Multivariate analysis (MANCOVA) performed to determine the significant difference among the sampling locations, between the coasts (East vs. West) andthe sexes (Males vs. Females) using carapace length (CL) as the covariate showed significant variations (p<0.001) in morphometric measurements among the sampling locations, between the coasts and the sexes (Table 2). Significant differences in the morphometric measurements were apparent among the sampling locations (Wilk’s lambda=0.03; F=26.48, p<0.001), between the coasts (Wilk’s lambda=0.58; F=14.43, p<0.001) and between the sexes (Wilk’s lambda=0.73; F=7.52, p<0.001). Furthermore, there were significant interaction effects of covariate (CL) with locations (Wilk’s lambda=0.64; F=2.30, p<0.001), coasts (Wilk’s lambda=0.89; F=2.44, p<0.001) and sexes (Wilk’s lambda=0.85; F=3.66, p<0.001). The carapace length (CL) was also found to vary significantly among the sampling locations (Wilk’s lambda=0.91; F=1.95, p<0.001); between the coasts (Wilk’s lambda=0.77; F=5.81, p<0.001) and between the sexes (Wilk’s lambda=0.73; F=7.52, p<0.001).
Table 2
MANCOVA tests for effects of sampling site (SS), standard length (SL) (covariate), and their interaction on body morphology of T. unimaculatus
Variables & their interaction
|
Wilk’s lambda
|
F
|
D.F.
|
Numerator D.F.
|
Denominator D.F.
|
p
|
Locations
|
0.03
|
26.48
|
4
|
128
|
2516.9
|
<0.001
|
CL
|
0.91
|
1.95
|
1
|
32
|
632.0
|
<0.001
|
Location: CL
|
0.64
|
2.30
|
4
|
128
|
2516.9
|
<0.001
|
Coast
|
0.58
|
14.43
|
1
|
32
|
638
|
<0.001
|
CL
|
0.77
|
5.81
|
1
|
32
|
638
|
<0.001
|
Coast: CL
|
0.89
|
2.44
|
1
|
32
|
638
|
<0.001
|
Sex
|
0.73
|
7.52
|
1
|
32
|
638
|
<0.001
|
CL
|
0.79
|
5.29
|
1
|
32
|
638
|
<0.001
|
Sex: CL
|
0.85
|
3.66
|
1
|
32
|
638
|
<0.001
|
The findings of the univariate test (ANOVA) performed to compare the morphometric measurement among the sampling locations, between the coasts (East vs. West), and between the sexes (Males vs. Females) are presented in Table 3. All the morphometric measurements showed a significantdifference (p<0.05) among the sampling locations. Most of the morphometric measurements except for TL, CW, T26, T78, T1920, T2122, T3132, T3233, T3743, and T3839 showed significant difference (p<0.05) when compared between the coasts (East vs. West).Morphometric measurements except for T16, T34, T45, T712, T812, T910, T1011, T1920, T2122, T2324, T2526, T2728, T2930, T3132, and T3437 were found to be significantly different when compared between the sexes.
