## 3 Results and Discussion
### Determination of Species
\begin{table}
\begin{tabular}{l l l l l l l l l l l l l} \hline
**Identifier** & **Compound** & **C. _mancellaria_ & **L. _capinia_** & **L. _scriata_** & **P. _regime_** & **Identifier** & **Compound** & **C. _mancellaria_ & **L. _capinia_** & **L. _scriata_** & **P. _regime_** \\ \hline A & Tetradecame & -2.00 & -2.00 & -2.00 & -2.00 & N & Linguistic Acid & -2.00 & -2.00 & -2.00 & -2.00 \\ B & FEA & -2.00 & -2.00 & -2.00 & N & O & Implicit Acid & -2.00 & -2.00 & -2.00 & -2.00 \\ C & Alkane A & N.0 & -2.00 & -2.00 & N & P & Otic Acid & -2.00 & -2.00 & -2.00 & -2.00 \\ D & Pentadecame (C\({}_{13}\)H\({}_{20}\)) & -2.00 & -2.00 & N & Q & Static Acid & -2.00 & -2.00 & -2.00 & -2.00 \\ E & TCAIE & -2.00 & -2.00 & -2.00 & N & R & 181 FR & -2.00 & -2.00 & -2.00 & -2.00 \\ F & Lauritz Acid & -2.00 & -2.00 & -2.00 & -2.00 & S & Anrolimation Acid & -2.00 & -2.00 & -2.00 \\ G & Isopropyl MytisThe quadrants of the variables plot (Figure 2) are also directly comparable to the quadrants of the corresponding DA chart (Figure 1). The length of each ray indicates the magnitude of the association. Long rays indicate variables that are important in describing the variation in sample profiles, whereas short rays that fall close to the origin are compounds that describe little to none of the variation. The distribution of the rays in Figure 2 is quite instructive. For example, rays B, K, T, U, W, and Y project into the lower left quadrant and tend to be found at higher levels in _L. cuprina_. Rays I, R, and S project into the lower right quadrant and tend to be found at higher levels in _P. regina_ and _C. macclaria_. Lastly, rays A, C, D, O, and P project into the top left quadrant and tend to be found at higher levels in _L. sericata_. Thus, the following observations are manifest:  
* _Lucilia cuprina_ is distinguishable by high concentrations of palmitoleic acid and several long-chain alkanes (alkane B, alkane C, alkane E, and alkane G). * _Phormia regina_ and _Cochlionytia macclaria_ are distinguishable by high concentrations of myrstic acid, 18:1 FFA, and arachidonic acid. * _Lucilia sericata_ is distinguishable by high concentrations of several alkanes, linoleic acid, and oleic acid. Figure 1: Discriminant analysis of the original variables for all four species, G1 generation, at all timepoints. The ellipses correspond to the 95% confidence limits of each species based upon its centroid and distribution of observations in the canonical variate (CV) space. Figure 2: Variables plot for discriminant analysis (DA) results in Figure 1. Identities for the rays projected from the origin correspond to the lettered compounds in Table 2.  
Lastly, when the DA model for the G1 generation was tested using leave-one-out cross-validation (Table 3), classification accuracies ranged from 89% (_P. regina_) to 96% (_L. sericata_) with an overall classification accuracy of 93%. Whereas Figure 1 allows for a qualitative assessment of the discrimination of the four species, classification accuracy is a quantitative way to assess the level of confusion between classes. Therefore, it is worth noting that of the four species, _P. regina_ and _C. macellaria_ had the lowest accuracies. For _P. regina_, 75% (three out of four) of the misclassifications were due to _P. regina_ observations erroneously classified as belonging to the _C. macellaria_ species. Similarly, 75% (three out of four) of the misclassifications were due to _C. macellaria_ observations erroneously classified as belonging to the _P. regina_ species. Achieving an overall classification accuracy of greater than 90% is an excellent result and this is sound evidence for the theory that taxonomic information can be gleaned from the lipid profiles.