geomorph (version 3.0.2)

phylo.modularity: Evaluate the degree of phylogenetic modular signal in morphometric datasets

Description

Function quantifies the degree of modularity between two or more hypothesized modules of Procrustes-aligned landmark coordinates in a phylogenetic context and compares this to patterns found by randomly assigning landmarks into subsets

Usage

phylo.modularity(A, partition.gp, phy, CI = FALSE, iter = 999, seed = NULL, print.progress = TRUE)

Arguments

A

A 3D array (p x k x n) containing GPA-aligned coordinates for all specimens, or a matrix (n x variables)

partition.gp

A list of which landmarks (or variables) belong in which partition (e.g. A,A,A,B,B,B,C,C,C)

phy

A phylogenetic tree of class phylo - see read.tree in library ape

CI

A logical argument indicating whether bootstrapping should be used for estimating confidence intervals

iter

Number of iterations for significance testing

seed

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.

print.progress

A logical value to indicate whether a progress bar should be printed to the screen. This is helpful for long-running analyses.

Value

Objects of class "CR" from modularity.test return a list of the following:

CR

Covariance ratio: The estimate of the observed modular signal.

CInterval

The bootstrapped 95 percent confidence intervals of the CR, if CI = TRUE.

CR.boot

The bootstrapped CR values, if CI = TRUE (For more than two partitions, this is the mean CR of pairwise CRs.)

P.value

The empirically calculated P-value from the resampling procedure.

CR.mat

For more than two partitions, the pairwise CRs among partitions.

random.CR

The CR calculated in each of the random permutations of the resampling procedure.

permutations

The number of random permutations used in the resampling procedure.

call

The match call.

Details

The function quantifies the degree of phylogenetic modularity in two or more hypothesized modules of shape data 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 aligned Procrustes coordinates. 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).

References

Adams, D.C. 2016.Evaluating modularity in morphometric data: Challenges with the RV coefficient and a new test measure. Methods in Ecology and Evolution. (Accepted).

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.

Examples

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, iter=999)
summary(MT) # Test summary
plot(MT) # Histogram of CR sampling distribution