Revision of the Australian Ozestheria fauna

1 Preparation

1.1 Loading FFT-coefficients

shape_8 <- read.csv("Condyle_kurz_vs2.csv", header=T, sep=";")

1.2 Data subsets

C_shape <- shape_8[which(shape_8$Species2 == 'C'), ]
D_shape <- shape_8[which(shape_8$Species2 == 'D'), ]
D3_shape <- shape_8[which(shape_8$Species2 == 'D3'), ]
E_shape <- shape_8[which(shape_8$Species2 == 'E'), ]
F_shape <- shape_8[which(shape_8$Species2 == 'F'), ]
G_shape <- shape_8[which(shape_8$Species2 == 'G'), ]
M_shape <- shape_8[which(shape_8$Species2 == 'M'), ]
M_shape <- M_shape[-24, ] #specimen not adequately oriented during photography
N_shape <- shape_8[which(shape_8$Species2 == 'N'), ]
T_shape <- shape_8[which(shape_8$Species2 == 'T'), ]
X1_shape <- shape_8[which(shape_8$Species2 == 'X1'), ]
X10_shape <- shape_8[which(shape_8$Species2 == 'X10'), ]
X11_shape <- shape_8[which(shape_8$Species2 == 'X11'), ]

dictyon_mean <- cbind("dictyon", as.data.frame(t(colMeans(shape_8[c(243:245), c(2:15)]))),"dictyon_mean","dictyon_mean", "mean")
colnames(dictyon_mean)[1:18] <- c("collection","A2","A3","A4","A5","A6","A7","A8","B2","B3","B4","B5","B6","B7","B8","Species","Species2","Sex")

berneyi_mean <- cbind("berneyi", as.data.frame(t(colMeans(shape_8[c(213:215), c(2:15)]))),"berneyi_mean","berneyi_mean", "mean")
colnames(berneyi_mean)[1:18] <- c("collection","A2","A3","A4","A5","A6","A7","A8","B2","B3","B4","B5","B6","B7","B8","Species","Species2","Sex")

All <- as.data.frame(rbind(C_shape, D_shape, D3_shape, E_shape, F_shape, G_shape, M_shape, N_shape, T_shape, X1_shape, X10_shape, X11_shape))
All_types <- as.data.frame(rbind(C_shape, D_shape, D3_shape, E_shape, F_shape, G_shape, M_shape, N_shape, T_shape, X1_shape, X10_shape, X11_shape, shape_8[c(1:3, 213:215,  241:249),]))
C_dictyon_lutraria_type <- as.data.frame(rbind(C_shape, shape_8[c(243:248),], dictyon_mean))
D_D3_rubra_elliptica <- as.data.frame(rbind(D_shape, D3_shape, shape_8[c(1, 241),]))
M_N_berneyi <- as.data.frame(rbind(M_shape, N_shape, shape_8[c(213:215),], berneyi_mean))

1.3 Distribution and correlation analyses

Pearson product moment correlation coefficient, following SOGA page 19/104.

1.3.1 Full set (C D D3 E F G M N T X1 X10 X11)

pairs.panels(All[2:15], smooth = F, ellipses = T)

1.3.2 Species distribution and correlation

1.3.2.1 C

n = 30
set.seed(333)
sample.idx <- sample(1:nrow(C_shape), size = n)
vars <- c("A2","A3","A4","A5","A6","A7","A8","B2","B3","B4","B5","B6","B7","B8")
pairs.panels(C_shape[sample.idx, vars], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species C')

1.3.2.2 D

pairs.panels(D_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species D')

1.3.2.3 D3

pairs.panels(D3_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species D3')

1.3.2.4 E

pairs.panels(E_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species E')

1.3.2.5 F

pairs.panels(F_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species F')

1.3.2.6 G

pairs.panels(G_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species G')

1.3.2.7 M

n = 29
set.seed(333)
sample.idx <- sample(1:nrow(M_shape), size = n)
vars <- c("A2","A3","A4","A5","A6","A7","A8","B2","B3","B4","B5","B6","B7","B8")
pairs.panels(M_shape[sample.idx, vars], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species M')

1.3.2.8 N

n = 30
set.seed(333)
sample.idx <- sample(1:nrow(N_shape), size = n)
vars <- c("A2","A3","A4","A5","A6","A7","A8","B2","B3","B4","B5","B6","B7","B8")
pairs.panels(N_shape[sample.idx, vars], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species N')

1.3.2.9 T

pairs.panels(T_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species T')

1.3.2.10 X1

pairs.panels(X1_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species X1')

1.3.2.11 X10

pairs.panels(X10_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species X10')

1.3.2.12 X11

pairs.panels(X11_shape[2:15], smooth = F, ellipses = F, 
             main = 'Pearson product moment correlation coefficient for species X11')

2 Principal Component Analysis (PCA)

2.1 C D D3 E F G M N T X1 X10 X11

All.pca <- princomp(All[c(2:15)])
ggord(All.pca, All$Species2,size = 2.5, vec_ext=0.03, axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0) #+ xlim(-0.08,0.07) + ylim(-0.075, 0.03)

ggord(All.pca, All$Species2,size = 2.5, vec_ext=0.03, axes = c("1", "3"), hull = TRUE, ellipse=FALSE, arrow = 0) #+ xlim(-0.08,0.07) + ylim(-0.04, 0.045)

PC1, PC2, and PC3 explain 65.1%, 9.8%, and 7.7% of the variance in the dataset, respectively.

2.2 C D D3 E F G M N T X1 X10 X11 plus type specimens

All_types.pca <- princomp(All_types[c(2:15)])
ggord(All_types.pca, All_types$Species2,size = 2.5, vec_ext=0.03,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0) #+ xlim(-0.08,0.07) + ylim(-0.075, 0.04)

ggord(All_types.pca, All_types$Species2,size = 2.5, vec_ext=0.03,axes = c("2", "3"), hull = TRUE, ellipse=FALSE, arrow = 0) #+ xlim(-0.075,0.0375) + ylim(-0.04, 0.045)

Biplot of scores and loadings on PC1 and PC2 as well as PC2 and PC3. PC1, PC2, and PC3 explain 63.0%, 11.5%, and 7.4% of the variance in the dataset, respectively. T and X10 yield similar shapes on the PC1 vs PC2 plane, but are clearly separated on the PC2 vs PC3 plane. X10 can be assigned to Ozestheria rufa following their overlap on the PC2 vs PC3 plane.

2.3 C_dictyon_lutraria_type

C_dictyon_lutraria_type.pca <- princomp(C_dictyon_lutraria_type[c(2:15)])
ggord(C_dictyon_lutraria_type.pca, C_dictyon_lutraria_type$Species2,size = 2.5, vec_ext=0.03,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0)

lutraria_drawing = drawing of lutraria in Brady (1886) lutraria = lutraria specimens J53362a, b

2.4 D_D3_rubra_elliptica

D_D3_rubra_elliptica.pca <- princomp(D_D3_rubra_elliptica[c(2:15)])
ggord(D_D3_rubra_elliptica.pca, D_D3_rubra_elliptica$Species2,size = 2.5, vec_ext=0.03,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0)

2.5 M_N_berneyi

M_N_berneyi.pca <- princomp(M_N_berneyi[c(2:15)])
ggord(M_N_berneyi.pca, M_N_berneyi$Species2,size = 2.5, vec_ext=0.03,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0)

ggord(M_N_berneyi.pca, M_N_berneyi$Species2,size = 2.5, vec_ext=0.03,axes = c("2", "3"), hull = TRUE, ellipse=FALSE, arrow = 0)

The type of Ozestheria berneyi (lower left corner in the PC1 vs PC2 plot) is an outlier to both M and N.

3 Linear Discriminant Analysis (LDA)

3.1 C D D3 E F G M N T X1 X10 X11

All.lda <- lda(Species2 ~ A2+A3+A4+A5+A6+A7+A8+B2+B3+B4+B5+B6+B7+B8, method = "moment", data = All, na.action = na.omit)
All.lda.values <- predict(All.lda)

ggord(All.lda, All$Species2,size = 2.5, vec_ext=0.03,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0)

ggord(All.lda, All$Species2,size = 2.5, vec_ext=0.03,axes = c("2", "3"), hull = TRUE, ellipse=FALSE, arrow = 0)

LD1, LD2, and LD3 explain 77.9%, 9.4%, and 7.2% of the between-group variance, respectively.

