Function quantifies the degree of morphological integration between modules of Procrustes-aligned coordinates
integration.test(A, A2 = NULL, partition.gp = NULL, iter = 999,
seed = NULL, print.progress = TRUE)A 3D array (p x k x n) containing GPA-aligned coordinates for all specimens, or a matrix (n x variables)
An optional 3D array (p x k x n) containing GPA-aligned coordinates for all specimens, or a matrix (n x variables) for a second partition
A list of which landmarks (or variables) belong in which partition (e.g. A,A,A,B,B,B,C,C,C) (required when only 1 dataset provided)
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 logical value to indicate whether a progress bar should be printed to the screen. This is helpful for long-running analyses.
Objects of class "pls" from integration.test return a list of the following:
The estimate of morphological integration: PLS.corr. The mean of pairwise PLS correlations between partitions is used when there are more than two partitions.
The pairwise r.pls, if the number of partitions is greater than 2.
The empirically calculated P-value from the resampling procedure.
The singular vectors of the left (x) block (for 2 modules only).
The singular vectors of the right (y) block (for 2 modules only).
The correlation coefficients found in each random permutation of the resampling procedure.
Values of left (x) block projected onto singular vectors (for 2 modules only).
Values of right (y) block projected onto singular vectors (for 2 modules only).
The singular value decomposition of the cross-covariances (for 2 modules only).
Input values for the left block (for 2 modules only).
Input values for the right block (for 2 modules only).
Left block (matrix) found from A1 (for 2 modules only).
Right block (matrix) found from A2 (for 2 modules only).
The number of random permutations used in the resampling procedure.
The match call.
The function quantifies the degree of morphological integration between modular partitions of shape data as
defined by landmark coordinates. It is assumed that the landmarks have previously been aligned using
Generalized Procrustes Analysis (GPA) [e.g., with gpagen]. The function may be used to assess
the degree of morphological integration between two or more sets of variables.
The function estimates the degree of morphological integration using a two-block partial least squares analysis (PLS). When used with landmark data, this analysis is referred to as singular warps analysis (Bookstein et al. 2003). If more than two partitions are defined, the average pairwise PLS correlation is utilized as the test statistic. The observed test value is then compared to a distribution of values obtained by randomly permuting the individuals (rows) in one partition relative to those in the other. A significant result is found when the observed PLS correlation is large relative to this distribution, and implies that the structures are integrated with one another (see Bookstein et al. 2003). If only two partitions are specified, a plot of PLS scores along the first set of PLS axes is optionally displayed, and thin-plate spline deformation grids along these axes are also shown if data were input as a 3D array.
Input for the analysis can take one of two forms. First, one can input a single dataset (as a matrix or 3D array, along with a vector describing which variables correspond to which partitions (for the case of a 3D array, which landmarks belong to which partitions is specified). Alternatively, when evaluating the integration between two structures or partitions, two datasets may be provided.
The generic functions, print, summary, and plot all work with modularity.test.
The generic function, plot, produces a two-block.pls plot. This function calls plot.pls, which has two additional
arguments (with defaults): label = NULL, warpgrids = TRUE. These arguments allow one to include a vector to label points and a logical statement to
include warpgrids, respectively. Warpgrids can only be included for 3D arrays of Procrustes residuals. The plot is a plot of PLS scores from
Block1 versus Block2 performed for the first set of PLS axes.
Bookstein, F. L., P. Gunz, P. Mitteroecker, H. Prossinger, K. Schaefer, and H. Seidler. 2003. Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution. J. Hum. Evol. 44:167-187.
two.b.pls, modularity.test, phylo.pls, and
phylo.integration
data(plethodon)
Y.gpa<-gpagen(plethodon$land) #GPA-alignment
#landmarks on the skull and mandible assigned to partitions
land.gps<-c("A","A","A","A","A","B","B","B","B","B","B","B")
IT <- integration.test(Y.gpa$coords, partition.gp=land.gps, iter=999)
summary(IT) # Test summary
plot(IT) # PLS plot
IT$left.pls.vectors # extracting just the left (first block) singular vectors
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