Supplementary materials for paper: Inferences to blacksmith production? French trade axe morphology and makers’ marks from the La Belle shipwreck
Robert Z. Selden, Jr. 13 August, 2022
# install
#devtools::install_github("mlcollyer/RRPP")
#devtools::install_github("geomorphR/geomorph", ref = "Stable", build_vignettes = TRUE)
# load
library(here)## here() starts at D:/github/fta3dgm
library(StereoMorph)
library(geomorph)## Loading required package: RRPP
## Loading required package: rgl
## Loading required package: Matrix
library(tidyverse)## ── Attaching packages
## ───────────────────────────────────────
## tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6 ✔ purrr 0.3.4
## ✔ tibble 3.1.8 ✔ dplyr 1.0.9
## ✔ tidyr 1.2.0 ✔ stringr 1.4.0
## ✔ readr 2.1.2 ✔ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
## ✖ tidyr::expand() masks Matrix::expand()
## ✖ dplyr::filter() masks stats::filter()
## ✖ dplyr::lag() masks stats::lag()
## ✖ tidyr::pack() masks Matrix::pack()
## ✖ tidyr::unpack() masks Matrix::unpack()
library(wesanderson)Landmark data were aligned to a global coordinate system (Kendall 1981,
1984; Slice 2001), achieved through generalised Procrustes
superimposition (Rohlf and Slice 1990) performed in R 4.0.4 (R Core
Development Team, 2021) using the geomorph library v. 3.3.2 (Adams et
al. 2017; Adams and Otárola-Castillo 2013). 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(coords, print.progress = FALSE)
plot(Y.gpa)
# geomorph data frame ----
gdf <- geomorph.data.frame(shape = Y.gpa$coords,
size = Y.gpa$Csize,
mark = qdata$mark)
# add centroid size to qdata ----
qdata$csz <- Y.gpa$Csize
# print qdata
knitr::kable(qdata, align = "lccc", caption = "Attributes included in qdata.")| cask | mark | csz | |
|---|---|---|---|
| 11373-2.20 | 11373 | asterisk | 447.6635 |
| 11373-2.21 | 11373 | asterisk | 499.3537 |
| 11373-2.23 | 11373 | DG | 421.9203 |
| 11373-2.28 | 11373 | asterisk | 502.4541 |
| 11375-2.3 | 11375 | DG | 444.6668 |
| 11375-2.40 | 11375 | DG | 442.0828 |
| 11375-2.45 | 11375 | DG | 468.6789 |
| 11411-2.10 | 11411 | DG | 471.1334 |
| 11411-2.24 | 11411 | DG | 419.2457 |
| 11411-2.29 | 11411 | DG | 420.7324 |
Attributes included in qdata.
# attributes for boxplots ----
csz <- qdata$csz # centroid size
cask <- qdata$cask # cask
mark <- qdata$mark # mark
# boxplot of axe centroid size by mark ----
csz.mark <- ggplot(qdata, aes(x = mark, y = csz, color = mark)) +
geom_boxplot() +
geom_dotplot(binaxis = 'y', stackdir = 'center', dotsize = 0.3) +
scale_colour_manual(values = wes_palette("Moonrise2")) +
theme(legend.position = "none") +
labs(x = 'Mark', y = 'Centroid Size')
# render plot
csz.mark## Bin width defaults to 1/30 of the range of the data. Pick better value with `binwidth`.
Principal components analysis (Jolliffe 2002) was used to visualise shape variation among the axes The shape changes described by each principal axis are commonly visualized using thin-plate spline warping of a reference 3D mesh (Klingenberg 2013; Sherratt et al. 2014).
# principal components analysis
pca<-gm.prcomp(Y.gpa$coords)
summary(pca)##
## Ordination type: Principal Component Analysis
## Centering by OLS mean
## Orthogonal projection of OLS residuals
## Number of observations: 10
## Number of vectors 9
##
## Importance of Components:
## Comp1 Comp2 Comp3 Comp4
## Eigenvalues 0.001094911 0.0005672721 0.0004241562 0.000152132
## Proportion of Variance 0.439364737 0.2276343415 0.1702049650 0.061047377
## Cumulative Proportion 0.439364737 0.6669990784 0.8372040435 0.898251421
## Comp5 Comp6 Comp7 Comp8
## Eigenvalues 0.000122029 6.542674e-05 3.593658e-05 0.0000187934
## Proportion of Variance 0.048967665 2.625437e-02 1.442059e-02 0.0075413950
## Cumulative Proportion 0.947219086 9.734735e-01 9.878940e-01 0.9954354443
## Comp9
## Eigenvalues 1.137502e-05
## Proportion of Variance 4.564556e-03
## Cumulative Proportion 1.000000e+00
# set plot parameters to plot by mark
pch.gps <- c(15,17)[as.factor(mark)]
col.gps <- wes_palette("Moonrise2")[as.factor(mark)]
col.hull <- c("#798E87","#C27D38")
# plot pca by mark
pc.plot1 <- plot(pca,
asp = 1,
pch = pch.gps,
col = col.gps)
shapeHulls(pc.plot1,
groups = mark,
group.cols = col.hull)
# plot x/y maxima/minima
## x - minima
mean.shape <- mshape(Y.gpa$coords)
plotRefToTarget(pca$shapes$shapes.comp1$min,
mean.shape)
## x - maxima
plotRefToTarget(pca$shapes$shapes.comp1$max,
mean.shape)
## y - minima
plotRefToTarget(pca$shapes$shapes.comp2$min,
mean.shape)
## y - maxima
plotRefToTarget(pca$shapes$shapes.comp2$max,
mean.shape)
# print pca with warp grids at max/min X and max/min Y
knitr::include_graphics('./figures/pca.warp.jpg')
Hypothesis: There are morphological differences between French trade axes from the La Belle shipwreck that bear an asterisk or DG makers’ marks.