3.2 C D D3 E F G M N T X1 X10 X11 plus type specimens

All_types.lda <- lda(Species2 ~ A2+A3+A4+A5+A6+A7+A8+B2+B3+B4+B5+B6+B7+B8, method = "moment", data = All_types, na.action = na.omit)
All_types.lda.values <- predict(All_types.lda)

ggord(All_types.lda, All_types$Species2,size = 2.5, vec_ext=0.03,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0)

ggord(All_types.lda, All_types$Species2,size = 2.5, vec_ext=0.03,axes = c("1", "3"), hull = TRUE, ellipse=FALSE, arrow = 0)

3.3 C_dictyon_lutraria_type

C_dictyon_lutraria_type.lda <- lda(Species2 ~ A2+A3+A4+A5+A6+A7+A8+B2+B3+B4+B5+B6+B7+B8, method = "moment", data = C_dictyon_lutraria_type, na.action = na.omit)
C_dictyon_lutraria_type.lda.values <- predict(C_dictyon_lutraria_type.lda)

ggord(C_dictyon_lutraria_type.lda, C_dictyon_lutraria_type$Species2,size = 2.5, vec_ext=0.01,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0)

lutraria_drawing = drawing of lutraria in Brady (1886) lutraria = lutraria specimens J53362a, b

3.4 D_D3_rubra_elliptica

D_D3_rubra_elliptica.lda <- lda(Species2 ~ A2+A3+A4+A5+A6+A7+A8+B2+B3+B4+B5+B6+B7+B8, method = "moment", data = D_D3_rubra_elliptica, na.action = na.omit)
D_D3_rubra_elliptica.lda.values <- predict(D_D3_rubra_elliptica.lda)

ggord(D_D3_rubra_elliptica.lda, D_D3_rubra_elliptica$Species2,size = 2.5, vec_ext=0.01,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0)

3.5 M_N_berneyi

M_N_berneyi.lda <- lda(Species2 ~ A2+A3+A4+A5+A6+A7+A8+B2+B3+B4+B5+B6+B7+B8, method = "moment", data = M_N_berneyi, na.action = na.omit)
M_N_berneyi.lda.values <- predict(M_N_berneyi.lda)

ggord(M_N_berneyi.lda, M_N_berneyi$Species2,size = 2.5, vec_ext=0.01,axes = c("1", "2"), hull = TRUE, ellipse=FALSE, arrow = 0)

The type of Ozestheria berneyi (lower left corner in the LD1 vs LD2 plot) is an outlier to both M and N, only the female shape is associated with N.

4 Classification of type specimens

Following Boedeker and Kearns (2019) Linear Discriminant Analysis for prediction of group membership

options(width = 120)
n.class <- 12
p <- 14 #number of predictors
N <- 233

### means of Fourier coefficients (predictors) within species (class) ###
mean.C <- c(mean(C_shape$A2), mean(C_shape$A3),mean(C_shape$A4),mean(C_shape$A5),mean(C_shape$A6),mean(C_shape$A7),mean(C_shape$A8), mean(C_shape$B2), mean(C_shape$B3), mean(C_shape$B4), mean(C_shape$B5), mean(C_shape$B6), mean(C_shape$B7), mean(C_shape$B8))

mean.D <- c(mean(D_shape$A2), mean(D_shape$A3),mean(D_shape$A4),mean(D_shape$A5),mean(D_shape$A6),mean(D_shape$A7),mean(D_shape$A8), mean(D_shape$B2), mean(D_shape$B3), mean(D_shape$B4), mean(D_shape$B5), mean(D_shape$B6), mean(D_shape$B7), mean(D_shape$B8))

mean.D3 <- c(mean(D3_shape$A2), mean(D3_shape$A3),mean(D3_shape$A4),mean(D3_shape$A5),mean(D3_shape$A6),mean(D3_shape$A7),mean(D3_shape$A8), mean(D3_shape$B2), mean(D3_shape$B3), mean(D3_shape$B4), mean(D3_shape$B5), mean(D3_shape$B6), mean(D3_shape$B7), mean(D3_shape$B8))

mean.E <- c(mean(E_shape$A2), mean(E_shape$A3),mean(E_shape$A4),mean(E_shape$A5),mean(E_shape$A6),mean(E_shape$A7),mean(E_shape$A8), mean(E_shape$B2), mean(E_shape$B3), mean(E_shape$B4), mean(E_shape$B5), mean(E_shape$B6), mean(E_shape$B7), mean(E_shape$B8))

mean.F <- c(mean(F_shape$A2), mean(F_shape$A3),mean(F_shape$A4),mean(F_shape$A5),mean(F_shape$A6),mean(F_shape$A7),mean(F_shape$A8), mean(F_shape$B2), mean(F_shape$B3), mean(F_shape$B4), mean(F_shape$B5), mean(F_shape$B6), mean(F_shape$B7), mean(F_shape$B8))

mean.G <- c(mean(G_shape$A2), mean(G_shape$A3),mean(G_shape$A4),mean(G_shape$A5),mean(G_shape$A6),mean(G_shape$A7),mean(G_shape$A8), mean(G_shape$B2), mean(G_shape$B3), mean(G_shape$B4), mean(G_shape$B5), mean(G_shape$B6), mean(G_shape$B7), mean(G_shape$B8))

mean.M <- c(mean(M_shape$A2), mean(M_shape$A3),mean(M_shape$A4),mean(M_shape$A5),mean(M_shape$A6),mean(M_shape$A7),mean(M_shape$A8), mean(M_shape$B2), mean(M_shape$B3), mean(M_shape$B4), mean(M_shape$B5), mean(M_shape$B6), mean(M_shape$B7), mean(M_shape$B8))

mean.N <- c(mean(N_shape$A2), mean(N_shape$A3),mean(N_shape$A4),mean(N_shape$A5),mean(N_shape$A6),mean(N_shape$A7),mean(N_shape$A8), mean(N_shape$B2), mean(N_shape$B3), mean(N_shape$B4), mean(N_shape$B5), mean(N_shape$B6), mean(N_shape$B7), mean(N_shape$B8))

mean.T <- c(mean(T_shape$A2), mean(T_shape$A3),mean(T_shape$A4),mean(T_shape$A5),mean(T_shape$A6),mean(T_shape$A7),mean(T_shape$A8), mean(T_shape$B2), mean(T_shape$B3), mean(T_shape$B4), mean(T_shape$B5), mean(T_shape$B6), mean(T_shape$B7), mean(T_shape$B8))

mean.X1 <- c(mean(X1_shape$A2), mean(X1_shape$A3),mean(X1_shape$A4),mean(X1_shape$A5),mean(X1_shape$A6),mean(X1_shape$A7),mean(X1_shape$A8), mean(X1_shape$B2), mean(X1_shape$B3), mean(X1_shape$B4), mean(X1_shape$B5), mean(X1_shape$B6), mean(X1_shape$B7), mean(X1_shape$B8))

mean.X10 <- c(mean(X10_shape$A2), mean(X10_shape$A3),mean(X10_shape$A4),mean(X10_shape$A5),mean(X10_shape$A6),mean(X10_shape$A7),mean(X10_shape$A8), mean(X10_shape$B2), mean(X10_shape$B3), mean(X10_shape$B4), mean(X10_shape$B5), mean(X10_shape$B6), mean(X10_shape$B7), mean(X10_shape$B8))

mean.X11 <- c(mean(X11_shape$A2), mean(X11_shape$A3),mean(X11_shape$A4),mean(X11_shape$A5),mean(X11_shape$A6),mean(X11_shape$A7),mean(X11_shape$A8), mean(X11_shape$B2), mean(X11_shape$B3), mean(X11_shape$B4), mean(X11_shape$B5), mean(X11_shape$B6), mean(X11_shape$B7), mean(X11_shape$B8))

mean.C <- as.matrix(mean.C)
mean.D <- as.matrix(mean.D)
mean.D3 <- as.matrix(mean.D3)
mean.E <- as.matrix(mean.E)
mean.F <- as.matrix(mean.F)
mean.G <- as.matrix(mean.G)
mean.M <- as.matrix(mean.M)
mean.N <- as.matrix(mean.N)
mean.T <- as.matrix(mean.T)
mean.X1 <- as.matrix(mean.X1)
mean.X10 <- as.matrix(mean.X10)
mean.X11 <- as.matrix(mean.X11)

### Variance-covariance matrix ###
cov.C <- cov(C_shape[2:15])
cov.D <- cov(D_shape[2:15])
cov.D3 <- cov(D3_shape[2:15])
cov.E <- cov(E_shape[2:15])
cov.F <- cov(F_shape[2:15])
cov.G <- cov(G_shape[2:15])
cov.M <- cov(M_shape[2:15])
cov.N <- cov(N_shape[2:15])
cov.T <- cov(T_shape[2:15])
cov.X1 <- cov(X1_shape[2:15])
cov.X10 <- cov(X10_shape[2:15])
cov.X11 <- cov(X11_shape[2:15])

### sample size ###
n.C <- dim(C_shape) [1]
n.D <- dim(D_shape) [1]
n.D3 <- dim(D3_shape) [1]
n.E <- dim(E_shape) [1]
n.F <- dim(F_shape) [1]
n.G <- dim(G_shape) [1]
n.M <- dim(M_shape) [1]
n.N <- dim(N_shape) [1]
n.T <- dim(T_shape) [1]
n.X1 <- dim(X1_shape) [1]
n.X10 <- dim(X10_shape) [1]
n.X11 <- dim(X11_shape) [1]

cov.df <- n.C+n.D+n.D3+n.E+n.F+n.G+n.M+n.N+n.T+n.X1+n.X10+n.X11-n.class

cov.d <- ((n.C-1)/cov.df)*cov.C+((n.D-1)/cov.df)*cov.D+((n.D3-1)/cov.df)*cov.D3+((n.E-1)/cov.df)*cov.E+((n.F-1)/cov.df)*cov.F+((n.G-1)/cov.df)*cov.G+((n.M-1)/cov.df)*cov.M+((n.N-1)/cov.df)*cov.N+((n.T-1)/cov.df)*cov.T+((n.X1-1)/cov.df)*cov.X1+((n.X10-1)/cov.df)*cov.X10+((n.X11-1)/cov.df)*cov.X11