Table 3
Summary of ANOVA performed on 32 morphometric measurements of T.unimaculatus collected along India to compare the difference between locations, coasts and sexes
Measurements
|
Location
|
Coast
|
Sex
|
F
|
p
|
F
|
p
|
F
|
p
|
TL
|
43.63
|
<0.001
|
2.12
|
>0.1
|
47.50
|
<0.001
|
CW
|
7.55
|
<0.001
|
0.55
|
>0.1
|
35.43
|
<0.001
|
T12
|
4.21
|
<0.001
|
10.93
|
<0.001
|
4.02
|
<0.05
|
T16
|
21.28
|
<0.001
|
36.01
|
<0.001
|
0.20
|
>0.1
|
T26
|
21.17
|
<0.001
|
2.82
|
>0.1
|
11.09
|
<0.001
|
T34
|
39.04
|
<0.001
|
42.06
|
<0.001
|
0.88
|
>0.1
|
T35
|
1.57
|
<0.001
|
10.89
|
<0.01
|
4.22
|
<0.05
|
T45
|
50.41
|
<0.001
|
5.49
|
<0.05
|
0.62
|
>0.1
|
T46
|
18.40
|
<0.001
|
15.98
|
<0.001
|
19.07
|
<0.001
|
T410
|
22.39
|
<0.001
|
7.05
|
<0.01
|
17.13
|
<0.001
|
T56
|
69.98
|
<0.001
|
109.70
|
<0.001
|
24.42
|
<0.001
|
T78
|
9.03
|
<0.001
|
2.55
|
>0.1
|
4.32
|
<0.05
|
T712
|
32.82
|
<0.001
|
43.87
|
<0.001
|
2.52
|
>0.1
|
T812
|
22.78
|
<0.001
|
21.29
|
<0.001
|
3.35
|
>0.1
|
T910
|
38.15
|
<0.001
|
26.06
|
<0.001
|
0.62
|
>0.1
|
T911
|
23.27
|
<0.001
|
63.16
|
<0.001
|
4.38
|
<0.05
|
T1011
|
57.66
|
<0.001
|
5.27
|
<0.05
|
2.08
|
>0.1
|
T1112
|
57.37
|
<0.001
|
48.64
|
<0.001
|
4.16
|
<0.05
|
T1920
|
37.70
|
<0.001
|
2.45
|
>0.1
|
0.01
|
>0.1
|
T2122
|
43.73
|
<0.001
|
0.71
|
>0.1
|
2.49
|
>0.1
|
T2324
|
38.49
|
<0.001
|
8.57
|
<0.01
|
1.50
|
>0.1
|
T2526
|
38.90
|
<0.001
|
17.98
|
<0.001
|
3.36
|
>0.1
|
T2728
|
27.61
|
<0.001
|
9.99
|
<0.01
|
3.54
|
>0.1
|
T2930
|
11.18
|
<0.001
|
0.48
|
>0.1
|
1.44
|
>0.1
|
T3031
|
24.72
|
<0.001
|
5.81
|
<0.05
|
8.09
|
<0.01
|
T3132
|
67.90
|
<0.001
|
2.59
|
>0.1
|
3.02
|
>0.1
|
T3233
|
59.93
|
<0.001
|
1.13
|
>0.1
|
24.70
|
<0.001
|
T3334
|
87.63
|
<0.001
|
5.85
|
<0.05
|
20.11
|
<0.001
|
T3437
|
40.10
|
<0.001
|
4.13
|
<0.05
|
2.16
|
>0.1
|
T3536
|
10.17
|
<0.001
|
12.42
|
<0.001
|
7.08
|
<0.01
|
T3743
|
30.10
|
<0.001
|
2.90
|
>0.1
|
71.81
|
<0.001
|
T3839
|
20.78
|
<0.001
|
1.10
|
>0.1
|
8.22
|
<0.01
|
The correlation of individual morphometric measurements with covariate (CL) before transformation and after transformation of morphometric measurements is shown in Fig. 3. All the morphometric measurements showed high to very high level of significant correlation (p<0.01) with CL. The correlation coefficient (r) varies from a minimum of 0.53 (for T3437) to a maximum of 0.95 (for CW and T410). However, after allometric correction, the correlation coefficient was drastically reduced from a minimum of 0.001 (for T3334) to a maximum of 23 (for T46). After allometric transformation, most of the morphometric measurements except for T26, T34, T35, T45, T46, T1011, T1112, T1920, T2122, T2324, T2526, T2728, T2930 were not found to be significantly (p>0.01) correlated with CL.
The data was found suitable for PCA as it passed the Bartlett’s test of sphericity test (χ2 = 18938.07, df=496, p<0.01), multicollinearity test (determinant=3.5x10−13) and Kaiser-Meyer-Olkin tests (overall MSA=0.81) to measure the sample adequacy. Principal component analysis (PCA) indicated that first eight principal components (PCs)individually explained the variance greater than average variance based on Kaiser Selectioncriteria (Eigenvalue >1.0). The first eight PCs cumulatively explained 73.97% of the total variance,wherein the first two PCs together explained 45.50% of the total variance (Fig. 4, Table 4).
