Plot the Procrustes distances between a set of shapes and a reference

Description

DistancesPlot creates a distances plot using ggplot2 (Wickman 2009).

Usage

DistancesPlot(dist)

Arguments

Details

Use ggplot2 to create a plot where each point represent distance between a particular shape and a reference shape.

Value

Return an ggplot2 object

Author(s)

Juan Manuel Cabrera

References

H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2009.

Examples

data("simulated_shape_distances")

#Plot distances between a set of simulated shapes a reference.

DistancesPlot(simulated_shape_distances)

Generalized Procrustes residuals calculation

Description

Calculates Procrustes residuals of landmark configurations

Usage

GpaResiduals(lands,gpa_coords)

Arguments

Details

Partial least squares analysis is a common tool to examine complex patterns of covariations between multiple sets of variables (Rohlf and Corti 2000; Bookstein et al. 2003). When one set of these variables consists of shape coordinates it is called singular warps analysis. Singular warp analysis is based on a singular decomposition of the cross-covariance matrix of two sets of variables measured from the same sample objects. Bookstein et al. (2013) gave this equation (1):

\sum = \left ( 1/N \right )X^{t}Y\

Where N is the sample size and X and Y are matrices for two sets of variables with N rows, corresponding to the same sample specimens, and columns according to the number of variables of each set. If each variable in both matrices is first mean-centered (by variable), then Equation (1) yields the cross-covariance matrix between variables in X and those in Y.

Most of the landmark-based morphometric studies use aligned shape coordinates (GPA) as variable for analyzing complex patterns of covariations between sets of landmarks coordinates data. However, whereas GPA mean-centers all specimen configurations – it superimposes the centroids of each specimen - GPA does not mean center each coordinate within the specimens, and therefore does not in itself provide suitable variables for use in Equation (1).

To avoid this problem GpaResiduals mean center the aligned coordinates to get Procrustes residuals which are more appropriate for calculating covariance (McNulty 2009).

If generalized procrustes coordinates are not provided, the function will calculate them using geomorph package (Adams & Otárola Castillo 2013)

Value

It returns a list containing:

Author(s)

Cabrera Juan Manuel

References

Adams, D. C., & Otárola-Castillo, E. (2013). geomorph: an R package for the collection and analysis of geometric morphometric shape data. Methods in Ecology and Evolution, 4(4), 393-399.

Bookstein, F. L., Gunz, P., Mitterœcker, P., Prossinger, H., Schæfer, K., & Seidler, H. (2003). Cranial integration in Homo: singular warps analysis of the midsagittal plane in ontogeny and evolution. Journal of Human Evolution, 44(2), 167-187.

McNulty, K. P. (2009). Computing singular warps from Procrustes aligned coordinates. Journal of human evolution, 57(2), 191-194.

Rohlf, F. J., & Corti, M. (2000). Use of two-block partial least-squares to study covariation in shape. Systematic Biology, 49(4), 740-753.

Examples

data("aegla_landmarks")
result<-GpaResiduals(lands = aegla_landmarks)

#GPA consensus (matrix)
result$consens

#GPA consensus (vector)
result$cvectorized

#GPA residual matrix
result$resid

Plot shapes

Description

Plot the differences between a set of morphometric shapes and a reference

Usage

PlotVariations(shapes, reference, path, save = F, w = 6, h = 6, d = 100, c_ref = "red", 
 c_target = "black", s_ref = 3, s_target = 2)

Arguments

This parameters are used to modify stored graph (save = TRUE):

Details

The function uses package ggplot2 (Wickman 2009) to create multiple plots representing the variations between a list of target shapes and a reference (consensus shape or another specimen data). If save=TRUE it creates a folder (named day_hh_mm) and stores the plots as images (.jpeg) at the provided path (if not provided it will store them in the working directory). There are several parameters for modify the graph for a suitable representation. This function could be used for example to analyze morphological variations of species over generations.

Author(s)

Cabrera Juan Manuel

References

H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2009.

See Also

SimEvo

Examples

 
data("aegla_consensus")
data("simulated_shapes")

#Sample one individual from simulated_shapes dataset

simu<-simulated_shapes[100]

#Create a shape variation graphic

graph<-PlotVariations(simu,aegla_consensus)

#Red dots represent the landmark coordinates of the reference shape and black
# dots represent the target shape. The length of the segments represent 
# distances between pairs of homologous landmarks
  
graph[[1]]

Extract landmark data

Description

Read landmark coordinates and scales from a TPS file

Usage

ReadLandmarkData(datafile, m_byscale = T)

Arguments

Details

The function returns landmark coordinates (array and data.frame format) and the scale of each specimen. If m_byscale = T the coordinates are multiple by the corresponding scale. ReadLandmarkData only works with TPS files that has only landmark coordinates (presence of CURVES and OUTLINES may cause malfunction).