### determinant
d <- det(cov.d)

### Coefficients of Linear classification function (loadings)
cj.C <- solve(cov.d)%*%mean.C
cj.D <- solve(cov.d)%*%mean.D
cj.D3 <- solve(cov.d)%*%mean.D3
cj.E <- solve(cov.d)%*%mean.E
cj.F <- solve(cov.d)%*%mean.F
cj.G <- solve(cov.d)%*%mean.G
cj.M <- solve(cov.d)%*%mean.M
cj.N <- solve(cov.d)%*%mean.N
cj.T <- solve(cov.d)%*%mean.T
cj.X1 <- solve(cov.d)%*%mean.X1
cj.X10 <- solve(cov.d)%*%mean.X10
cj.X11 <- solve(cov.d)%*%mean.X11

### Intercepts
cj0.C <- -.5*t(cj.C)%*%mean.C
cj0.D <- -.5*t(cj.D)%*%mean.D
cj0.D3 <- -.5*t(cj.D3)%*%mean.D3
cj0.E <- -.5*t(cj.E)%*%mean.E
cj0.F <- -.5*t(cj.F)%*%mean.F
cj0.G <- -.5*t(cj.G)%*%mean.G
cj0.M <- -.5*t(cj.M)%*%mean.M
cj0.N <- -.5*t(cj.N)%*%mean.N
cj0.T <- -.5*t(cj.T)%*%mean.T
cj0.X1 <- -.5*t(cj.X1)%*%mean.X1
cj0.X10 <- -.5*t(cj.X10)%*%mean.X10
cj0.X11 <- -.5*t(cj.X11)%*%mean.X11

4.1 Typicality all specimens

### Typicality probabilities ###
typicality <- matrix(NA, N, n.class)
colnames(typicality) <- c("typC","typD","typD3","typE","typF","typG","typM","typN","typT","typX1","typX10","typX11")
for(q in 1:N) {
  case <- matrix(NA,12,1)
  case <- c(All[q,2],All[q,3],All[q,4],All[q,5],All[q,6],All[q,7],All[q,8],All[q,9],All[q,10],All[q,11],All[q,12],All[q,13],All[q,14],All[q,15])
  d2.C <- (t(case-mean.C))%*%solve(cov.d)%*%(case-mean.C)
  typicality[q,1] <- pchisq(d2.C, df = 14, lower.tail = FALSE)
  d2.D <- (t(case-mean.D))%*%solve(cov.d)%*%(case-mean.D)
  typicality[q,2] <- pchisq(d2.D, df = 14, lower.tail = FALSE)
  d2.D3 <- (t(case-mean.D3))%*%solve(cov.d)%*%(case-mean.D3)
  typicality[q,3] <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
  d2.E <- (t(case-mean.E))%*%solve(cov.d)%*%(case-mean.E)
  typicality[q,4] <- pchisq(d2.E, df = 14, lower.tail = FALSE)
  d2.F <- (t(case-mean.F))%*%solve(cov.d)%*%(case-mean.F)
  typicality[q,5] <- pchisq(d2.F, df = 14, lower.tail = FALSE)
  d2.G <- (t(case-mean.G))%*%solve(cov.d)%*%(case-mean.G)
  typicality[q,6] <- pchisq(d2.G, df = 14, lower.tail = FALSE)
  d2.M <- (t(case-mean.M))%*%solve(cov.d)%*%(case-mean.M)
  typicality[q,7] <- pchisq(d2.M, df = 14, lower.tail = FALSE)
  d2.N <- (t(case-mean.N))%*%solve(cov.d)%*%(case-mean.N)
  typicality[q,8] <- pchisq(d2.N, df = 14, lower.tail = FALSE)
  d2.T <- (t(case-mean.T))%*%solve(cov.d)%*%(case-mean.T)
  typicality[q,9] <- pchisq(d2.T, df = 14, lower.tail = FALSE)
  d2.X1 <- (t(case-mean.X1))%*%solve(cov.d)%*%(case-mean.X1)
  typicality[q,10] <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
  d2.X10 <- (t(case-mean.X10))%*%solve(cov.d)%*%(case-mean.X10)
  typicality[q,11] <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
  d2.X11 <- (t(case-mean.X11))%*%solve(cov.d)%*%(case-mean.X11)
  typicality[q,12] <- pchisq(d2.X11, df = 14, lower.tail = FALSE)
}
typicality <- round(typicality, digits=2)
typicality <- cbind(All[ ,c(1,17:18)], typicality)
typicality

