## 3 Results and Discussion
### Effect of Genetic Diversity  
A key issue this project sought to address was the effect of genetic diversity on a specimen's chemical profile. Specifically, do G1 pupae yield a markedly different suite of compounds than pupae belonging to the G10 generation, whose genetic diversity has been homogenized over successive generations of inbreeding? When the results from the G10 generations were analyzed by DA (see Figures 3 and 4 and Table 4), the results were like those for the G1 generation. Note that the orientation of the species within the DA plot is rotated \(\sim\)180\({}^{\circ}\) relative to Figure 2. This is not as significant as the relative positions of the classes and the overall separation between species, which is more evident in this data set (Figure 3). The correlations between variables and the observations are also very similar (Figure 4), although rotated relative to Figure 2 as mentioned above. One exception was compound R (18:1 or octadecenoic acid), which was no longer strongly correlated with any of the other compounds. Lastly, when the DA model for the G10 generation was tested using leave-one-out cross-validation (Table 4), classification accuracies ranged from 94% (_P. regina_) to 98% (_L. cuprina_) with an overall classification accuracy of 96%. In similar fashion to the G1 generation, most of the misclassifications for _P. regina_, 67% (four out of seven) were due to _P. regina_ observations that were erroneously classified as belonging to the _C. macellaria_ species, and vice versa. Similarly, all misclassifications for _C. macellaria_ (two out of two) were due to _C. macellaria_ observations that were erroneously classified as belonging to the _P. regina_ species. The overall performance of the DA model is better for the G10 generation (96%) than it was for the G1 generation (93%). This small increase in accuracy may be explained by reducing the intra-species variation through repeated inbreeding. DA was also used to attempt to discriminate samples hailing from the G1 and G10 generation of each species (i.e., _C. macellaria_ G1 samples were compared to _C. macellaria_ G10 samples, _L. cuprina_ G1 samples were compared to _L. cuprina_ G10 samples, etc.). When DA is applied to only two classes (as in a series of pair-wise comparisons), a Receiver Operating Characteristic (ROC) curve can be constructed. ROC curves depict the binary classification accuracy of the system, and the area under a ROC curve varies from 0.5 (no discrimination) to 1.0 (perfect discrimination). The classification accuracy and ROC results for the G1 and G10 generations of all four species are shown in Table 5. The species whose G1 and G10 generations were the most distinguishable was _P. regina_, with a classification accuracy of 82.2% and a ROC area under the curve (AUC) of 0.88. Therefore, the effects of genetic homogenization were the most significant for this species. The species whose G1 and G10 generations were the least distinguishable was _L. sericata_, with a classification \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**From/To** & _C. macellaria_ & _L. cuprina_ & _L. sericata_ & _P. regina_ & **Total** & **\% Correct** \\ \hline _C. macellaria_ & 52 & 0 & 0 & 2 & 54 & 96.3 \\ _L. cuprina_ & 0 & 48 & 1 & 0 & 49 & 98.0 \\ _L. sericata_ & 0 & 0 & 52 & 2 & 54 & 96.3 \\ _P. regina_ & 2 & 0 & 1 & 51 & 54 & 94.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Leave-one-out confusion matrix for the G10 generation chemical profiles. Figure 4: Variables plot for the discriminant analysis results in Figure 3. Identities for the projected rays from the origin correspond to the lettered compounds in Table 2.  
accuracy of 58.9% and ROC AUC of 0.65. Therefore, the effects of genetic homogenization were the least significant for this species. DA was also performed by treating samples of G1 pupae as unknowns and classifying them per the DA model constructed from G10 pupae.