geomorph (version 1.1-1)

morphol.integr: Quantify morphological integration between two modules

Description

Function quantifies the degree of morphological integration between two modules of Procrustes-aligned coordinates

Usage

morphol.integr(A, WithinConfig = FALSE, A2 = NULL,
    landgroups = NULL, method = c("PLS", "RV"), iter = 999)

Arguments

A

An array (p x k x n) containing landmark coordinates for the first module

WithinConfig

A logical value indicating whether morphological integration is to be assessed within or across structures

A2

An optional array (p x k x n) containing landmark coordinates for the second module (WithinConfig=FALSE)

landgroups

A list of which landmarks belong in which partition (WithinConfig=TRUE)

method

Method to estimate morphological integration; see below for details

iter

Number of iterations for significance testing

Value

• Function returns a list with the following components:
• value
  The estimate of morphological integration: PLS.corr or RV
• pvalue
  The significance level of the observed signal
• Xscores
  PLS scores for the first block of landmarks (PLS method only)
• Yscores
  PLS scores for the second block of landmarks (PLS method only)

Details

The function quantifies the degree of morphological integration between two modules 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 separate structures (WithinConfig=FALSE) or between two modules defined within the same landmark configuration (WithinConfig=TRUE). For both options, two analytical approaches are currently implemented to assess the degree of morphological integration. If "method=PLS" (the default) the function estimates the degree of morphological integration using two-block partial least squares, or PLS. When used with landmark data, this analysis is referred to as singular warps analysis (Bookstein et al. 2003). When "method=PLS", the scores along the X & Y PLS axes are also returned. Alternatively, if "method=RV" the function estimates the degree of morphological integration using the RV coefficient (Klingenberg 2009). Significance testing for both approaches is found by permuting the objects in one data matrix relative to those in the other. A histogram of coefficients obtained via resampling is presented, with the observed value designated by an arrow in the plot. If the degree of morphological integration between more than two sets of landmarks is of interest, one may use the average RV coefficent as implemented in the function compare.modular.partitions.

References

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

Examples

data(plethodon)
Y.gpa<-gpagen(plethodon$land)    #GPA-alignment
land.gps<-c("A","A","A","A","A","B","B","B","B","B","B","B")

#Morphological integration using PLS
morphol.integr(Y.gpa$coords,landgroups=land.gps,WithinConfig=TRUE,method="PLS",iter=99)

#Morphological integration using RV
morphol.integr(Y.gpa$coords,landgroups=land.gps,WithinConfig=TRUE,method="RV",iter=99)