##     collection Species2    Sex typC typD typD3 typE typF typG typM typN typT typX1 typX10 typX11
## 8        82575        C      F 0.69 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 9        82576        C      M 0.22 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 12       89647        C      M 0.11 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 86       91283        C F_eggs 0.11 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 87       91284        C      M 0.46 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 88       91287        C      M 0.19 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 89       91290        C      M 0.30 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.04
## 90       91291        C      M 0.51 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.02
## 91       91293        C      M 0.25 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 92       91295        C      M 0.80 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 93       91298        C      M 0.06 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 94       91300        C      F 0.05 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 95       91302        C      M 0.04 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 96       91304        C      F 0.40 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 97       91305        C      F 0.07 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 98       91306        C      F 0.13 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 99       91308        C      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 100      91314        C      M 0.40 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.02
## 101      91315        C      M 0.08 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 102      91317        C      F 0.62 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 103      91318        C      F 0.37 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 104      91319        C      M 0.58 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 105      91320        C      M 0.77 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.01
## 106      91322        C      M 0.70 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 107      91323        C      M 0.07 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 108      91325        C      F 0.41 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 109      91326        C      F 0.30 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 110      91327        C      F 0.79 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 111      91328        C      F 0.51 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 112      91329        C      M 0.95 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 113      91330        C      F 0.86 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 114      91331        C      M 0.90 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 115      91332        C      F 0.13 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 116      91333        C      M 0.03 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 117      91334        C      F 0.19 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 118      91336        C      F 0.01 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 119      91337        C      M 0.04 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 120      91338        C      F 0.64 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 121      91339        C      F 0.60 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 122      91340        C      F 0.73 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 123      91341        C      M 0.77 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 124      91342        C      M 0.26 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 125      91343        C      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.01
## 126      91344        C      F 0.83 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 127      91345        C      M 0.63 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 128      91347        C      M 0.05 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 129      91349        C      F 0.27 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 130      91350        C      F 0.62 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 131      91351        C      M 0.02 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 132      91352        C      F 0.34 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 133      91353        C      M 0.01 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 134      91354        C      F 0.26 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 135      91355        C      M 0.46 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 136      91356        C      F 0.06 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 137      91357        C      M 0.08 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 138      91358        C      F 0.33 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 139      91359        C      F 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 140      91360        C      F 0.07 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 141      91361        C      M 0.70 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.01
## 142      91362        C      M 0.25 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 143      91363        C      F 0.44 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.01
## 144      91365        C      F 0.34 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 145      91366        C      M 0.13 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 146      91367        C      M 0.17 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 147      91368        C      F 0.81 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 148      91369        C      M 0.32 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 149      91370        C      M 0.04 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.01   0.00   0.00
## 150      91371        C      F 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 151      91372        C      F 0.80 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 152      91373        C      M 0.06 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 153      91374        C      F 0.21 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 154      91375        C      F 0.57 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 155      91376        C      F 0.93 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 156      91379        D F_eggs 0.00 0.05  0.10 0.00 0.00 0.01 0.00 0.01 0.00  0.00   0.00   0.00
## 157      91380        D      M 0.00 0.45  0.30 0.00 0.13 0.00 0.00 0.01 0.00  0.81   0.00   0.00
## 160      91383        D F_eggs 0.00 0.60  0.55 0.00 0.00 0.05 0.10 0.41 0.00  0.01   0.00   0.00
## 161      91384        D F_eggs 0.00 0.47  0.19 0.00 0.00 0.00 0.00 0.15 0.00  0.10   0.00   0.00
## 162      91385        D      F 0.00 0.44  0.09 0.00 0.00 0.00 0.11 0.60 0.00  0.02   0.00   0.00
## 163      91386        D      M 0.00 0.08  0.00 0.00 0.45 0.00 0.00 0.01 0.00  0.28   0.00   0.00
## 164      91387        D      M 0.00 0.96  0.47 0.00 0.06 0.01 0.00 0.19 0.00  0.79   0.00   0.00
## 165      91389        D F_eggs 0.00 0.85  0.85 0.00 0.01 0.00 0.00 0.43 0.00  0.20   0.00   0.00
## 166      91390        D      F 0.00 0.08  0.02 0.00 0.00 0.01 0.00 0.00 0.00  0.00   0.00   0.00
## 167      91391        D      F 0.00 0.48  0.25 0.00 0.02 0.00 0.00 0.23 0.00  0.09   0.00   0.00
## 168      91392        D      M 0.00 0.13  0.04 0.00 0.00 0.00 0.00 0.08 0.00  0.01   0.00   0.00
## 169      91393        D F_eggs 0.00 0.92  0.74 0.00 0.00 0.13 0.00 0.49 0.00  0.35   0.00   0.00
## 170      91394        D      M 0.00 0.64  0.64 0.00 0.07 0.00 0.00 0.01 0.00  0.33   0.00   0.00
## 171      91395        D      M 0.00 0.91  0.76 0.00 0.11 0.00 0.00 0.31 0.00  0.57   0.00   0.00
## 172      91396        D      F 0.00 0.89  0.62 0.00 0.04 0.01 0.00 0.03 0.00  0.46   0.00   0.00
## 173      91397        D      F 0.00 0.19  0.00 0.00 0.00 0.00 0.03 0.16 0.00  0.02   0.00   0.00
## 174      91398        D      M 0.00 0.01  0.00 0.00 0.00 0.01 0.00 0.00 0.00  0.00   0.00   0.00
## 175      91401        D      F 0.00 0.23  0.31 0.00 0.00 0.00 0.00 0.00 0.00  0.03   0.00   0.00
## 176      91402        D      F 0.00 0.66  0.21 0.00 0.02 0.00 0.00 0.20 0.00  0.06   0.00   0.00
## 177      91403        D      M 0.00 0.14  0.00 0.00 0.01 0.00 0.00 0.00 0.00  0.02   0.00   0.00
## 178      91404        D      M 0.00 0.82  0.15 0.00 0.09 0.00 0.01 0.39 0.00  0.14   0.00   0.00
## 182      91410        D      M 0.00 0.95  0.73 0.00 0.05 0.00 0.00 0.09 0.00  0.56   0.00   0.00
## 183      91411        D      M 0.00 0.51  0.11 0.00 0.03 0.00 0.00 0.00 0.00  0.29   0.00   0.00
## 184      91412        D      F 0.00 0.95  0.77 0.00 0.01 0.06 0.08 0.85 0.00  0.10   0.00   0.00
## 185      91413        D      M 0.00 0.18  0.28 0.00 0.00 0.00 0.00 0.00 0.00  0.03   0.00   0.00
## 186      91414        D      F 0.00 0.92  0.42 0.00 0.02 0.00 0.00 0.50 0.00  0.57   0.00   0.00
## 187      91415        D      F 0.00 0.24  0.18 0.00 0.00 0.01 0.00 0.03 0.00  0.33   0.00   0.00
## 188      91416        D      M 0.00 0.70  0.42 0.00 0.32 0.00 0.00 0.01 0.00  0.52   0.00   0.00
## 189      91417        D      F 0.00 0.69  0.39 0.00 0.15 0.00 0.00 0.03 0.00  0.49   0.00   0.00
## 190      91418        D      F 0.00 0.92  0.42 0.00 0.02 0.00 0.00 0.38 0.00  0.55   0.00   0.00
## 191      91419        D      F 0.00 0.84  0.44 0.00 0.04 0.00 0.00 0.14 0.00  0.20   0.00   0.00
## 158      91381       D3      F 0.00 0.34  0.79 0.00 0.00 0.01 0.00 0.21 0.00  0.03   0.00   0.00
## 159      91382       D3      M 0.00 0.00  0.12 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 179      91407       D3      M 0.00 0.96  0.99 0.00 0.01 0.09 0.00 0.37 0.00  0.13   0.00   0.00
## 180      91408       D3      M 0.00 0.46  0.84 0.00 0.00 0.33 0.00 0.19 0.00  0.00   0.00   0.00
## 181      91409       D3      M 0.00 0.76  0.59 0.00 0.02 0.00 0.00 0.05 0.00  0.20   0.00   0.00
## 192      91420        E      M 0.00 0.00  0.00 0.89 0.00 0.00 0.15 0.00 0.00  0.00   0.00   0.00
## 193      91421        E F_eggs 0.00 0.00  0.00 0.90 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 194      91422        E F_eggs 0.00 0.00  0.00 0.81 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 195      91423        E F_eggs 0.00 0.00  0.00 0.58 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 196      91424        E      F 0.00 0.00  0.00 0.94 0.00 0.00 0.12 0.00 0.00  0.00   0.00   0.00
## 197      91425        E      F 0.00 0.00  0.00 0.93 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 198      91426        E      M 0.00 0.00  0.00 0.85 0.00 0.01 0.00 0.00 0.00  0.00   0.00   0.00
## 199      91427        E      M 0.00 0.00  0.00 0.98 0.00 0.00 0.00 0.00 0.00  0.00   0.01   0.00
## 200      91428        E      F 0.00 0.00  0.00 0.46 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 201      91429        E      F 0.00 0.00  0.00 0.80 0.00 0.00 0.00 0.00 0.00  0.00   0.07   0.00
## 202      91430        E      M 0.00 0.00  0.00 0.64 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 