geomorph (version 2.0.1)

bilat.symmetry: Analysis of bilateral symmetry

Description

Function performs an analysis of directional and fluctuating asymmetry for bilaterally symmetric objects

Usage

bilat.symmetry(A, ind = NULL, side = NULL, replicate = NULL,
  object.sym = FALSE, land.pairs = NULL, warpgrids = TRUE, mesh = NULL,
  verbose = FALSE)

Arguments

A

An array (p x k x n) containing GPA-aligned coordinates for a set of specimens [for "object.sym=FALSE, A is of dimension (n x k x 2n)]

ind

A vector containing labels for each individual. For matching symmetry, the matched pairs receive the same label (replicates also receive the same label).

side

An optional vector (for matching symmetry) designating which object belongs to which 'side-group'

replicate

An optional vector designating which objects belong to which group of replicates

object.sym

A logical value specifying whether the analysis should proceed based on object symmetry {=TRUE} or matching symmetry {=FALSE}

land.pairs

An optional matrix (for object symmetry) containing numbers for matched pairs of landmarks across the line of symmetry

warpgrids

A logical value indicating whether deformation grids for directional and fluctuating components of asymmetry

mesh

A mesh3d object to be warped to represent shape deformation of the directional and fluctuating components of asymmetry if {warpgrids= TRUE} (see warpRefMesh).

verbose

A logical value indicating whether the output is basic or verbose (see Value below)

Value

• Function returns a list with the following components:
• ANOVA.shape
  Procrustes ANOVA table assessing patterns of shape asymmetry
• ANOVA.size
  Procrustes ANOVA table assessing patterns of shape asymmetry (when {object.sym=FALSE})
• symm.shape
  The symmetric component of shape variation of the aligned specimens ({when verbose=TRUE})
• asymm.shape
  The asymmetric component of shape variation of the aligned specimens ({when verbose=TRUE})

Details

The function quantifies components of shape variation for a set of specimens as described by their patterns of symmetry and asymmetry. Here, shape variation is decomposed into variation among individuals, variation among sides (directional asymmetry), and variation due to an individual x side interaction (fluctuating symmetry). These components are then statistically evaluated using Procrustes ANOVA and Goodall's F tests (i.e. an isotropic model of shape variation). Methods for both matching symmetry and object symmetry can be implemented. Matching symmetry is when each object contains mirrored pairs of structures (e.g., right and left hands) while object symmetry is when a single object is symmetric about a midline (e.g., right and left sides of human faces). Analytical and computational details concerning the analysis of symmetry in geometric morphometrics can be found in Mardia et al. 2000; Klingenberg et al. 2002. Analyses of symmetry for matched pairs of objects is implemented when {object.sym=FALSE}. Here, a 3D array [p x k x 2n] contains the landmark coordinates for all pairs of structures (2 structures for each of n specimens). Because the two sets of structures are on opposite sides, they represent mirror images, and one set must be reflected prior to the analysis to allow landmark correspondence. IT IS ASSUMED THAT THE USER HAS DONE THIS PRIOR TO PERFORMING THE SYMMETRY ANALYSIS. Reflecting a set of specimens may be accomplished by multiplying one coordinate dimension by '-1' for these structures (either the x-, the y-, or the z-dimension). A vector containing information on individuals and sides must also be supplied. Replicates of each specimen may also be included in the dataset, and when specified will be used as measurement error (see Klingenberg and McIntyre 1998). Analyses of object symmetry is implemented when {object.sym=TRUE}. Here, a 3D array [p x k x n] contains the landmark coordinates for all n specimens. To obtain information about asymmetry, the function generates a second set of objects by reflecting them about one of their coordinate axes. The landmarks across the line of symmetry are then relabeled to obtain landmark correspondence. The user must supply a list of landmark pairs. A vector containing information on individuals must also be supplied. Replicates of each specimen may also be included in the dataset, and when specified will be used as measurement error.

References

Klingenberg, C.P. and G.S. McIntyre. 1998. Quantitative genetics of geometric shape in the mouse mandible. Evolution. 55:2342-2352. Mardia, K.V., F.L. Bookstein, and I.J. Moreton. 2000. Statistical assessment of bilateral symmetry of shapes. Biometrika. 87:285-300. Klingenberg, C.P., M. Barluenga, and A. Meyer. 2002. Shape analysis of symmetric structures: quantifying variation among individuals and asymmetry. Evolution. 56:1909-1920.

Examples

#Example of matching symmetry

data(mosquito)
bilat.symmetry(mosquito$wingshape,ind=mosquito$ind,side=mosquito$side,
replicate=mosquito$replicate,object.sym=FALSE)

#Example of object symmetry

data(scallops)
bilat.symmetry(scallops$coorddata,ind=scallops$ind,object.sym=TRUE,land.pairs=scallops$land.pairs)