compare.modular.partitions: Compare modular signal to alternative landmark subsets

Description

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

Usage

compare.modular.partitions(A, partition.gp, iter = 999)

Arguments

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)

iter

Number of iterations for significance testing

Value

Function returns a list with the following components:
RVThe estimate of the observed modular signal
pvalueThe significance level of the observed signal
RV.minThe minimal RV coefficient found via landmark permutation
RV.min.partitionsA list of landmarks assigned to partitions that yields the minimal RV coefficient

Details

The function quantifies the degree of modularity in two or more hypothesized modules of shape data as defined by landmark coordinates, and compares this to the degree of modular signal found in random assignment of landmarks to modules. 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 RV coefficient (Klingenberg 2009). If more than two modules are defined, the average RV coefficient is utilized (see Klingenberg 2009). The RV 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 RV coefficient is small relative to this distribution (see Klingenberg 2009). A histogram of coefficients obtained via resampling is presented, with the observed value designated by an arrow in the plot. Landmark groups can be defined using define.modules, or made by hand (see example below). To use this method with other data (i.e., a set of length measurements), the input A should be a matrix of n rows of specimens and variables arranged in columns. In this case, the partition.gp input should have each variable assigned to a partition.

References

Klingenberg, C. P. 2009. Morphometric integration and modularity in configurations of landmarks: tools for evaluating a priori hypotheses. Evol. Develop. 11:405-421.

Examples

Run this code

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")

compare.modular.partitions(Y.gpa$coords,land.gps,iter=99)
#Result implies that the skull and mandible are not independent modules

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