203      91431        F      M 0.00 0.01  0.00 0.00 0.24 0.00 0.00 0.00 0.00  0.02   0.00   0.00
## 204      91432        F      M 0.00 0.01  0.00 0.00 0.40 0.00 0.00 0.00 0.00  0.08   0.00   0.00
## 205      91433        F      M 0.00 0.00  0.00 0.00 0.43 0.00 0.00 0.00 0.00  0.09   0.00   0.00
## 206      91434        F      M 0.00 0.00  0.00 0.00 0.18 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 207      91435        F      M 0.00 0.00  0.00 0.00 0.04 0.00 0.00 0.00 0.00  0.00   0.00   0.00
## 208      91527        G      F 0.00 0.00  0.00 0.00 0.00 0.91 0.01 0.16 0.00  0.00   0.00   0.00
## 209      91528        G      F 0.00 0.00  0.00 0.00 0.00 0.94 0.00 0.00 0.00  0.00   0.00   0.00
## 210      91529        G      M 0.00 0.01  0.12 0.00 0.00 0.94 0.00 0.01 0.00  0.00   0.00   0.00
## 211      91530        G      M 0.00 0.00  0.02 0.00 0.00 0.54 0.00 0.03 0.00  0.00   0.00   0.00
## 212      91531        G      M 0.00 0.02  0.01 0.00 0.00 0.87 0.00 0.01 0.00  0.00   0.00   0.00
## 6        82573        M      F 0.00 0.00  0.00 0.00 0.00 0.00 0.99 0.25 0.00  0.00   0.00   0.00
## 7        82574        M      M 0.00 0.01  0.00 0.00 0.00 0.00 0.90 0.60 0.00  0.00   0.00   0.00
## 13       91147        M      F 0.00 0.00  0.00 0.00 0.00 0.00 0.11 0.00 0.00  0.00   0.00   0.00
## 14       91148        M      F 0.00 0.05  0.00 0.00 0.00 0.01 0.55 0.89 0.00  0.00   0.00   0.00
## 15       91149        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.27 0.07 0.00  0.00   0.00   0.00
## 16       91150        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.24 0.00 0.00  0.00   0.00   0.00
## 17       91154        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.22 0.04 0.00  0.00   0.00   0.00
## 18       91155        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.22 0.00 0.00  0.00   0.00   0.00
## 19       91156        M F_eggs 0.00 0.00  0.00 0.00 0.00 0.00 0.47 0.00 0.00  0.00   0.00   0.00
## 20       91157        M      M 0.00 0.04  0.01 0.00 0.00 0.00 0.72 0.32 0.00  0.00   0.00   0.00
## 21       91158        M      M 0.00 0.01  0.00 0.01 0.00 0.01 0.99 0.77 0.00  0.00   0.00   0.00
## 22       91159        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.96 0.26 0.00  0.00   0.00   0.00
## 23       91163        M F_eggs 0.00 0.00  0.00 0.00 0.00 0.00 0.57 0.53 0.00  0.00   0.00   0.00
## 24       91164        M F_eggs 0.00 0.00  0.00 0.00 0.00 0.00 0.93 0.24 0.00  0.00   0.00   0.00
## 25       91165        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.94 0.20 0.00  0.00   0.00   0.00
## 26       91166        M F_eggs 0.00 0.00  0.00 0.00 0.00 0.00 0.51 0.01 0.00  0.00   0.00   0.00
## 27       91167        M      F 0.00 0.00  0.00 0.01 0.00 0.00 0.75 0.02 0.00  0.00   0.00   0.00
## 28       91168        M F_eggs 0.00 0.00  0.00 0.02 0.00 0.00 0.99 0.59 0.00  0.00   0.00   0.00
## 29       91169        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.63 0.05 0.00  0.00   0.00   0.00
## 30       91170        M      F 0.00 0.00  0.00 0.00 0.00 0.00 0.93 0.35 0.00  0.00   0.00   0.00
## 31       91171        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.97 0.37 0.00  0.00   0.00   0.00
## 32       91172        M      F 0.00 0.00  0.00 0.22 0.00 0.00 0.94 0.03 0.00  0.00   0.00   0.00
## 33       91173        M      F 0.00 0.00  0.00 0.00 0.00 0.00 0.93 0.03 0.00  0.00   0.00   0.00
## 35       91175        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.76 0.38 0.00  0.00   0.00   0.00
## 36       91176        M      F 0.00 0.00  0.00 0.01 0.00 0.00 0.82 0.01 0.00  0.00   0.00   0.00
## 37       91177        M      F 0.00 0.00  0.00 0.15 0.00 0.00 0.36 0.00 0.00  0.00   0.00   0.00
## 38       91178        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.61 0.03 0.00  0.00   0.00   0.00
## 39       91179        M      M 0.00 0.00  0.00 0.02 0.00 0.00 0.96 0.07 0.00  0.00   0.00   0.00
## 40       91180        M      M 0.00 0.00  0.00 0.00 0.00 0.00 0.18 0.00 0.00  0.00   0.00   0.00
## 4        82401        N      M 0.00 0.24  0.05 0.00 0.00 0.08 0.33 0.85 0.00  0.01   0.00   0.00
## 5        82534        N      M 0.00 0.27  0.22 0.00 0.00 0.03 0.00 0.37 0.00  0.08   0.00   0.00
## 10       82577        N      F 0.00 0.02  0.01 0.00 0.00 0.00 0.04 0.79 0.00  0.00   0.00   0.00
## 11       82578        N      M 0.00 0.11  0.05 0.00 0.00 0.00 0.03 0.68 0.00  0.02   0.00   0.00
## 41       91182        N      M 0.00 0.95  0.69 0.00 0.03 0.02 0.00 0.48 0.00  0.59   0.00   0.00
## 42       91186        N      F 0.00 0.02  0.04 0.00 0.00 0.01 0.05 0.82 0.00  0.00   0.00   0.00
## 43       91187        N      F 0.00 0.47  0.22 0.00 0.00 0.00 0.01 0.85 0.00  0.38   0.00   0.00
## 44       91188        N      F 0.00 0.00  0.00 0.00 0.00 0.00 0.04 0.15 0.00  0.00   0.00   0.00
## 45       91189        N      M 0.00 0.02  0.00 0.00 0.00 0.00 0.13 0.49 0.00  0.00   0.00   0.00
## 46       91190        N      F 0.00 0.03  0.01 0.00 0.00 0.02 0.27 0.78 0.00  0.00   0.00   0.00
## 47       91191        N      M 0.00 0.17  0.17 0.00 0.00 0.00 0.00 0.21 0.00  0.04   0.00   0.00
## 48       91204        N      M 0.00 0.96  0.42 0.00 0.02 0.00 0.01 0.59 0.00  0.87   0.00   0.00
## 49       91205        N      M 0.00 0.30  0.11 0.00 0.00 0.00 0.11 0.91 0.00  0.04   0.00   0.00
## 50       91206        N      F 0.00 0.00  0.00 0.15 0.00 0.00 0.65 0.13 0.00  0.00   0.00   0.00
## 51       91207        N      M 0.00 0.60  0.33 0.00 0.00 0.64 0.11 0.80 0.00  0.02   0.00   0.00
## 52       91208        N      M 0.00 0.63  0.36 0.00 0.00 0.03 0.01 0.50 0.00  0.12   0.00   0.00
## 53       91209        N F_eggs 0.00 0.20  0.02 0.00 0.00 0.00 0.02 0.43 0.00  0.02   0.00   0.00
## 54       91210        N      F 0.00 0.64  0.52 0.00 0.00 0.03 0.25 0.84 0.00  0.06   0.00   0.00
## 55       91211        N      M 0.00 0.02  0.00 0.00 0.00 0.00 0.00 0.21 0.00  0.00   0.00   0.00
## 56       91212        N      F 0.00 0.00  0.00 0.00 0.00 0.00 0.05 0.47 0.00  0.00   0.00   0.00
## 57       91213        N      M 0.00 0.16  0.09 0.00 0.00 0.09 0.42 0.89 0.00  0.00   0.00   0.00
## 58       91214        N F_eggs 0.00 0.00  0.00 0.00 0.00 0.00 0.36 0.29 0.00  0.00   0.00   0.00
## 59       91215        N F_eggs 0.00 0.00  0.00 0.00 0.00 0.00 0.01 0.08 0.00  0.00   0.00   0.00
## 60       91221        N      F 0.00 0.10  0.01 0.00 0.00 0.05 0.35 0.97 0.00  0.01   0.00   0.00
## 61       91222        N      M 0.00 0.20  0.03 0.00 0.00 0.12 0.12 0.92 0.00  0.02   0.00   0.00
## 62       91223        N      M 0.00 0.33  0.02 0.00 0.00 0.00 0.38 0.85 0.00  0.02   0.00   0.00
## 63       91224        N      M 0.00 0.38  0.24 0.00 0.00 0.34 0.09 0.95 0.00  0.01   0.00   0.00
## 64       91225        N      F 0.00 0.27  0.10 0.00 0.00 0.00 0.23 0.70 0.00  0.00   0.00   0.00
## 65       91226        N      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.05 0.00  0.00   0.00   0.00
## 66       91227        N      F 0.00 0.02  0.02 0.03 0.00 0.09 0.61 0.62 0.00  0.00   0.00   0.00
## 67       91228        N      F 0.00 0.03  0.03 0.00 0.00 0.02 0.00 0.47 0.00  0.01   0.00   0.00
## 68       91229        N      F 0.00 0.03  0.00 0.00 0.00 0.01 0.06 0.63 0.00  0.01   0.00   0.00
## 69       91230        N      M 0.00 0.06  0.01 0.00 0.00 0.00 0.01 0.68 0.00  0.01   0.00   0.00
## 70       91231        N      M 0.00 0.06  0.00 0.00 0.00 0.00 0.01 0.56 0.00  0.00   0.00   0.00
## 71       91232        N      M 0.00 0.68  0.32 0.00 0.00 0.01 0.01 0.87 0.00  0.06   0.00   0.00
## 72       91233        N      M 0.00 0.69  0.21 0.00 0.01 0.00 0.01 0.85 0.00  0.46   0.00   0.00
## 73       91234        N      M 0.00 0.08  0.06 0.00 0.00 0.05 0.04 0.68 0.00  0.00   0.00   0.00
## 74       91235        N      F 0.00 0.10  0.04 0.00 0.00 0.01 0.15 0.90 0.00  0.00   0.00   0.00
## 75       91236        N F_eggs 0.00 0.02  0.00 0.00 0.00 0.04 0.06 0.80 0.00  0.00   0.00   0.00
## 76       91237        N      M 0.00 0.42  0.08 0.00 0.00 0.04 0.00 0.62 0.00  0.01   0.00   0.00
## 77       91239        N      M 0.00 0.39  0.07 0.00 0.00 0.02 0.12 0.75 0.00  0.08   0.00   0.00
## 78       91240        N      M 0.00 0.81  0.42 0.00 0.01 0.10 0.12 0.83 0.00  0.20   0.00   0.00
## 79       91241        N      M 0.00 0.25  0.06 0.00 0.00 0.06 0.08 0.75 0.00  0.00   0.00   0.00
## 80       91242        N      F 0.00 0.05  0.02 0.00 0.00 0.06 0.09 0.95 0.00  0.00   0.00   0.00
## 81       91243        N      F 0.00 0.03  0.00 0.00 0.00 0.00 0.25 0.88 0.00  0.00   0.00   0.00
## 82       91244        N      F 0.00 0.00  0.00 0.00 0.00 0.00 0.68 0.54 0.00  0.00   0.00   0.00
## 83       91245        N      F 0.00 0.01  0.00 0.00 0.00 0.00 0.09 0.62 0.00  0.00   0.00   0.00
## 84       91246        N      F 0.00 0.13  0.02 0.00 0.00 0.01 0.33 0.93 0.00  0.00   0.00   0.00
## 85       91247        N      F 0.00 0.60  0.43 0.00 0.00 0.20 0.33 0.99 0.00  0.02   0.00   0.00
## 225     Cae727        T      F 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.66  0.00   0.00   0.00
## 226     Cae728        T      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.76  0.00   0.00   0.00
## 228     Cae730        T      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.70  0.00   0.00   0.00
## 220     Cae722       X1      M 0.00 0.64  0.22 0.00 0.21 0.00 0.00 0.00 0.00  0.97   0.00   0.00
## 221     Cae723       X1      M 0.00 0.02  0.00 0.00 0.32 0.00 0.00 0.00 0.00  0.66   0.00   0.00
## 222     Cae724       X1      M 0.00 0.15  0.02 0.00 0.02 0.00 0.00 0.00 0.00  0.86   0.00   0.00
## 223     Cae725       X1 F_eggs 0.00 0.25  0.07 0.00 0.08 0.00 0.00 0.02 0.00  0.80   0.00   0.00
## 224     Cae726       X1 F_eggs 0.00 0.37  0.03 0.00 0.01 0.00 0.00 0.02 0.00  0.86   0.00   0.00
## 227     Cae729       X1      F 0.00 0.15  0.00 0.00 0.01 0.00 0.00 0.04 0.00  0.67   0.00   0.00
## 229     Cae743       X1      M 0.00 0.61  0.22 0.00 0.21 0.00 0.00 0.01 0.00  0.90   0.00   0.00
## 230     Cae746       X1      M 0.00 0.42  0.02 0.00 0.21 0.00 0.00 0.01 0.00  0.95   0.00   0.00
## 231     Cae748       X1      M 0.00 0.16  0.01 0.00 0.02 0.00 0.00 0.00 0.00  0.92   0.00   0.00
## 232     Cae755       X1      M 0.00 0.65  0.38 0.00 0.70 0.00 0.00 0.01 0.00  0.89   0.00   0.00
## 233     Cae756       X1      M 0.00 0.26  0.01 0.00 0.03 0.00 0.00 0.05 0.00  0.74   0.00   0.00
## 234     Cae757       X1      M 0.00 0.87  0.31 0.00 0.13 0.00 0.00 0.14 0.00  1.00   0.00   0.00
## 235     Cae758       X1      M 0.00 0.36  0.01 0.00 0.48 0.00 0.00 0.00 0.00  0.44   0.00   0.00
## 236     Cae759       X1 F_eggs 0.00 0.40  0.10 0.00 0.00 0.00 0.00 0.02 0.00  0.56   0.00   0.00
## 216     Cae718      X10      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.47   0.00
## 217     Cae719      X10      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.98   0.00
## 218     Cae720      X10      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.01  0.00   0.98   0.00
## 219     Cae721      X10      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.85   0.00
## 237     Cae770      X11      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.91
## 238     Cae771      X11 F_eggs 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.53
## 239     Cae772      X11      M 0.00 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.77
## 240     Cae773      X11      F 0.02 0.00  0.00 0.00 0.00 0.00 0.00 0.00 0.00  0.00   0.00   0.73

