)
A phylogenetic tree of class = "phylo" - see read.tree in library ape
An object covariance matrix describing the phylogenetic relationships among species, which may be used in place of `tree
A logical value to indicate whether GLS-centering or OLS-centering (the default) should be used
A logical value to indicate whether the tree should be scaled to unit height
An optional value for scaling the tree by its phylogenetic signal (as represented by the parameter lambda)
A logical value to indicate whether significance testing should be performed
Number of iterations for significance testing
An optional argument for setting the seed for random permutations of the resampling procedure. If left NULL (the default), the exact same P-values will be found for repeated runs of the analysis (with the same number of iterations). If seed = "random", a random seed will be used, and P-values will vary. One can also specify an integer for specific seed values, which might be of interest for advanced users.
A value indicating the magnitude below which
components should be omitted, following projection. See ordinate
for details.
Dean Adams and Michael Collyer
The function estimates the degree of phylogenetic signal across dimensions of shape space, based on Procrustes shape variables for a given phylogeny. The method is intended to interrogate patterns of phylogenetic signal that are not uniformly distributed across shape space, but rather are concentrated in one or a few dimensions. The degree of phylogenetic signal in data is estimated using a matrix generalization of Blomberg's Kappa (K), and the phylogenetic signal represented by this matrix is decomposed into linear combinations that describe directions of phylogenetic signal within the dataspace containing decreasing levels of phylogenetic signal (Mitteroecker et al. 2024). Two summary measures based on the eigenvalues of K are calculated: the determinant of K (detK) and the trace of K (traceK). Both describe the degree of phylogenetic signal in multivariate data. In addition, the multivariate version of the K-statistic (Kmult: Adams 2014) is also provided. All three statistics are evaluated via permutation, where the shape data is permuted among the tips of the phylogeny. Effect sizes are also provided.
It should be noted that by default the function uses OLS centering when calculating the phylogenetic
signal matrix, unlike most authors who have used GLS centering. Both OLS and GLS centering were
proposed in Blomberg et al.s (2003) original exploration of phylogenetic signal. However, for both
mathematical and computational reasons OLS is used here (see justification in Mitteroecker et al.
2024). Both measures are highly rank correlated with one another (Mitteroecker et al. 2024). Additionally,
using using BLOMBERG = TRUE will result in GLS centering, in which case the statistic Kmult
obtained with this function will be identical to that obtained when using physignal.
Importantly, because detK and traceK are based on the covariance matrix K, singularity can become an issue. In particular, geometric morphometric shape data will not be of full rank, as several dimensions are standardized during the Generalized Procrustes Analysis (one may also have fewer observations than variables, which will also generate redundancies). For this reason, a principal components analysis of the data is performed, and the redundant dimensions are removed so that detK and traceK may be computed (see Mitteroecker et al. 2024). Additionally, in cases where the number of trait dimensions (p) exceeds the number of species (n), i.e., p > n, there are n - 1 rather than p dimensions, but there are no more than n - 2 dimensions of K, because of additional singularity imposed by a matrix product that finds ratio of residual covariance matrices. In these cases, an additional dimension is removed (leaving n - 2) to ensure that K-statistics across permutations are not invariant.
The generic functions, print, summary, and plot all work
with physignal.eigen. The ability to plot the species in the space of K-components is
available (see example).
Mitteroecker, P., M.L. Collyer, and D.C. Adams. 2024. Exploring phylogenetic signal in multivariate phenotypes by maximizing Blomberg's K. Systematic Biology. (In Press).
Blomberg SP, Garland T, Ives AR. 2003. Testing for phylogenetic signal in comparative data: behavioral traits are more labile. Evolution, 57:717-745.
Adams, D.C. 2014. A generalized K statistic for estimating phylogenetic signal from shape and other high-dimensional multivariate data. Systematic Biology. 63:685-697.
gm.prcomp, physignal
if (FALSE) {
data(plethspecies)
Y.gpa <- gpagen(plethspecies$land) #GPA-alignment
#Test for phylogenetic signal in shape
PSe.shape <- physignal.eigen(Y = Y.gpa$coords, phy = plethspecies$phy)
summary(PSe.shape)
plot(PSe.shape)
plot(PSe.shape, type = "vectors")
KC.plot <- plot(PSe.shape$KC)
add.tree(KC.plot, plethspecies$phy, edge.col = 4)
}
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