# Lab Exersize 2
Tutorial 1
```
library(borealis)
data("pupfish", package="geomorph")
str(pupfish)
edge.landmarks <- 11:56
pup.links <- matrix(c(edge.landmarks[-length(edge.landmarks)], edge.landmarks[-1]),
ncol = 2, byrow = FALSE)
pup.links <- rbind(pup.links[-c(23,28,38),],
matrix(c(4,11, 1,3, 3,9, 9,38, 33,7, 34,8, 4,48, 1,46, 49,56),
ncol = 2, byrow = TRUE) )
landmark.plot(pupfish, links = pup.links)
pup.gpa <- align.procrustes(pupfish$coords)
names(pup.gpa)
pup.gdf <- listed.gdf(pup.gpa)
names(pup.gdf)
names(pup.gdf$gdf)
pup.gdf$gdf$Csize <- pupfish$CS
pup.gdf$gdf$sex <- pupfish$Sex
pup.gdf$gdf$pop <- pupfish$Pop
pup.gdf$gdf$pop.sex <- as.factor(paste(pup.gdf$gdf$pop, pup.gdf$gdf$sex, sep = "_"))
pup.pca <- gm.prcomp(pup.gdf$gdf$coords)
plot(pup.pca, col = as.factor(pup.gdf$gdf$pop.sex))
legend("topright", levels(pup.gdf$gdf$pop.sex),
col = c(1:length(levels(pup.gdf$gdf$pop.sex))),
pch = 1, box.lwd = 0)
i <- 1e4-1 # number of iterations
size.model <- procD.lm(coords ~ log(Csize), data=pup.gdf$gdf, iter=i)
anova(size.model)
sex.model <- procD.lm(coords ~ log(Csize) + sex, data=pup.gdf$gdf, iter=i)
anova(sex.model)
anova(size.model, sex.model)
pop.model <- procD.lm(coords ~ log(Csize) + pop, data=pup.gdf$gdf, iter=i)
sex.pop.model <- procD.lm(coords ~ log(Csize) + sex + pop, data=pup.gdf$gdf, iter=i)
anova(size.model, pop.model, sex.pop.model)
sex.by.pop.model <- procD.lm(coords ~ log(Csize) + sex * pop, data=pup.gdf$gdf, iter=i)
anova(sex.pop.model, sex.by.pop.model)
sex.by.pop.model <- procD.lm(coords ~ log(Csize) + sex + pop + sex:pop, data=pup.gdf$gdf, iter=i)
pop.unique.model <- procD.lm(coords ~ log(Csize) * pop, data=pup.gdf$gdf, iter=i)
anova(pop.model, pop.unique.model)
plotAllometry(fit = pop.unique.model, size = pup.gdf$gdf$Csize,
col = pup.gdf$gdf$pop, xlab = "log centroid size")
```
Problem 1
```
pop.unique.model2 <- procD.lm(coords ~ log(Csize) * pop + sex, data=pup.gdf$gdf, iter=i)
anova(sex.pop.model, pop.unique.model2)
plotAllometry(fit = pop.unique.model2, size = pup.gdf$gdf$Csize,
col = pup.gdf$gdf$pop.sex, xlab = "log centroid size")
```
Anova Results
```
Analysis of Variance, using Residual Randomization
Permutation procedure: Randomization of null model residuals
Number of permutations: 10000
Estimation method: Ordinary Least Squares
Effect sizes (Z) based on F distributions
ResDf Df RSS SS MS Rsq F
coords ~ log(Csize) + sex + pop (Null) 50 1 0.027002 0.000000
coords ~ log(Csize) * pop + sex 49 1 0.025351 0.0016509 0.0016509 0.029343 3.1909
Total 53 0.056262
Z P Pr(>F)
coords ~ log(Csize) + sex + pop (Null)
coords ~ log(Csize) * pop + sex 2.5575 0.0067
Total
```
Sex and population are an important factors influencing pupfish shape (permutation-based Procrustes ANOVA, F= 3.1909, p = .0067). The interaction between population and size was significant in determining that these groups have unique allometries.