4.2 lutraria

### 9 Classify specimen to species
lutraria <- shape_8[248, c(2:15)] #new specimen to classify
lutraria <- as.matrix(lutraria)
# get classification score
p.C <- lutraria%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- lutraria%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- lutraria%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- lutraria%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- lutraria%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- lutraria%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- lutraria%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- lutraria%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- lutraria%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- lutraria%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- lutraria%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- lutraria%*%cj.X11+cj0.X11+log(All.lda$prior[12])
# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

lutraria.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(lutraria.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(lutraria.posteriors) <- "lutraria.posteriors"
lutraria.posteriors <- round(lutraria.posteriors, digits=3)
lutraria.posteriors

##     lutraria.posteriors
## C                 0.442
## D                 0.005
## D3                0.331
## E                 0.000
## F                 0.150
## G                 0.000
## M                 0.000
## N                 0.000
## T                 0.000
## X1                0.072
## X10               0.000
## X11               0.000

#typicality probability
d2.C <- (t(as.vector(lutraria)-mean.C))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(lutraria)-mean.D))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(lutraria)-mean.D3))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(lutraria)-mean.E))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(lutraria)-mean.F))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(lutraria)-mean.G))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(lutraria)-mean.M))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(lutraria)-mean.N))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(lutraria)-mean.T))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(lutraria)-mean.X1))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(lutraria)-mean.X10))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(lutraria)-mean.X11))%*%solve(cov.d)%*%(as.vector(lutraria)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

lutraria.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(lutraria.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(lutraria.typicality) <- "lutraria.typicality"
lutraria.typicality <- round(lutraria.typicality, digits=6)
lutraria.typicality

##     lutraria.typicality
## C                     0
## D                     0
## D3                    0
## E                     0
## F                     0
## G                     0
## M                     0
## N                     0
## T                     0
## X1                    0
## X10                   0
## X11                   0

It is most likely that the drawing of Ozestheria lutraria in Brady (1886) belongs to C (44.2%) or D3 (33.1%). But, according to the low “typicality probabilities”, the drawing of O. lutraria remains an outlier for either species.

4.3 dictyon

### 9 Classify specimen to species
dictyon <- colMeans(shape_8[c(243:245), c(2:15)]) #new specimen to classify

# get classification score
p.C <- dictyon%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- dictyon%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- dictyon%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- dictyon%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- dictyon%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- dictyon%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- dictyon%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- dictyon%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- dictyon%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- dictyon%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- dictyon%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- dictyon%*%cj.X11+cj0.X11+log(All.lda$prior[12])
# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

dictyon.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(dictyon.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(dictyon.posteriors) <- "dictyon.posteriors"
dictyon.posteriors <- round(dictyon.posteriors, digits=2)
dictyon.posteriors

##     dictyon.posteriors
## C                    1
## D                    0
## D3                   0
## E                    0
## F                    0
## G                    0
## M                    0
## N                    0
## T                    0
## X1                   0
## X10                  0
## X11                  0

#typicality probability
d2.C <- (t(as.vector(dictyon)-mean.C))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(dictyon)-mean.D))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(dictyon)-mean.D3))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(dictyon)-mean.E))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(dictyon)-mean.F))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(dictyon)-mean.G))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(dictyon)-mean.M))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(dictyon)-mean.N))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(dictyon)-mean.T))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(dictyon)-mean.X1))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(dictyon)-mean.X10))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(dictyon)-mean.X11))%*%solve(cov.d)%*%(as.vector(dictyon)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

dictyon.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(dictyon.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(dictyon.typicality) <- "dictyon.typicality"
dictyon.typicality <- round(dictyon.typicality, digits=6)
dictyon.typicality

##     dictyon.typicality
## C             0.124826
## D             0.000000
## D3            0.000000
## E             0.000000
## F             0.000000
## G             0.000000
## M             0.000000
## N             0.000000
## T             0.000000
## X1            0.000000
## X10           0.000000
## X11           0.000000

The mean shape of the three syntypes of Ozestheria dictyon can be assigned to and is typical of C (100%).

4.4 rubra

### 9 Classify specimen to species
rubra <- shape_8[1, c(2:15)] #new specimen to classify
rubra <- as.matrix(rubra)
# get classification score
p.C <- rubra%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- rubra%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- rubra%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- rubra%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- rubra%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- rubra%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- rubra%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- rubra%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- rubra%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- rubra%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- rubra%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- rubra%*%cj.X11+cj0.X11+log(All.lda$prior[12])
# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

rubra.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(rubra.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(rubra.posteriors) <- "rubra.posteriors"
rubra.posteriors <- round(rubra.posteriors, digits=3)
rubra.posteriors

##     rubra.posteriors
## C              0.000
## D              0.978
## D3             0.004
## E              0.000
## F              0.000
## G              0.000
## M              0.000
## N              0.001
## T              0.000
## X1             0.017
## X10            0.000
## X11            0.000

#rubra <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
#rownames(rubra) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
#colnames(rubra) <- "rubra"
#rubra

#typicality probability
d2.C <- (t(as.vector(rubra)-mean.C))%*%solve(cov.d)%*%(as.vector(rubra)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(rubra)-mean.D))%*%solve(cov.d)%*%(as.vector(rubra)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(rubra)-mean.D3))%*%solve(cov.d)%*%(as.vector(rubra)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(rubra)-mean.E))%*%solve(cov.d)%*%(as.vector(rubra)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(rubra)-mean.F))%*%solve(cov.d)%*%(as.vector(rubra)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(rubra)-mean.G))%*%solve(cov.d)%*%(as.vector(rubra)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(rubra)-mean.M))%*%solve(cov.d)%*%(as.vector(rubra)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(rubra)-mean.N))%*%solve(cov.d)%*%(as.vector(rubra)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(rubra)-mean.T))%*%solve(cov.d)%*%(as.vector(rubra)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(rubra)-mean.X1))%*%solve(cov.d)%*%(as.vector(rubra)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(rubra)-mean.X10))%*%solve(cov.d)%*%(as.vector(rubra)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(rubra)-mean.X11))%*%solve(cov.d)%*%(as.vector(rubra)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

rubra.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(rubra.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(rubra.typicality) <- "rubra.typicality"
rubra.typicality <- round(rubra.typicality, digits=6)
rubra.typicality

##     rubra.typicality
## C           0.000000
## D           0.957211
## D3          0.473871
## E           0.000000
## F           0.039319
## G           0.010612
## M           0.000030
## N           0.074841
## T           0.000000
## X1          0.538961
## X10         0.000000
## X11         0.000000

The type specimen of Ozestheria rubra can be assigned to D (97.8%).

