Chapter 1 Linear ~ shape/size
This study begins by asking which linear measure/s—if any—can be said to covary with Perdiz arrow point shape and size? To assess covariance, Procrustes-aligned shape and centroid size are used in a pair of two-block partial least-squares analysis with each linear (caliper collected) metric.
1.1 Load packages + data
# download most recent software version
#devtools::install_github("geomorphR/geomorph", ref = "Stable", build_vignettes = TRUE)
#devtools::install_github("mlcollyer/RRPP")
# load analysis packages
library(here)
library(StereoMorph)
library(geomorph)
library(ggplot2)
library(dplyr)
library(ggpubr)
library(wesanderson)
# read shape data and define number of sLMs
shapes <- readShapes("shapes")
shapesGM <- readland.shapes(shapes,
nCurvePts = c(10,3,5,5,3,10))
# read qualitative data
qdata <- read.csv("qdata.perdiz.csv",
header = TRUE,
row.names = 1)
# add derived vars to data
# maximum blade length (derived)
qdata$maxbl <- qdata$maxl - qdata$maxstl
# maximum shoulder width (derived)
qdata$maxshw <- qdata$maxw - qdata$maxstw1.2 Generalised Procrustes Analysis
Landmark data were aligned to a global coordinate system (Kendall 1981, 1984; Slice 2001), achieved through generalized Procrustes superimposition (Rohlf and Slice 1990) performed in R 4.1.3 (R Core Development Team, 2022) using the geomorph library v. 4.0.3 (Adams et al. 2017; Adams and Otarola-Castillo 2013; Baken et al. 2021). Procrustes superimposition translates, scales, and rotates the coordinate data to allow for comparisons among objects (Gower 1975; Rohlf and Slice 1990). The geomorph package uses a partial Procrustes superimposition that projects the aligned specimens into tangent space subsequent to alignment in preparation for the use of multivariate methods that assume linear space (Rohlf 1999; Slice 2001).
# gpa
Y.gpa <- gpagen(shapesGM, print.progress = FALSE)
## plot
plot(Y.gpa)
# dataframe
gdf <- geomorph.data.frame(shape = Y.gpa$coords,
size = Y.gpa$Csize)1.3 2BPLS Maximum length
1.3.1 Shape
# is Perdiz arrow point shape correlated with linear var?
shapeml <- two.b.pls(Y.gpa$coords,
qdata$maxl,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(shapeml)##
## Call:
## two.b.pls(A1 = Y.gpa$coords, A2 = qdata$maxl, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.1855
##
## Effect Size (Z): -0.17271
##
## P-value: 0.5668
##
## Based on 10000 random permutations## plot
plot(shapeml)
1.3.2 Size
# is Perdiz arrow point size correlated with linear var?
sizeml <- two.b.pls(Y.gpa$Csize,
qdata$maxl,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(sizeml)##
## Call:
## two.b.pls(A1 = Y.gpa$Csize, A2 = qdata$maxl, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.3445
##
## Effect Size (Z): 2.7643
##
## P-value: 0.0041
##
## Based on 10000 random permutations## plot
plot(sizeml)
1.4 2BPLS Maximum blade length
1.4.1 Shape
# is Perdiz arrow point shape correlated with linear var?
shapembl <- two.b.pls(Y.gpa$coords,
qdata$maxbl,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(shapembl)##
## Call:
## two.b.pls(A1 = Y.gpa$coords, A2 = qdata$maxbl, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.2858
##
## Effect Size (Z): 1.27424
##
## P-value: 0.1049
##
## Based on 10000 random permutations## plot
plot(shapembl)
1.4.2 Size
# is Perdiz arrow point size correlated with linear var?
sizembl <- two.b.pls(Y.gpa$Csize,
qdata$maxbl,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(sizembl)##
## Call:
## two.b.pls(A1 = Y.gpa$Csize, A2 = qdata$maxbl, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.3381
##
## Effect Size (Z): 2.69984
##
## P-value: 0.0044
##
## Based on 10000 random permutations## plot
plot(sizembl)
1.5 2BPLS Maximum shoulder width
1.5.1 Shape
# is Perdiz arrow point shape correlated with linear var?
shapemshw <- two.b.pls(Y.gpa$coords,
qdata$maxshw,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(shapemshw)##
## Call:
## two.b.pls(A1 = Y.gpa$coords, A2 = qdata$maxshw, iter = 9999,
## seed = NULL, print.progress = FALSE)
##
##
##
## r-PLS: 0.3082
##
## Effect Size (Z): 1.49334
##
## P-value: 0.07
##
## Based on 10000 random permutations## plot
plot(shapemshw)
1.5.2 Size
# is Perdiz arrow point size correlated with linear var?
sizemshw <- two.b.pls(Y.gpa$Csize,
qdata$maxshw,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(sizemshw)##
## Call:
## two.b.pls(A1 = Y.gpa$Csize, A2 = qdata$maxshw, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.111
##
## Effect Size (Z): 0.89959
##
## P-value: 0.3712
##
## Based on 10000 random permutations## plot
plot(sizemshw)
1.6 2BPLS Maximum width
1.6.1 Shape
# is Perdiz arrow point shape correlated with linear var?
shapemw <- two.b.pls(Y.gpa$coords,
qdata$maxw,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(shapemw)##
## Call:
## two.b.pls(A1 = Y.gpa$coords, A2 = qdata$maxw, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.2963
##
## Effect Size (Z): 1.36161
##
## P-value: 0.0923
##
## Based on 10000 random permutations## plot
plot(shapemw)