The respective loadings of the morphometric measurements to the first eight principal components along with the eigenvalues, explained variance (%) and cumulative explained variance (%) is shown in Table 4. Morphometric measurements having significant loadings for PC1 and PC2 are shown in variables PCA biplot (Fig. 5).
Top ten morphometric measurements with the highest significant loadings on PC1 and PC2 are T2122, TL, T1920, T2324, T410, T2526, T712, CW, T35 and T911. The corresponding morphometric measurements have been highlighted and presented in Fig. 6.
Table 4
Morphometric measurements showing their respective loadings and eigen values to the first eight principal components
Morphometric measurements
|
PC1
|
PC2
|
PC3
|
PC4
|
PC5
|
PC6
|
PC7
|
PC8
|
TL*
|
-0.90
|
0.13
|
-0.26
|
0.07
|
-0.08
|
0.09
|
-0.02
|
0.02
|
CW*
|
-0.75
|
0.15
|
0.04
|
-0.20
|
0.09
|
0.16
|
0.14
|
-0.08
|
T12
|
-0.19
|
0.29
|
-0.23
|
-0.06
|
0.67
|
0.00
|
-0.11
|
-0.11
|
T16
|
0.19
|
0.70
|
0.24
|
0.00
|
-0.28
|
0.17
|
0.23
|
0.12
|
T26
|
-0.24
|
0.57
|
-0.19
|
-0.06
|
0.11
|
-0.03
|
-0.06
|
0.59
|
T34
|
0.04
|
0.67
|
0.16
|
-0.14
|
-0.25
|
-0.19
|
-0.22
|
-0.22
|
T35*
|
0.04
|
0.76
|
0.22
|
-0.02
|
0.00
|
-0.26
|
-0.17
|
0.24
|
T45
|
-0.53
|
0.13
|
0.37
|
0.33
|
0.33
|
-0.03
|
0.11
|
0.30
|
T46
|
0.07
|
-0.31
|
0.16
|
-0.28
|
0.18
|
-0.27
|
-0.45
|
0.26
|
T410*
|
-0.83
|
0.25
|
-0.19
|
-0.09
|
0.23
|
0.06
|
0.10
|
-0.03
|
T56
|
-0.23
|
0.02
|
-0.67
|
-0.48
|
0.14
|
-0.05
|
-0.14
|
-0.07
|
T78
|
-0.21
|
0.23
|
-0.23
|
0.05
|
0.17
|
-0.29
|
0.45
|
0.27
|
T712*
|
0.22
|
0.78
|
0.27
|
0.03
|
-0.13
|
0.18
|
0.04
|
0.00
|
T812
|
-0.34
|
0.62
|
-0.04
|
0.02
|
0.16
|
-0.02
|
0.02
|
-0.40
|
T910
|
0.14
|
0.67
|
0.14
|
-0.28
|
-0.16
|
0.03
|
-0.12
|
0.03
|
T911*
|
-0.02
|
0.74
|
0.35
|
-0.12
|
0.14
|
-0.06
|
-0.16
|
-0.22
|
T1011
|
-0.57
|
0.03
|
0.44
|
0.18
|
0.45
|
0.11
|
0.01
|
-0.15
|
T1112
|
-0.24
|
0.14
|
-0.69
|
-0.33
|
0.00
|
-0.17
|
0.05
|
-0.08
|
T1920*
|
-0.85
|
-0.23
|
0.20
|
-0.15
|
0.00
|
-0.02
|
-0.02
|
0.07
|
T2122*
|
-0.89
|
-0.20
|
0.23
|
-0.07
|
-0.06
|
-0.03
|
0.00
|
0.01
|
T2324*
|
-0.86
|
-0.21
|
0.32
|
-0.08
|
-0.07
|
-0.06
|
-0.04
|
-0.03
|
T2526*
|
-0.81
|
-0.22
|
0.37
|
-0.09
|
-0.06
|
-0.10
|
0.00
|
-0.06
|
T2728
|
-0.58
|
-0.32
|
0.51
|
-0.21
|
0.01
|
-0.08
|
-0.10
|
-0.01
|
T2930
|
-0.39
|
0.00
|
0.05
|
-0.53
|
-0.09
|
0.49
|
0.18
|
0.15
|
T3031
|
-0.59
|
-0.14
|
-0.17
|
-0.04
|
-0.21
|
0.20
|
-0.28
|
0.12
|
T3132
|
-0.74
|
0.03
|
-0.17
|
0.18
|
-0.29
|
-0.19
|
-0.10
|
0.03
|
T3233
|
-0.64
|
0.18
|
-0.34
|
0.29
|
-0.22
|
-0.21
|
-0.04
|
-0.04
|
T3334
|
-0.67
|
0.13
|
-0.22
|
0.43
|
-0.16
|
-0.12
|
-0.09
|
-0.07
|
T3437
|
-0.56
|