4.5 elliptica

### 9 Classify specimen to species
elliptica <- shape_8[241, c(2:15)] #new specimen to classify
elliptica <- as.matrix(elliptica)
# get classification score
p.C <- elliptica%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- elliptica%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- elliptica%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- elliptica%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- elliptica%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- elliptica%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- elliptica%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- elliptica%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- elliptica%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- elliptica%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- elliptica%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- elliptica%*%cj.X11+cj0.X11+log(All.lda$prior[12])
# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

elliptica.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(elliptica.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(elliptica.posteriors) <- "elliptica.posteriors"
elliptica.posteriors <- round(elliptica.posteriors, digits=3)
elliptica.posteriors

##     elliptica.posteriors
## C                  0.000
## D                  0.211
## D3                 0.001
## E                  0.000
## F                  0.010
## G                  0.000
## M                  0.000
## N                  0.091
## T                  0.000
## X1                 0.686
## X10                0.000
## X11                0.000

#typicality probability
d2.C <- (t(as.vector(elliptica)-mean.C))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(elliptica)-mean.D))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(elliptica)-mean.D3))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(elliptica)-mean.E))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(elliptica)-mean.F))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(elliptica)-mean.G))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(elliptica)-mean.M))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(elliptica)-mean.N))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(elliptica)-mean.T))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(elliptica)-mean.X1))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(elliptica)-mean.X10))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(elliptica)-mean.X11))%*%solve(cov.d)%*%(as.vector(elliptica)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

elliptica.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(elliptica.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(elliptica.typicality) <- "elliptica.typicality"
elliptica.typicality <- round(elliptica.typicality, digits=6)
elliptica.typicality

##     elliptica.typicality
## C               0.000000
## D               0.113626
## D3              0.019960
## E               0.000000
## F               0.060601
## G               0.000000
## M               0.000011
## N               0.057743
## T               0.000000
## X1              0.277728
## X10             0.000000
## X11             0.000000

The drawing of Ozestheria elliptica can be assigned to X1 (68.6%), D (21.1%) or N (9.1%).

4.6 berneyiF

### 9 Classify specimen to species
berneyi <- shape_8[213, c(2:15)] #new specimen to classify
berneyi <- as.matrix(berneyi)
# get classification score
p.C <- berneyi%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- berneyi%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- berneyi%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- berneyi%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- berneyi%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- berneyi%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- berneyi%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- berneyi%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- berneyi%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- berneyi%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- berneyi%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- berneyi%*%cj.X11+cj0.X11+log(All.lda$prior[12])
# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

berneyi.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(berneyi.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(berneyi.posteriors) <- "berneyi.posteriors"
berneyi.posteriors <- round(berneyi.posteriors, digits=3)
berneyi.posteriors

##     berneyi.posteriors
## C                0.000
## D                0.001
## D3               0.000
## E                0.000
## F                0.000
## G                0.000
## M                0.001
## N                0.997
## T                0.000
## X1               0.000
## X10              0.000
## X11              0.000

#typicality probability
d2.C <- (t(as.vector(berneyi)-mean.C))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(berneyi)-mean.D))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(berneyi)-mean.D3))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(berneyi)-mean.E))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(berneyi)-mean.F))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(berneyi)-mean.G))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(berneyi)-mean.M))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(berneyi)-mean.N))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(berneyi)-mean.T))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(berneyi)-mean.X1))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(berneyi)-mean.X10))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(berneyi)-mean.X11))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

berneyi.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(berneyi.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(berneyi.typicality) <- "berneyi.typicality"
berneyi.typicality <- round(berneyi.typicality, digits=6)
berneyi.typicality

##     berneyi.typicality
## C             0.000000
## D             0.000982
## D3            0.000021
## E             0.000000
## F             0.000000
## G             0.000015
## M             0.000975
## N             0.045654
## T             0.000000
## X1            0.000001
## X10           0.000000
## X11           0.000000

The drawing of Ozestheria berneyi (female) can be assigned to N (99.7%).

4.7 berneyiM

### 9 Classify specimen to species
berneyi <- shape_8[214, c(2:15)] #new specimen to classify
berneyi <- as.matrix(berneyi)
# get classification score
p.C <- berneyi%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- berneyi%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- berneyi%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- berneyi%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- berneyi%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- berneyi%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- berneyi%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- berneyi%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- berneyi%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- berneyi%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- berneyi%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- berneyi%*%cj.X11+cj0.X11+log(All.lda$prior[12])
# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

berneyi.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(berneyi.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(berneyi.posteriors) <- "berneyi.posteriors"
berneyi.posteriors <- round(berneyi.posteriors, digits=3)
berneyi.posteriors

##     berneyi.posteriors
## C                0.000
## D                0.025
## D3               0.000
## E                0.000
## F                0.000
## G                0.000
## M                0.001
## N                0.974
## T                0.000
## X1               0.000
## X10              0.000
## X11              0.000

#typicality probability
d2.C <- (t(as.vector(berneyi)-mean.C))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(berneyi)-mean.D))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(berneyi)-mean.D3))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(berneyi)-mean.E))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(berneyi)-mean.F))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(berneyi)-mean.G))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(berneyi)-mean.M))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(berneyi)-mean.N))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(berneyi)-mean.T))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(berneyi)-mean.X1))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(berneyi)-mean.X10))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(berneyi)-mean.X11))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

berneyi.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(berneyi.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(berneyi.typicality) <- "berneyi.typicality"
berneyi.typicality <- round(berneyi.typicality, digits=6)
berneyi.typicality

##     berneyi.typicality
## C             0.000000
## D             0.419684
## D3            0.061387
## E             0.000000
## F             0.001626
## G             0.011840
## M             0.100272
## N             0.890740
## T             0.000000
## X1            0.008804
## X10           0.000000
## X11           0.000000

The drawing of Ozestheria berneyi (male) can be assigned to N (97.4%).

4.8 berneyi

### 9 Classify specimen to species
berneyi <- shape_8[215, c(2:15)] #new specimen to classify
berneyi <- as.matrix(berneyi)
# get classification score
p.C <- berneyi%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- berneyi%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- berneyi%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- berneyi%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- berneyi%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- berneyi%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- berneyi%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- berneyi%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- berneyi%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- berneyi%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- berneyi%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- berneyi%*%cj.X11+cj0.X11+log(All.lda$prior[12])
# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

berneyi.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(berneyi.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(berneyi.posteriors) <- "berneyi.posteriors"
berneyi.posteriors <- round(berneyi.posteriors, digits=3)
berneyi.posteriors

##     berneyi.posteriors
## C                0.000
## D                0.877
## D3               0.036
## E                0.000
## F                0.000
## G                0.001
## M                0.000
## N                0.084
## T                0.000
## X1               0.002
## X10              0.000
## X11              0.000

#typicality probability
d2.C <- (t(as.vector(berneyi)-mean.C))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(berneyi)-mean.D))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(berneyi)-mean.D3))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(berneyi)-mean.E))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(berneyi)-mean.F))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(berneyi)-mean.G))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(berneyi)-mean.M))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(berneyi)-mean.N))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(berneyi)-mean.T))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(berneyi)-mean.X1))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(berneyi)-mean.X10))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(berneyi)-mean.X11))%*%solve(cov.d)%*%(as.vector(berneyi)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

berneyi.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(berneyi.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(berneyi.typicality) <- "berneyi.typicality"
berneyi.typicality <- round(berneyi.typicality, digits=6)
berneyi.typicality

##     berneyi.typicality
## C             0.000000
## D             0.002515
## D3            0.000994
## E             0.000000
## F             0.000021
## G             0.000052
## M             0.000000
## N             0.000363
## T             0.000000
## X1            0.000065
## X10           0.000000
## X11           0.000000

The type specimen of Ozestheria berneyi can be assigned to D (probability 87.7%) or N (8.4%), it is not typical of M and should be considered an outlier shape of O. berneyi.

