04: Day 4 Material
General Introduction
Today we will briefly introduce some geomorph functions
for performing the analyses described yesterday. Note:
You should be able to read in your data and perform the analyses from
earlier this week!
1: Trajectory Analysis
Here is a simple example of trajectory analysis:
data(pupfish)
fit <- procD.lm(coords ~ Pop * Sex,
data = Pupfish,
iter = 999,
print.progress = FALSE)
reveal.model.designs(fit)## Reduced Full
## Pop 1 Pop
## Sex Pop Pop + Sex
## Pop:Sex Pop + Sex Pop + Sex + Pop:Sex <- Null/Full inherent in pairwiseanova(fit)##
## Analysis of Variance, using Residual Randomization
## Permutation procedure: Randomization of null model residuals
## Number of permutations: 1000
## 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)
## Pop 1 0.008993 0.0089927 0.15964 16.076 3.9997 0.001 ***
## Sex 1 0.015917 0.0159169 0.28255 28.453 4.1103 0.001 ***
## Pop:Sex 1 0.003453 0.0034532 0.06130 6.173 3.7015 0.001 ***
## Residuals 50 0.027970 0.0005594 0.49651
## Total 53 0.056333
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Call: procD.lm(f1 = coords ~ Pop * Sex, iter = 999, data = Pupfish,
## print.progress = FALSE)TA <- trajectory.analysis(fit,
groups = Pupfish$Pop,
traj.pts = Pupfish$Sex)
summary(TA, attribute = "MD") # Magnitude difference (absolute difference between path distances)##
## Trajectory analysis
##
## 1000 permutations.
##
## Points projected onto trajectory PCs
##
## Trajectories:
## Trajectories hidden (use show.trajectories = TRUE to view)
##
## Observed path distances by group
##
## Marsh Sinkhole
## 0.04611590 0.02568508
##
## Pairwise absolute differences in path distances, plus statistics
## d UCL (95%) Z Pr > d
## Marsh:Sinkhole 0.02043082 0.01274369 2.66641 0.001summary(TA, attribute = "TC", angle.type = "deg") # Correlations (angles) between trajectories##
## Trajectory analysis
##
## 1000 permutations.
##
## Points projected onto trajectory PCs
##
## Trajectories:
## Trajectories hidden (use show.trajectories = TRUE to view)
##
## Pairwise correlations between trajectories, plus statistics
## r angle UCL (95%) Z Pr > angle
## Marsh:Sinkhole 0.7393716 42.32209 23.72507 3.601856 0.001# Plot results
TP <- plot(TA,
pch = as.numeric(Pupfish$Pop) + 20,
bg = as.numeric(Pupfish$Sex),
cex = 0.7, col = "gray")
add.trajectories(TP,
traj.pch = c(21, 22),
start.bg = 1,
end.bg = 2)
legend("topright",
levels(Pupfish$Pop),
pch = c(21, 22),
pt.bg = 1)
2: Disparity Analysis
Here is a simple example of a disparity analysis:
data("pupfish")
Group <- pupfish$Group <- interaction(pupfish$Pop, pupfish$Sex)
fit <- procD.lm(coords ~ Group, data = pupfish)
PW <- pairwise(fit, groups = Group)
summary(PW, test.type = "var")##