0.05
|
-0.11
|
0.25
|
-0.05
|
0.36
|
-0.41
|
0.09
|
T3536
|
-0.67
|
-0.03
|
0.20
|
-0.19
|
-0.14
|
-0.37
|
0.25
|
-0.08
|
T3743
|
-0.56
|
0.26
|
-0.31
|
0.30
|
0.11
|
0.22
|
-0.01
|
-0.04
|
T3839
|
-0.72
|
0.06
|
-0.07
|
-0.09
|
-0.21
|
0.07
|
0.19
|
0.00
|
Eigen Value
|
9.91
|
4.65
|
2.84
|
1.60
|
1.46
|
1.13
|
1.06
|
1.03
|
Variance Explained (%)
|
30.96
|
14.54
|
8.86
|
5.01
|
4.55
|
3.54
|
3.30
|
3.20
|
Cumulative Variance Explained (%)
|
30.96
|
45.50
|
54.37
|
59.38
|
63.92
|
67.46
|
70.76
|
73.97
|
* Top ten morphometric measurements with the highest significant loadings on PC1 and PC2 |
Bivariate PCA biplots of PC1 against PC2 describing the variations in morphometric measurements between locations, coasts and sexes areshown in Figure 7, 8 and 9 respectively. No clear separation was observed among the locations, between the coasts or between the sexes, as the overlapping in PCA scores was apparent.
The confusion matrix and statistics to measure the performance of linear discriminant analysis (LDA) models developed consequent to principal component analysis to optimize the separation among the groups (locations, coasts, and sexes) is given Table 5 and the pictorial separation has been illustrated as LDA plots in Fig. 10, 11 and 12.
The accuracy (ACC) and misclassification rate (MR) of the LDA model for discriminating among different sampling locations were 0.70 and 0.30,respectively. Location-wise sensitivity (True Positive Rate, TPR) and precision (Positive Prediction Value, PPV) were less than 0.90and 0.80, respectively for all the sampling locations with the lowest values estimated for SEZ (TPR=0.20 and PPV=0.39). Furthermore, the kappa coefficient that measures the agreement between classification and truth valueswas found to be low (Kappa= 0.62). Therefore, no clear separation was observed among any of the sampling location (Fig. 8). The accuracy (ACC), misclassification rate (MR), sensitivity (TPR) and precision (PPV) of the LDA model for discriminating between the coasts were 0.74, 0.26, 0.84 and 0.75, respectively. The Kappa coefficient for the model was also low (Kappa=0.45) and therefore, clear horizontal overlapping was observed between the coasts,which indicate that the samples were not different between the coasts (Fig. 9). The lowest accuracy (ACC), highest misclassification rate (MR), lowest sensitivity (TPR), precision (PPV) and Kappa of 0.58, 0.42, 0.65, 0.61 and 0.15, respectively were observed for the LDA model developed to discriminate between the sexes which was also apparent from the horizontal overlapping between the sexes (Fig. 10). Moreover, the Mcnemar’s test p values for the LDAs of locations and coasts were significant (p ≤ 0.001) which indicates that there are significant differences in the frequencies of false positive and false negative during classification