4.9 rufa

### 9 Classify specimen to species
rufa <- colMeans(shape_8[c(2:3), c(2:15)]) #new specimen to classify

# get classification score
p.C <- rufa%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- rufa%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- rufa%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- rufa%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- rufa%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- rufa%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- rufa%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- rufa%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- rufa%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- rufa%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- rufa%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- rufa%*%cj.X11+cj0.X11+log(All.lda$prior[12])

# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

rufa.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(rufa.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(rufa.posteriors) <- "rufa.posteriors"
rufa.posteriors <- round(rufa.posteriors, digits=3)
rufa.posteriors

##     rufa.posteriors
## C                 0
## D                 0
## D3                0
## E                 0
## F                 0
## G                 0
## M                 0
## N                 0
## T                 0
## X1                0
## X10               1
## X11               0

#typicality probability
d2.C <- (t(as.vector(rufa)-mean.C))%*%solve(cov.d)%*%(as.vector(rufa)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(rufa)-mean.D))%*%solve(cov.d)%*%(as.vector(rufa)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(rufa)-mean.D3))%*%solve(cov.d)%*%(as.vector(rufa)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(rufa)-mean.E))%*%solve(cov.d)%*%(as.vector(rufa)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(rufa)-mean.F))%*%solve(cov.d)%*%(as.vector(rufa)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(rufa)-mean.G))%*%solve(cov.d)%*%(as.vector(rufa)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(rufa)-mean.M))%*%solve(cov.d)%*%(as.vector(rufa)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(rufa)-mean.N))%*%solve(cov.d)%*%(as.vector(rufa)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(rufa)-mean.T))%*%solve(cov.d)%*%(as.vector(rufa)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(rufa)-mean.X1))%*%solve(cov.d)%*%(as.vector(rufa)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(rufa)-mean.X10))%*%solve(cov.d)%*%(as.vector(rufa)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(rufa)-mean.X11))%*%solve(cov.d)%*%(as.vector(rufa)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

rufa.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(rufa.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(rufa.typicality) <- "rufa.typicality"
rufa.typicality <- round(rufa.typicality, digits=6)
rufa.typicality

##     rufa.typicality
## C          0.000000
## D          0.000000
## D3         0.000000
## E          0.000000
## F          0.000000
## G          0.000000
## M          0.000000
## N          0.000000
## T          0.000000
## X1         0.000000
## X10        0.042888
## X11        0.000000

The mean shape of the type specimens of Ozestheria rufa can be assigned to X10 (100%).

4.10 sarsii

### 9 Classify specimen to species
sarsii <- shape_8[242, c(2:15)] #new specimen to classify
sarsii <- as.matrix(sarsii)

# get classification score
p.C <- sarsii%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- sarsii%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- sarsii%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- sarsii%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- sarsii%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- sarsii%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- sarsii%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- sarsii%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- sarsii%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- sarsii%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- sarsii%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- sarsii%*%cj.X11+cj0.X11+log(All.lda$prior[12])

# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

sarsii.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(sarsii.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(sarsii.posteriors) <- "sarsii.posteriors"
sarsii.posteriors <- round(sarsii.posteriors, digits=3)
sarsii.posteriors

##     sarsii.posteriors
## C               0.000
## D               0.000
## D3              0.000
## E               0.000
## F               0.000
## G               0.000
## M               0.000
## N               0.000
## T               0.027
## X1              0.000
## X10             0.973
## X11             0.000

#typicality probability
d2.C <- (t(as.vector(sarsii)-mean.C))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(sarsii)-mean.D))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(sarsii)-mean.D3))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(sarsii)-mean.E))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(sarsii)-mean.F))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(sarsii)-mean.G))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(sarsii)-mean.M))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(sarsii)-mean.N))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(sarsii)-mean.T))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(sarsii)-mean.X1))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(sarsii)-mean.X10))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(sarsii)-mean.X11))%*%solve(cov.d)%*%(as.vector(sarsii)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

sarsii.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(sarsii.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(sarsii.typicality) <- "sarsii.typicality"
sarsii.typicality <- round(sarsii.typicality, digits=6)
sarsii.typicality

##     sarsii.typicality
## C            0.000000
## D            0.000000
## D3           0.000000
## E            0.000000
## F            0.000000
## G            0.000000
## M            0.000000
## N            0.000000
## T            0.002529
## X1           0.000000
## X10          0.020235
## X11          0.000000

The shape of Ozestheria sarsii is most similar to X10, with some probability of O. sarsii belonging to T.

4.11 pellucida

### 9 Classify specimen to species
pellucida <- shape_8[249, c(2:15)] #new specimen to classify
pellucida <- as.matrix(pellucida)

# get classification score
p.C <- pellucida%*%cj.C+cj0.C+log(All.lda$prior[1])
p.D <- pellucida%*%cj.D+cj0.D+log(All.lda$prior[2])
p.D3 <- pellucida%*%cj.D3+cj0.D3+log(All.lda$prior[3])
p.E <- pellucida%*%cj.E+cj0.E+log(All.lda$prior[4])
p.F <- pellucida%*%cj.F+cj0.F+log(All.lda$prior[5])
p.G <- pellucida%*%cj.G+cj0.G+log(All.lda$prior[6])
p.M <- pellucida%*%cj.M+cj0.M+log(All.lda$prior[7])
p.N <- pellucida%*%cj.N+cj0.N+log(All.lda$prior[8])
p.T <- pellucida%*%cj.T+cj0.T+log(All.lda$prior[9])
p.X1 <- pellucida%*%cj.X1+cj0.X1+log(All.lda$prior[10])
p.X10 <- pellucida%*%cj.X10+cj0.X10+log(All.lda$prior[11])
p.X11 <- pellucida%*%cj.X11+cj0.X11+log(All.lda$prior[12])

# posterior probability
post.C <- (exp(p.C-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D <- (exp(p.D-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.D3 <- (exp(p.D3-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.E <- (exp(p.E-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.F <- (exp(p.F-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.G <- (exp(p.G-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.M <- (exp(p.M-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.N <- (exp(p.N-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.T <- (exp(p.T-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X1 <- (exp(p.X1-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X10 <- (exp(p.X10-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))
post.X11 <- (exp(p.X11-p.C))/(exp(p.D-p.C)+exp(p.C-p.C)+exp(p.D3-p.C)+exp(p.E-p.C)+exp(p.F-p.C)+exp(p.G-p.C)+exp(p.M-p.C)+exp(p.N-p.C)+exp(p.T-p.C)+exp(p.X1-p.C)+exp(p.X10-p.C)+exp(p.X11-p.C))

pellucida.posteriors <- as.matrix(c(post.C, post.D, post.D3, post.E, post.F, post.G, post.M, post.N, post.T, post.X1, post.X10, post.X11))
rownames(pellucida.posteriors) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(pellucida.posteriors) <- "pellucida.posteriors"
pellucida.posteriors <- round(pellucida.posteriors, digits=3)
pellucida.posteriors

##     pellucida.posteriors
## C                  0.000
## D                  0.000
## D3                 0.000
## E                  0.013
## F                  0.000
## G                  0.000
## M                  0.060
## N                  0.000
## T                  0.000
## X1                 0.000
## X10                0.926
## X11                0.000

#typicality probability
d2.C <- (t(as.vector(pellucida)-mean.C))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.C)
  typicality.C <- pchisq(d2.C, df = 14, lower.tail = FALSE)
d2.D <- (t(as.vector(pellucida)-mean.D))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.D)
  typicality.D <- pchisq(d2.D, df = 14, lower.tail = FALSE)
d2.D3 <- (t(as.vector(pellucida)-mean.D3))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.D3)
  typicality.D3 <- pchisq(d2.D3, df = 14, lower.tail = FALSE)
d2.E <- (t(as.vector(pellucida)-mean.E))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.E)
  typicality.E <- pchisq(d2.E, df = 14, lower.tail = FALSE)
d2.F <- (t(as.vector(pellucida)-mean.F))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.F)
  typicality.F <- pchisq(d2.F, df = 14, lower.tail = FALSE)
d2.G <- (t(as.vector(pellucida)-mean.G))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.G)
  typicality.G <- pchisq(d2.G, df = 14, lower.tail = FALSE)
d2.M <- (t(as.vector(pellucida)-mean.M))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.M)
  typicality.M <- pchisq(d2.M, df = 14, lower.tail = FALSE)
d2.N <- (t(as.vector(pellucida)-mean.N))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.N)
  typicality.N <- pchisq(d2.N, df = 14, lower.tail = FALSE)
d2.T <- (t(as.vector(pellucida)-mean.T))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.T)
  typicality.T <- pchisq(d2.T, df = 14, lower.tail = FALSE)
d2.X1 <- (t(as.vector(pellucida)-mean.X1))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.X1)
  typicality.X1 <- pchisq(d2.X1, df = 14, lower.tail = FALSE)
d2.X10 <- (t(as.vector(pellucida)-mean.X10))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.X10)
  typicality.X10 <- pchisq(d2.X10, df = 14, lower.tail = FALSE)
d2.X11 <- (t(as.vector(pellucida)-mean.X11))%*%solve(cov.d)%*%(as.vector(pellucida)-mean.X11)
  typicality.X11 <- pchisq(d2.X11, df = 14, lower.tail = FALSE)

pellucida.typicality <- as.matrix(c(typicality.C, typicality.D, typicality.D3, typicality.E, typicality.F, typicality.G, typicality.M, typicality.N, typicality.T, typicality.X1, typicality.X10, typicality.X11))
rownames(pellucida.typicality) <- c("C", "D", "D3", "E", "F", "G", "M", "N", "T", "X1", "X10", "X11")
colnames(pellucida.typicality) <- "pellucida.typicality"
pellucida.typicality <- round(pellucida.typicality, digits=6)
pellucida.typicality

##     pellucida.typicality
## C               0.000000
## D               0.000000
## D3              0.000000
## E               0.000008
## F               0.000000
## G               0.000000
## M               0.000012
## N               0.000000
## T               0.000001
## X1              0.000000
## X10             0.000402
## X11             0.000000

The shape of the type specimen of Ozestheria pellucida is most similar to but not typical of X10, indicating that none of the examined lineages can be assigned to O. pellucida.