## Pairwise comparisons
##
## Groups: Marsh.F Sinkhole.F Marsh.M Sinkhole.M
##
## RRPP: 1000 permutations
##
##
## Observed variances by group
##
## Marsh.F Sinkhole.F Marsh.M Sinkhole.M
## 0.0003439300 0.0005803226 0.0003607052 0.0008318581
##
## Pairwise distances between variances, plus statistics
## d UCL (95%) Z Pr > d
## Marsh.F:Sinkhole.F 2.363925e-04 0.0002473769 1.518166 0.053
## Marsh.F:Marsh.M 1.677513e-05 0.0002492051 -1.346688 0.902
## Marsh.F:Sinkhole.M 4.879280e-04 0.0002412492 3.180101 0.001
## Sinkhole.F:Marsh.M 2.196174e-04 0.0002806646 1.160169 0.130
## Sinkhole.F:Sinkhole.M 2.515355e-04 0.0002726187 1.441515 0.075
## Marsh.M:Sinkhole.M 4.711529e-04 0.0002662683 2.741881 0.002# ALTERNATIVELY
MD <- morphol.disparity(fit, print.progress = FALSE)##
## *** Attempting to define groups from terms in the model fit. If results are peculiar, define groups precisely and check model formula.)summary(MD)##
## Call:
## morphol.disparity(f1 = fit, print.progress = FALSE)
##
##
##
## Randomized Residual Permutation Procedure Used
## 1000 Permutations
##
## Procrustes variances for defined groups
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## 0.0003439300 0.0003607052 0.0005803226 0.0008318581
##
##
## Pairwise absolute differences between variances
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## Marsh.F 0.000000e+00 1.677513e-05 0.0002363925 0.0004879280
## Marsh.M 1.677513e-05 0.000000e+00 0.0002196174 0.0004711529
## Sinkhole.F 2.363925e-04 2.196174e-04 0.0000000000 0.0002515355
## Sinkhole.M 4.879280e-04 4.711529e-04 0.0002515355 0.0000000000
##
##
## P-Values
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## Marsh.F 1.000 0.902 0.053 0.001
## Marsh.M 0.902 1.000 0.130 0.002
## Sinkhole.F 0.053 0.130 1.000 0.075
## Sinkhole.M 0.001 0.002 0.075 1.000P <- plot(fit, type = "PC", pch = 21, bg = pupfish$Group)
shapeHulls(P,
Group,
group.cols = c(1, 3, 2, 4))
3: Integration and Modularity
Here are SOME of the integration/modularity analyses available:
Overall Integration (and comparing it across regions)
data("plethodon")
Y.gpa <- gpagen(plethodon$land,
print.progress = FALSE)
#Separate data by species
coords.gp <- coords.subset(Y.gpa$coords,
plethodon$species)
#Z_Vrel by species
Vrel.gp <- Map(function(x) integration.Vrel(x), coords.gp)
compare.ZVrel(Vrel.gp$Jord, Vrel.gp$Teyah)##
## Effect sizes
##
## Vrel.gp$Jord Vrel.gp$Teyah
## -0.2978931 -0.2642648
##
## Effect sizes for pairwise differences in rel.eig effect size
##
## Vrel.gp$Jord Vrel.gp$Teyah
## Vrel.gp$Jord 0.00000000 0.09804249
## Vrel.gp$Teyah 0.09804249 0.00000000
##
## P-values
##
## Vrel.gp$Jord Vrel.gp$Teyah
## Vrel.gp$Jord 1.0000000 0.9218986
## Vrel.gp$Teyah 0.9218986 1.0000000Integration among subsets
data(pupfish) # GPA previously performed
group <- factor(paste(pupfish$Pop, pupfish$Sex, sep = "."))
