geomorph (version 2.1.6)

plotAllometry: Plot allometric patterns in landmark data

Description

Function plots allometry curves for a set of specimens

Usage

plotAllometry(f1, f2 = NULL, method = c("CAC", "RegScore", "PredLine"),
  warpgrids = TRUE, iter = 249, label = NULL, mesh = NULL,
  logsz = TRUE, RRPP = FALSE, verbose = FALSE)

Arguments

f1

A formula (of the form shape ~ size); shape can be a matrix (n x [p1 x k]) or 3D array (p1 x k x n) containing GPA-aligned coordinates for the specimens

f2

An optional right hand formula for groups (e.g., ~ groups); must be a single factor

method

Method for estimating allometric shape components; see below for details

warpgrids

A logical value indicating whether deformation grids for small and large shapes should be displayed (note: if groups are provided no TPS grids are shown)

iter

Number of iterations for significance testing

label

An optional vector indicating labels for each specimen that are to be displayed

mesh

A mesh3d object to be warped to represent shape deformation of the minimum and maximum size if {warpgrids= TRUE} (see warpRefMesh).

logsz

A logical value indicating whether log(size) is used

RRPP

A logical value to indicate if a randomized residual permutation procedure (RRPP) should be used for statistical tests

verbose

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

Value

• Function returns an ANOVA table of statistical results for size: df, SS, MS, F, Z,Prand. If verbose=TRUE, function returns a list with the following components:
• ProcDist.lm
  An ANOVA table as above
• allom.score
  A matrix of the allometry shape scores
• logSize
  A matrix of log size
• pred.shape
  A matrix containing the predicted shapes from the regression
• resid.shape
  The residual shape component (RSC) of the data ("method=CAC" only)

code

procD.lm

Details

The function performs a regression of shape on size, and generates a plot that describes the multivariate relationship between size and shape derived from landmark data (i.e., allometry). It is assumed that the landmarks have previously been aligned using Generalized Procrustes Analysis (GPA) [e.g., with gpagen]. The abscissa of the plot is size (or log of size) while the ordinate represents shape [NOTE: the function takes the input size and performed log-transformation automatically by default (logsz = TRUE), as log(Size) should be used]. Three complementary approaches can be implemented to visualize allometry:

1. If "method=CAC" (the default) the function calculates the common allometric component of the shape data, which is an estimate of the average allometric trend within groups (Mitteroecker et al. 2004). The function also calculates the residual shape component (RSC) for the data.

If "method=RegScore" the function calculates shape scores from the regression of shape on size, and plots these versus size (Drake and Klingenberg 2008). For a single group, these shape scores are mathematically identical to the CAC (Adams et al. 2013). If "method=PredLine" the function calculates predicted values from a regression of shape on size, and plots the first principal component of the predicted values versus size as a stylized graphic of the allometric trend (Adams and Nistri 2010).

References

Adams, D.C., F.J. Rohlf, and D.E. Slice. 2013. A field comes of age: geometric morphometrics in the 21st century. Hystrix. 24:7-14. Adams, D. C., and A. Nistri. 2010. Ontogenetic convergence and evolution of foot morphology in European cave salamanders (Family: Plethodontidae). BMC Evol. Biol. 10:1-10. Drake, A. G., and C. P. Klingenberg. 2008. The pace of morphological change: Historical transformation of skull shape in St Bernard dogs. Proceedings of the Royal Society B, Biological Sciences 275:71'76. Mitteroecker, P., P. Gunz, M. Bernhard, K. Schaefer, and F. L. Bookstein. 2004. Comparison of cranial ontogenetic trajectories among great apes and humans. J. Hum. Evol. 46:679-698.

Examples

data(ratland)
Y.gpa<-gpagen(ratland,PrinAxes=FALSE)    #GPA-alignment

#Using CAC for plot
plotAllometry(Y.gpa$coords ~ Y.gpa$Csize, method="CAC", iter=9)

#Using Regression Scores for plot
plotAllometry(Y.gpa$coords ~ Y.gpa$Csize, method="RegScore", iter=9)

#Using predicted allometry curve for plot
plotAllometry(Y.gpa$coords ~ Y.gpa$Csize, method="PredLine", iter=9)