Function quantifies the degree of modularity between two or more hypothesized modules of Procrustes shape variables in a phylogenetic context and compares this to patterns found by randomly assigning landmarks into subsets
phylo.modularity(
A,
partition.gp,
phy,
CI = FALSE,
iter = 999,
seed = NULL,
print.progress = TRUE
)Objects of class "CR" from modularity.test return a list of the following:
Covariance ratio: The estimate of the observed modular signal.
The bootstrapped 95 percent confidence intervals of the CR, if CI = TRUE.
The bootstrapped CR values, if CI = TRUE. For more than two partitions, this is the mean CR of pairwise CRs.
The empirically calculated P-value from the resampling procedure.
The multivariate effect size associated with sigma.d.ratio.
For more than two partitions, the pairwise CRs among partitions.
The CR calculated in each of the random permutations of the resampling procedure.
The phylogenetic transformation matrix, needed for certain other analyses.
The number of random permutations used in the resampling procedure.
The match call.
A 3D array (p x k x n) containing Procrustes shape variables for all specimens, or a matrix (n x variables)
A list of which landmarks (or variables) belong in which partition: (e.g. A, A, A, B, B, B, C, C, C)
A phylogenetic tree of class = "phylo" - see read.tree in library ape
A logical argument indicating whether bootstrapping should be used for estimating confidence intervals
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.
Dean Adams
The function quantifies the degree of phylogenetic modularity in two or more hypothesized modules of Procrustes shape variables as defined by landmark coordinates, under a Brownian motion model of evolution. The degree of modularity is characterized by the covariance ratio covariance ratio (CR: see Adams 2016). The phylogenetic version of the approach procedure utilizes the evolutionary covariance matrix among traits found under a Brownian motion model of evolution as the basis of the analysis. This is the same matrix used to evaluate patterns of phylogenetic morphological integration as described in Adams and Felice (2014).
Input may be either a 2D matrix of phenotypic values, or a 3D array of Procrustes shape variables. It
is assumed that the landmarks have previously been aligned using Generalized Procrustes Analysis (GPA) [e.g.,
with gpagen]. The degree of modularity is quantified using the CR coefficient (Adams 2016). If more than
two modules are defined, the average pairwise CR coefficient is utilized. The CR coefficient for the observed modular
hypothesis is then compared to a distribution of values obtained by randomly assigning landmarks into subsets, with the
restriction that the number of landmarks in each subset is identical to that observed in each of the original partitions.
A significant modular signal is found when the observed CR coefficient is small relative to this distribution (see Adams 2016).
Such a result implies that there is significantly greater independence among modules than is expected under the null
hypothesis of random associations of variables (neither modular nor integrated structure). This
result is consistent with the identification of significant modular structure in the data. For landmark data, the CR coefficient
found from the average CR across a 90 degree rotation of the data is used as the test statistic (see Adams 2016).
In addition, a multivariate effect size describing the strength of the effect is
estimated from the empirically-generated sampling distribution (see details in Adams and Collyer 2019).
Adams, D.C. 2016.Evaluating modularity in morphometric data: Challenges with the RV coefficient and a new test measure. Methods in Ecology and Evolution. 7:565-572.
Adams, D.C. and R. Felice. 2014. Assessing phylogenetic morphological integration and trait covariation in morphometric data using evolutionary covariance matrices. PLOS ONE. 9(4):e94335.
Adams, D.C. and M.L. Collyer. 2019. Comparing the strength of modular signal, and evaluating alternative modular hypotheses, using covariance ratio effect sizes with morphometric data. Evolution. 73:2352-2367.
if (FALSE) {
data(plethspecies)
Y.gpa <- gpagen(plethspecies$land) #GPA-alignment
land.gps <- c("A","A","A","A","A","B","B","B","B","B","B")
MT <- phylo.modularity(Y.gpa$coords, partition.gp = land.gps,
phy = plethspecies$phy,
CI = FALSE)
summary(MT) # Test summary
plot(MT) # Histogram of CR sampling distribution
}
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