geomorph (version 2.0.1)

trajectory.analysis: Quantify and compare shape change trajectories

Description

Function estimates attributes of shape change trajectories or motion trajectories for a set of Procrustes-aligned specimens and compares them statistically

Usage

trajectory.analysis(f1, data = NULL, estimate.traj = TRUE,
  traj.pts = NULL, iter = 99)

Arguments

f1

A formula for the linear model (e.g., y~x1+x2)

data

An optional value specifying a data frame containing all data (not required)

estimate.traj

A logical value indicating whether trajectories are estimated from original data; described below

iter

Number of iterations for significance testing

traj.pts

An optional value specifying the number of points in each trajectory (if estimate.traj=FALSE)

Value

• If "estimate.traj=TRUE", the function returns a list with the following components:
• procDist.lm
  Procrustes ANOVA table
• traj.size
  A matrix of pairwise differences in trajectory size
• p.size
  A matrix of pairwise significance levels for trajectory size
• traj.orient
  A matrix of pairwise differences in trajectory orientation
• p.orient
  A matrix of pairwise significance levels for trajectory orientation
• traj.shape
  A matrix of pairwise differences in trajectory shape (if applicable)
• p.shape
  A matrix of pairwise significance levels for trajectory shape
• If "estimate.traj=FALSE", the function returns a list with the following components:
• MANOVA.location.covariation
  Procrustes ANOVA table
• ANOVA.Size
  Results of permutational-ANOVA assessing variation in trajectory size
• ANOVA.Dir
  Results of permutational-ANOVA assessing variation in trajectory orientation
• ANOVA.Shape
  Results of permutational-ANOVA assessing variation in trajectory shape (if applicable)

Details

The function quantifies phenotypic shape change trajectories from a set of specimens, and assesses variation in these parameters via permutation. A shape change trajectory is defined by a sequence of shapes in tangent space. These trajectories can be quantified various attributes (their size, orientation, and shape), and comparisons of these attribute enables the statistical comparison of shape change trajectories (see Collyer and Adams 2013; Collyer and Adams 2007; Adams and Collyer 2007; Adams and Collyer 2009). Data input is specified by a formula (e.g., Y~X), where 'Y' specifies the response variables (trajectory data), and 'X' contains one or more independent variables (discrete or continuous). The response matrix 'Y' must be in the form of a two-dimensional data matrix of dimension (n x [p x k]), rather than a 3D array. The function two.d.array can be used to obtain a two-dimensional data matrix from a 3D array of landmark coordinates. It is assumed that the order of the specimens 'Y' matches the order of specimens in 'X'. There are two primary modes of analysis through this function. If "estimate.traj=TRUE" the function estimates shape trajectories using the least-squares means for groups, based on a two-factor model (e.g., Y~A+B+A:B). Under this implementation, the last factor in 'X' must be the interaction term, and the preceding two factors must be the effects of interest. Covariates may be included in 'X', and must precede the factors of interest (e.g., Y~cov+A*B). In this implementation, 'Y' contains a matrix of landmark coordinates. It is assumed that the landmarks have previously been aligned using Generalized Procrustes Analysis (GPA) [e.g., with gpagen]. If "estimate.traj=FALSE" the trajectories are assembled directly from the set of shapes provided in 'Y'. With this implementation, the user must specify the number of shapes that comprise each trajectory. This approach is useful when the set of shapes forming each trajectory have been quantified directly (e.g., when motion paths are compared: see Adams and Cerney 2007). With this implementation, variation in trajectory size, shape, and orientation are evaluated for each term in 'X'.(see Adams and Cerney 2007). Once the function has performed the analysis, it generates a plot of the trajectories as visualized in the space of principal components (PC1 vs. PC2). The first point in each trajectory is displayed as white, the last point is black, and any middle points on the trajectories are in gray. The colors of trajectories follow the order in which they are found in the dataset, using R's standard color palette: black, red, green3, blue, cyan, magenta, yellow, and gray.

References

Collyer, M.L., and D.C. Adams. 2013. Phenotypic trajectory analysis: Comparison of shape change patterns in evolution and ecology. Hystrix. 24:75-83. Adams, D. C. 2010. Parallel evolution of character displacement driven by competitive selection in terrestrial salamanders. BMC Evol. Biol. 10:1-10. Adams, D. C., and M. M. Cerney. 2007. Quantifying biomechanical motion using Procrustes motion analysis. J. Biomech. 40:437-444. Adams, D. C., and M. L. Collyer. 2007. The analysis of character divergence along environmental gradients and other covariates. Evolution 61:510-515. Adams, D. C., and M. L. Collyer. 2009. A general framework for the analysis of phenotypic trajectories in evolutionary studies. Evolution 63:1143-1154. Collyer, M. L., and D. C. Adams. 2007. Analysis of two-state multivariate phenotypic change in ecological studies. Ecology 88:683-692.

Examples

#1: Estimate trajectories from LS means in 2-factor model
data(plethodon)
Y.gpa<-two.d.array(gpagen(plethodon$land)$coords)

trajectory.analysis(Y.gpa~plethodon$species*plethodon$site,iter=15)

#2: Compare motion trajectories
data(motionpaths)

#Motion paths represented by 5 time points per motion

trajectory.analysis(motionpaths$trajectories~motionpaths$groups,
estimate.traj=FALSE, traj.pts=5,iter=15)