## 3 Results and Discussion  
### Determination of Species  
The relative abundance of the 26 compounds of interest for the G1 generations are presented in a heat map in Table 2. Wherever possible, the identity of the compound has been reported. However, due to similar retention times and indistinguishable mass spectra, the exact identities of some of the hydrocarbons remain elusive. These have been compared against the retention times of an n-alkane mix and differentiated based upon their retention indices. Similarly, the compounds labeled \"14:1 FFA\" and \"18:1 FFA\" are mono-unsaturated 14:1 and 18:1 free fatty acids, but the precise location of the double bond is unknown. There is a high degree of qualitative similarity between the four species, particularly with respect to the expression of fatty acids. For example, palmitoleic acid, palmitic acid, linoleic acid, and oleic acid are observed at relatively high levels in all samples for all species. Substantially more variability is evident in the hydrocarbon compound class, with certain alkanes commonly seen in some species, yet wholly absent in other species. For example:  
1. alkane A (retention index (RI) = 1465) was only present in _L. sericata_. 2. pentadecane, alkane C (RI = 2800), alkane F (RI = 2934), and alkane G (RI = 3084) were present in all species except _P. regina_. 3. alkane D (RI = 2867) was only present in _C. macellaria_. Less obvious in Table 2, but still just as important to the statistical analysis, are the more nuanced quantitative differences in the detection of these compounds among the different species (i.e., differences in the relative amounts of each of the major compounds). It is often customary to reduce the dimensionality of a dataset first via PCA prior to attempting DA. This is typically done to sidestep one of the inherent limitations of DA, where each grouping must possess more observations (i.e., pupa exemplars) than variables (i.e., compounds of interest, or principal components thereof). A preliminary round of PCA therefore serves as a convenient way to reduce the number of variables whilst still capturing a sizeable amount of the variance in the data. For this data set, PCA of the G1 generation (data not shown) tended to over-emphasize the differences between _Lucilia cuprina_ and _Lucilia sericata_ at the expense of the differences between _Cochlomyia macellaria_ and _Phormia regina_, and therefore obfuscated more than it aided. Improved discrimination of species was achieved in this study by performing DA on the dataset directly without the intermediate PCA step. DA results for the G1 generation were prepared by this method and an observations plot is shown in Figure 1. This plot illustrates the two species that are readily differentiable (_L. cuprina_ and _L. sericata_) and two species that are more apt to be confused (_C. macellaria_ and _P. regina_). A variables plot is also provided in Figure 2. This type of plot serves as a \"roadmap\" for interpreting the DA results in Figure 1. Each ray in the variables plot represents one of the 26 compounds of interest. Rays that form an acute angle represent compounds whose abundances are highly correlated. For example, rays I, R, and S, correspond to myristic acid, octadecenoic acid (18:1), and arachidonic acid, which tend to rise and fall together. Similarly, rays T, U, W, and Y, represent long-chain alkanes (waxes) that are also correlated. Rays that form obtuse angles are highly anti-correlated. For example, linoleic acid (ray O) and arachidonic acid (ray S) are negatively correlated. Rays at right angles reflect compounds with little or no correlation.