Tutorial 2
```
create.tps(
input.filename = "Ofas.RNAi.nota.digitization.csv",
output.filename = "Ofas.RNAi.nota.tps",
id.factors = c('digitizer','treatment'),
include.scale = TRUE,
invert.scale = TRUE)
bug.nota <- read.tps("Ofas.RNAi.nota.tps", keep.original.ids = TRUE)
nota.lines <- matrix(c(1,2, 2,3, 3,4, 4,5, 5,6, 6,7, 7,8, 8,1, 2,6),
ncol = 2, byrow = TRUE)
bug.nota <- align.reflect(bug.nota, links = nota.lines)
bug.gpa <- align.procrustes(bug.nota)
x <- bug.gpa$Csize > 500
bug.gpa$Csize[x] <- NA
x <- bug.gpa$metadata$treatment == "vr"
bug.gpa$metadata$treatment[x] <- "vg"
x <- bug.gpa$metadata$treatment == "wildtype"
bug.gpa$metadata$treatment[x] <- "wt"
bug.gdf <- listed.gdf(bug.gpa)
bug.pca <- gm.prcomp(bug.gdf$gdf$coords)
ggGMMplot(bug.pca,
group = bug.gdf$gdf$treatment,
group.title = 'treatment',
convex.hulls = TRUE,
include.legend = TRUE )
```
Problem 2
```
i <- 1e4-1
bug.gdf <- listed.gdf(bug.gpa)
bug.model1 <- procD.lm(coords ~ log(Csize), data = bug.gdf$gdf, iter = i)
bug.model2 <- procD.lm(coords ~ log(Csize) + digitizer, data = bug.gdf$gdf, iter = i)
anova(bug.model1, bug.model2)
```
First, I wanted to look at whether or not the digitizer affected the size of the milkweed bug.
```
Analysis of Variance, using Residual Randomization
Permutation procedure: Randomization of null model residuals
Number of permutations: 10000
Estimation method: Ordinary Least Squares
Effect sizes (Z) based on F distributions
ResDf Df RSS SS MS Rsq F Z P Pr(>F)
coords ~ log(Csize) (Null) 88 1 2.2163 0.00000
coords ~ log(Csize) + digitizer 80 8 0.9453 1.2711 0.15888 0.57208 13.446 5.9842 1e-04
Total 89 2.2218
```
The sample digitizer had a significant effect on the size of the sample, meaning there was non insignificant human error (permutation-based Procrustes ANOVA, F= 13.446, p < .001)
Then I wanted to see if there was any allometry changes between treatment. This was done by modeling treatment and size (and controlling for digitizer), and then modeling an interaction between shape and treatment, to see if the rate of the change in size was affected by treatment.
```
bug.model3 <- procD.lm(coords ~ log(Csize) + treatment + digitizer, data = bug.gdf$gdf, iter = i)
bug.model4 <- procD.lm(coords ~ log(Csize) * treatment + digitizer, data = bug.gdf$gdf, iter = i)
anova(bug.model3, bug.model4)
```
```
Analysis of Variance, using Residual Randomization
Permutation procedure: Randomization of null model residuals
Number of permutations: 10000
Estimation method: Ordinary Least Squares
Effect sizes (Z) based on F distributions
ResDf Df RSS SS MS Rsq F Z P Pr(>F)
coords ~ log(Csize) + treatment + digitizer (Null) 71 1 0.13921 0.0000000
coords ~ log(Csize) * treatment + digitizer 62 9 0.12141 0.017802 0.001978 0.0080123 1.0101 0.12622 0.4545
Total
```
There is no evidence of allometry between bug size and treatments (permutation-based Procrustes ANOVA, F= 1.0101, p = .4545)
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