Table 5 Confusion/Error matrix and statistics to measure the performance of linear discriminant analysis (LDA) models developed to investigate the separation among the sampling locations and between the coasts and sexes
|
|
Actual cases (Locations)
|
|
|
Locations
|
SEC
|
SEN
|
SEZ
|
SWS
|
SWV
|
Predicted total cases
|
Predicted cases (Locations)
|
SEC
|
115
|
12
|
2
|
17
|
4
|
150
|
SEN
|
3
|
133
|
14
|
20
|
6
|
176
|
SEZ
|
4
|
6
|
20
|
7
|
14
|
51
|
SWS
|
8
|
19
|
6
|
117
|
4
|
154
|
SWV
|
0
|
0
|
56
|
2
|
84
|
142
|
|
Actual total cases
|
130
|
170
|
98
|
163
|
112
|
673
|
Statistics
|
Sensitivity (TPR)
|
0.89
|
0.78
|
0.20
|
0.72
|
0.75
|
Statistics
|
Location
|
Specificity (NPR)
|
0.94
|
0.92
|
0.95
|
0.93
|
0.90
|
ACC
|
0.70
|
Precision (PPV)
|
0.77
|
0.76
|
0.39
|
0.76
|
0.59
|
MR
|
0.30
|
NPV
|
0.97
|
0.93
|
0.88
|
0.91
|
0.95
|
NIR
|
0.25
|
Prevalence
|
0.19
|
0.25
|
0.15
|
0.24
|
0.17
|
p (ACC>NIR)
|
<0.001
|
Detection rate
|
0.17
|
0.20
|
0.03
|
0.17
|
0.13
|
Kappa
|
0.62
|
Detection preval.
|
0.22
|
0.26
|
0.08
|
0.23
|
0.21
|
p (Mcnemar)
|
<0.001
|
Balanced ACC
|
0.91
|
0.85
|
0.58
|
0.82
|
0.82
|
|
|
|
Actual cases (Coasts)
|
|
|
Coasts
|
East
|
West
|
Predicted total cases
|
Predicted cases (Coasts)
|
East
|
333
|
110
|
443
|
West
|
65
|
165
|
230
|
|
Actual total cases
|
398
|
275
|
673
|
|
Statistics
|
Coasts
|
Statistics
|
Coasts
|
Statistics
|
Sensitivity (TPR)
|
0.84
|
ACC
|
0.74
|
Specificity (NPR)
|
0.60
|
MR
|
0.26
|
Precision (PPV)
|
0.75
|
NIR
|
0.59
|
NPV
|
0.72
|
p (ACC>NIR)
|
<0.001
|
Prevalence
|
0.59
|
Kappa
|
0.45
|
Detection rate
|
0.50
|
p (Mcnemar)
|
<0.001
|
Detection preval.
|
0.66
|
|
|
Balanced ACC
|
0.72
|
|
|
|
|
Actual cases (Sexes)
|
|
|
Sexes
|
Male
|
Female
|
Predicted total cases
|
Predicted cases(Sexes)
|
Males
|
238
|
152
|
390
|
Females
|
130
|
153
|
283
|
|
Actual total cases
|
368
|
305
|
673
|
|
Statistics
|
Sexes
|
Statistics
|
Sexes
|
Statistics
|
Sensitivity (TPR)
|
0.65
|
ACC
|
0.58
|
Specificity (NPR)
|
0.50
|
MR
|
0.42
|
Precision (PPV)
|
0.61
|
NIR
|
0.55
|
NPV
|
0.54
|
p (ACC>NIR)
|
<0.04
|
Prevalence
|
0.55
|
Kappa
|
0.15
|
Detection rate
|
0.35
|
p (Mcnemar’s)
|
0.21
|
Detection preval.
|
0.58
|
|
|
Balanced ACC
|
0.57
|
|
|
ACC: Accuracy; MR: Misclassification Rate (1-Accuracy); NIR: No Information Rate, i.e., largest proportion of observed classes; Sensitivity: True Positive Rate (TPR); Specificity: True Negative Rate (TNR); Precision (PPV): Positive Prediction Value; NPV: Negative Prediction Value