# size as a function of mark ----
fit.size.mark <- procD.lm(size ~ mark,
data = gdf,
print.progress = FALSE,
iter = 9999)
## differences in size by mark?
anova(fit.size.mark)##
## Analysis of Variance, using Residual Randomization
## Permutation procedure: Randomization of null model residuals
## Number of permutations: 10000
## Estimation method: Ordinary Least Squares
## Sums of Squares and Cross-products: Type I
## Effect sizes (Z) based on F distributions
##
## Df SS MS Rsq F Z Pr(>F)
## mark 1 3695.3 3695.3 0.4334 6.1193 1.6529 0.0253 *
## Residuals 8 4831.0 603.9 0.5666
## Total 9 8526.3
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Call: procD.lm(f1 = size ~ mark, iter = 9999, data = gdf, print.progress = FALSE)
# shape as a function of mark ----
fit.shape.mark <- procD.lm(shape ~ mark,
data = gdf,
print.progress = FALSE,
iter = 9999)
## differences in shape by mark? ----
anova(fit.shape.mark)##
## Analysis of Variance, using Residual Randomization
## Permutation procedure: Randomization of null model residuals
## Number of permutations: 10000
## Estimation method: Ordinary Least Squares
## Sums of Squares and Cross-products: Type I
## Effect sizes (Z) based on F distributions
##
## Df SS MS Rsq F Z Pr(>F)
## mark 1 0.0062247 0.0062247 0.27754 3.0732 2.1133 0.00995 **
## Residuals 8 0.0162036 0.0020255 0.72246
## Total 9 0.0224283
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Call: procD.lm(f1 = shape ~ mark, iter = 9999, data = gdf, print.progress = FALSE)
Are the blade and butt of the axes morphologically integrated?
land.gps <- c("A","A","B","B","A","A","A","A","A","A","B","B","B","B","B","B","B","B",
"B","B","B","B","B","B","B","B","B","B","B","B","B","B","B","B","A","A",
"A","A","A","A","A")
it <- integration.test(Y.gpa$coords,
partition.gp = land.gps,
print.progress = FALSE,
iter = 9999)
summary(it)##
## Call:
## integration.test(A = Y.gpa$coords, partition.gp = land.gps, iter = 9999,
## print.progress = FALSE)
##
##
##
## r-PLS: 0.9397
##
## Effect Size (Z): 2.50736
##
## P-value: 0.002
##
## Based on 10000 random permutations
## integration plot
plot(it)
mod <- modularity.test(Y.gpa$coords,
partition.gp = land.gps,
iter = 9999,
print.progress = FALSE)
summary(mod)##
## Call:
## modularity.test(A = Y.gpa$coords, partition.gp = land.gps, iter = 9999,
## print.progress = FALSE)
##
##
##
## CR: 0.90151
##
## P-value: 5e-04
##
## Effect Size: -4.31951
##
## Based on 10000 random permutations
## modularity plot
plot(mod)
# mean shapes ----
new.coords<-coords.subset(A = Y.gpa$coords,
group = qdata$mark)
names(new.coords)## [1] "asterisk" "DG"
# group shape means
mean <- lapply(new.coords, mshape)
# plot mean shapes
plot(mean$asterisk) # mean shape for axes with asterisk mark
plot(mean$DG) # mean shape for axes with DG mark
# comparison plot of French trade axes bearing asterisk (gray)
# and DG (black) marks
plotRefToTarget(mean$asterisk,
mean$DG,
method = "point",
mag = 2)
This version of the analysis was generated on 2022-08-13 06:24:33 using the following computational environment and dependencies:
# what R packages and versions were used?
if ("devtools" %in% installed.packages()) devtools::session_info()## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.2.1 (2022-06-23 ucrt)
## os Windows 10 x64 (build 19044)
## system x86_64, mingw32
## ui RTerm
## language (EN)
## collate English_United States.utf8
## ctype English_United States.utf8
## tz America/Chicago
## date 2022-08-13
## pandoc 2.17.1.1 @ C:/Program Files/RStudio/bin/quarto/bin/ (via rmarkdown)
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Current Git commit details are:
# where can I find this commit?
if ("git2r" %in% installed.packages() & git2r::in_repository(path = ".")) git2r::repository(here::here()) ## Local: main D:/github/fta3dgm
## Remote: main @ origin (https://github.com/seldenlab/fta3dgm)
## Head: [6f7692d] 2021-05-14: <install>
Adams, Dean C., Michael L. Collyer, Antigoni Kaliontzopoulou, and Emma Sherratt. 2017. “Package ’geomorph’: Geometric Morphometric Analyses of 2D/3D Landmark Data. R package version 3.0.5.” http://geomorphr.github.io/geomorph/.
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———. 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.
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Sherratt, E., D. J. Gower, C. P. Klingenberg, and M. Wilkinson. 2014. “Evolution of Cranial Shape in Caecilians (Amphibia: Gymnophiona).” Evolutionary Biology 41 (4): 528–45. https://doi.org/https://doi.org/10.1007/s11692-014-9287-2.
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.