1.6.2 Size
# is Perdiz arrow point size correlated with linear var?
sizemw <- two.b.pls(Y.gpa$Csize,
qdata$maxw,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(sizemw)##
## Call:
## two.b.pls(A1 = Y.gpa$Csize, A2 = qdata$maxw, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.206
##
## Effect Size (Z): 1.67231
##
## P-value: 0.0944
##
## Based on 10000 random permutations## plot
plot(sizemw)
1.7 2BPLS Maximum thickness
1.7.1 Shape
# is Perdiz arrow point shape correlated with linear var?
shapemth <- two.b.pls(Y.gpa$coords,
qdata$maxth,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(shapemth)##
## Call:
## two.b.pls(A1 = Y.gpa$coords, A2 = qdata$maxth, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.2108
##
## Effect Size (Z): 0.2434
##
## P-value: 0.4067
##
## Based on 10000 random permutations## plot
plot(shapemth)
1.7.2 Size
# is Perdiz arrow point size correlated with linear var?
sizemth <- two.b.pls(Y.gpa$Csize,
qdata$maxth,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(sizemth)##
## Call:
## two.b.pls(A1 = Y.gpa$Csize, A2 = qdata$maxth, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.1291
##
## Effect Size (Z): 1.0525
##
## P-value: 0.3059
##
## Based on 10000 random permutations## plot
plot(sizemth)
1.8 2BPLS Maximum stem length
1.8.1 Shape
# is Perdiz arrow point shape correlated with linear var?
shapemstl <- two.b.pls(Y.gpa$coords,
qdata$maxstl,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(shapemstl)##
## Call:
## two.b.pls(A1 = Y.gpa$coords, A2 = qdata$maxstl, iter = 9999,
## seed = NULL, print.progress = FALSE)
##
##
##
## r-PLS: 0.4003
##
## Effect Size (Z): 2.42637
##
## P-value: 0.0052
##
## Based on 10000 random permutations## plot
plot(shapemstl)
1.8.2 Size
# is Perdiz arrow point size correlated with linear var?
sizemstl <- two.b.pls(Y.gpa$Csize,
qdata$maxstl,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(sizemstl)##
## Call:
## two.b.pls(A1 = Y.gpa$Csize, A2 = qdata$maxstl, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.1762
##
## Effect Size (Z): 1.45327
##
## P-value: 0.1478
##
## Based on 10000 random permutations## plot
plot(sizemstl)
1.9 2BPLS Maximum stem width
1.9.1 Shape
# is Perdiz arrow point shape correlated with linear var?
shapemstw <- two.b.pls(Y.gpa$coords,
qdata$maxstw,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(shapemstw)##
## Call:
## two.b.pls(A1 = Y.gpa$coords, A2 = qdata$maxstw, iter = 9999,
## seed = NULL, print.progress = FALSE)
##
##
##
## r-PLS: 0.1585
##
## Effect Size (Z): -0.64787
##
## P-value: 0.7304
##
## Based on 10000 random permutations## plot
plot(shapemstw)
1.9.2 Size
# is Perdiz arrow point size correlated with linear var?
sizemstw <- two.b.pls(Y.gpa$Csize,
qdata$maxstw,
iter = 9999,
seed = NULL,
print.progress = FALSE)## Data in either A1 or A2 do not have names. It is assumed data in both A1 and A2 are ordered the same.summary(sizemstw)##
## Call:
## two.b.pls(A1 = Y.gpa$Csize, A2 = qdata$maxstw, iter = 9999, seed = NULL,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.4524
##
## Effect Size (Z): 3.67031
##
## P-value: 2e-04
##
## Based on 10000 random permutations## plot
plot(sizemstw)
References
Adams, Dean C., Michael L. Collyer, Antigoni Kaliontzopoulou, and Emma Sherratt. 2017. “Package geomorph: Geometric Morphometric Analyses of Landmark Data. R package version 3.0.5.” http://geomorphr.github.io/geomorph/.
Adams, Dean C., and Erik Otarola-Castillo. 2013. “geomorph: An R Package for the Collection and Analysis of Geometric Morphometric Shape Data.” Methods in Ecology and Evolution 4 (4): 393–99. https://doi.org/10.1111/2041-210x.12035.
Baken, Erica K., Michael L. Collyer, Antigoni Kaliontzopoulou, and Dean C. Adams. 2021. “geomorph v4.0 and gmShiny: Enhanced analytics and a new graphical interface for a comprehensive morphometric experience.” Journal Article. Methods in Ecology and Evolution. https://doi.org/10.1111/2041-210x.13723.
Gower, J. C. 1975. “Generalized Procrustes Analysis.” Psychometrika 40 (1): 33–51. https://doi.org/https://doi.org/10.1007/BF02291478.
Kendall, David G. 1981. “The Statistics of Shape.” In Interpreting Multivariate Data, edited by V. Barnett, 75–80. New York: Wiley.
———. 1984. “Shape Manifolds, Procrustean Metrics, and Complex Projective Spaces.” Bulletin of the London Mathematical Society 16 (2): 81–121. https://doi.org/10.1112/blms/16.2.81.
R Core Development Team,. 2022. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. http://www.R-project.org/.
Rohlf, F. James. 1999. “Shape Statistics: Procrustes Superimpositions and Tangent Spaces.” Journal of Classification 16 (2): 197–223. https://doi.org/10.1007/s003579900054.
Rohlf, F. James, and Dennis Slice. 1990. “Extensions of the Procrustes Method for the Optimal Superimposition of Landmarks.” Systematic Zoology 39 (1): 40–59. https://doi.org/10.2307/2992207.
Slice, Dennis E. 2001. “Landmark Coordinates Aligned by Procrustes Analysis Do Not Lie in Kendall’s Shape Space.” Systematic Biology 50 (1): 141–49. https://doi.org/10.1080/10635150119110.