Value

It returns a 3 element list:

Author(s)

Cabrera Juan Manuel

Calculate Procrustes distance between shapes

Description

Use the Procrustes method to calculate distances between a set of shapes and a reference.

Usage

ShapeDist(shapes, reference)

Arguments

Details

Procrustes distance provides a measure of coincidence of two point sets xi and yi, i=1..N. For this purpose the variance of point deviations is calculated at the optimal superposition of the sets. It allows to characterize the shape proximity of a given simplex to shape of a reference one.

Value

A matrix containing procrustes distance between shapes. Procrustes distance is the square root of the sum of squared differences in the posititions of the landmarks in two shapes (Dryden and Mardia 1998). This can be used to describe the difference between many landmark configurations (Rohlf and Slive 1990).

Author(s)

Cabrera Juan Manuel

References

Dryden, I. L., & Mardia, K. V. (1998). Statistical shape analysis (Vol. 4). Chichester: Wiley.

Rohlf, F. J., & Slice, D. (1990). Extensions of the Procrustes method for the optimal superimposition of landmarks. Systematic Biology, 39(1), 40-59.

Examples

data("aegla_landmarks")
data("aegla_consensus")

#Calculate distances between set of shapes and a reference
ShapeDist(shapes = aegla_landmarks, reference = aegla_consensus)

Simulation of Shape Variation

Description

SimEvo performs a simulation of shape variation using a modification of Lande's evolutionary model Polly 2004

Usage

SimEvo(vari, consensusvec, resids, ngen, fsamp)

Arguments

Details

Lande's evolutionary model defines mean morphological variation over generations \Delta Z as:

\Delta Z = \beta G

where G is the additive genetic covariance matrix, and \beta are selection coefficients applied to the morphological structure. Polly 2004 proposes a modification of this equation in order to use it with morphological data instead of genetic data:

\Delta Z = \beta P H

where P is the phenotypic covariance matrix, and H is an heritability matrix (See Polly 2004 for more information). resids will be used as the phenotypic covariance matrix, and vari will be used to simulate \beta H term. After ngen simulations steps the new shape will be reconstructed from the starting shape consensusvec . The number of plots representing the new shapes can be modify using fsamp .

Value

It returns a list of ngen/fsamp shapes (landmarks coordinates)

Author(s)

Cabrera Juan Manuel

References

Polly, P. D. (2004). On the simulation of the evolution of morphological shape: multivariate shape under selection and drift. Palaeontologia Electronica, 7(2), 1-28.

Examples

 
data("aegla_landmarks")

#Use GpaResiduals function to obtain GPA residual matrix and consensus
# coordinates from landmark configuration

a_data=GpaResiduals(aegla_landmarks)

#Simulate morphological evolution with a variation rate "vari"
# trough "ngen" generations and retrieve the last generation shape coordinates

simshape = SimEvo(vari = 2, consensusvec = a_data$cvectorized, 
resids = a_data$resid, ngen = 10000, fsamp = 10000)

#Plot consensus shape and the simulated shape

par(mfrow=c(1, 2))
plot(a_data$consens,type = "p",main = "Reference", xlab = "", ylab = "")
plot(simshape[[1]],type = "p",col = "red",main = "Target", xlab = "", ylab = "")

#Or you can use PlotVariations to see the difference more clearly

PlotVariations(simshape,a_data$consens)

Landmark coordinates data from consensus configuration of freshwater crabs

Description

Aegla uruguayana consensus shape coordinates.

Usage

data("aegla_consensus")

References

Diawol, V. P., Giri, F., & Collins, P. A. (2015). Shape and size variations of Aegla uruguayana (Anomura-Aeglidae) under laboratory conditions. A geometric morphometric approach to the growth. Iheringia Série Zoologia, 105(1), 76-83.

Landmark coordinates data from freshwater crabs

Description

Geometric morphometric data of Aegla uruguayana cephalothorax (21 landmarks).

Usage

data("aegla_landmarks")

References

Diawol, V. P., Giri, F., & Collins, P. A. (2015). Shape and size variations of Aegla uruguayana (Anomura-Aeglidae) under laboratory conditions. A geometric morphometric approach to the growth. Iheringia Série Zoologia, 105(1), 76-83.

Procrustes distances data

Description

Procrustes distance between a set of simulated shapes and their ancestry over generations.

Usage

data("simulated_shape_distances")

Simulated shapes

Description

Simulated landmark data using evomorph SimEvo function on Aegla uruguayana data.

Usage

data("simulated_shapes")

References

Diawol, V. P., Giri, F., & Collins, P. A. (2015). Shape and size variations of Aegla uruguayana (Anomura-Aeglidae) under laboratory conditions. A geometric morphometric approach to the growth. Iheringia Série Zoologia, 105(1), 76-83.