# Subset 3D array by group, returning a list of 3D arrays
tail.LM <- c(1:3, 5:9, 18:38)
head.LM <- (1:56)[-tail.LM]
tail.coords <- pupfish$coords[tail.LM, , ]
head.coords <- pupfish$coords[head.LM, , ]
IT <- integration.test(tail.coords,
head.coords,
print.progress = FALSE)##
## No names for A2. Data are assumed to be ordered as in A.summary(IT)##
## Call:
## integration.test(A = tail.coords, A2 = head.coords, print.progress = FALSE)
##
##
##
## r-PLS: 0.917
##
## Effect Size (Z): 5.4983
##
## P-value: 0.001
##
## Based on 1000 random permutationsplot(IT)
Compare Strength of Integration acrouss groups
tail.coords.gp <- coords.subset(tail.coords, group)
head.coords.gp <- coords.subset(head.coords, group)
# Obtain Integration for groups
integ.tests <- Map(function(x,y)
integration.test(x, y, iter = 999,
print.progress = FALSE),
head.coords.gp, tail.coords.gp)
compare.pls(integ.tests)##
## Effect sizes
##
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## 3.1956225 1.4571455 0.6488562 2.7097203
##
## Effect sizes for pairwise differences in PLS effect size
##
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## Marsh.F 0.0000000 0.9283614 1.9682801 0.877886
## Marsh.M 0.9283614 0.0000000 0.7894939 1.491679
## Sinkhole.F 1.9682801 0.7894939 0.0000000 2.172603
## Sinkhole.M 0.8778860 1.4916787 2.1726031 0.000000
##
## P-values
##
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## Marsh.F 1.00000000 0.3532201 0.04903581 0.3800056
## Marsh.M 0.35322012 1.0000000 0.42982338 0.1357834
## Sinkhole.F 0.04903581 0.4298234 1.00000000 0.0298102
## Sinkhole.M 0.38000560 0.1357834 0.02981020 1.0000000Modularity
land.gp <- rep(1,56); land.gp[tail.LM] <- 2
MT <- modularity.test(pupfish$coords,
land.gp,
CI = FALSE,
print.progress = FALSE)
summary(MT)##
## Call:
## modularity.test(A = pupfish$coords, partition.gp = land.gp, CI = FALSE,
## print.progress = FALSE)
##
##
##
## CR: 0.8771
##
## P-value: 0.003
##
## Effect Size: -4.5427
##
## Based on 1000 random permutationsplot(MT)
Compare Strength of Modularity Across Groups
coords.gp <- coords.subset(pupfish$coords, group)
modul.tests <- Map(function(x)
modularity.test(x,
land.gp,
print.progress = FALSE),
coords.gp)
compare.CR(modul.tests, CR.null = FALSE)##
## NOTE: more negative effects represent stronger modular signal!
##
##
## Effect sizes
##
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## -2.816188 -5.778451 -3.363544 -4.534488
##
## Effect sizes for pairwise differences in CR effect size
##
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## Marsh.F 0.000000 2.5466647 1.8303913 1.017783
## Marsh.M 2.546665 0.0000000 0.1496676 1.693290
## Sinkhole.F 1.830391 0.1496676 0.0000000 1.251317
## Sinkhole.M 1.017783 1.6932905 1.2513171 0.000000
##
## P-values
##
## Marsh.F Marsh.M Sinkhole.F Sinkhole.M
## Marsh.F 1.00000000 0.01087579 0.06719144 0.30878104
## Marsh.M 0.01087579 1.00000000 0.88102690 0.09040019
## Sinkhole.F 0.06719144 0.88102690 1.00000000 0.21081881
## Sinkhole.M 0.30878104 0.09040019 0.21081881 1.000000004: Data Prep/Clean-up
Estimating Missing Data
NOTE: First we create some missing data for illustration
data(plethodon)
Y.gpa <- gpagen(plethodon$land, print.progress = FALSE)
plethland<-Y.gpa$coords
plethland[3, , 2] <- plethland[8, , 2] <- NA #create missing landmarks
plethland[3, , 5] <- plethland[8, , 5] <- plethland[9,,5] <- NA
plethland[3, , 10] <- NA Now estimate
new.tps <- estimate.missing(plethland, method = "TPS")
new.reg <- estimate.missing(plethland, method = "Reg")Fix Positional Differences among regions
See fixed.angle
Combine landmark configurations
See combine.subsets
5: Things to Explore on Your Own
- Remember Days 1 - 4
- Perform phylogenetic ANOVA, phylogenetic PLS, and other PCMs.
- Visualize shapes from everything!
- Plot summaries from these analyses to accompany the statistical findings
- Explore function options and output (there are many!)