We measured the distances between key points (marked on the figure below) on a large number of Tilapia of various sizes. We then performed a principal component analysis on the locations of these key points. The variation captured by these components can be displayed by animating the drawing.
PCA on the raw coordinate data yielded a component that correlated highly (~0.92) with the weight of the fish, but it is hard to see any change of shape in the animation. Note that the animations show only the inner parts of the fish - we have no information about what happens to the bits outside of the measured points. Lower order components showed no correlation with weight.
We therefore normalised the fish coordinates by the standard length of the fish (SL in the drawing above) and repeated the PCA. This gave three components with significant, but not very high (~0.4) correlations with weight (or Log(weight)). Note that the variations shown in these animations are exaggerated to illustrate the effects.
We therefore performed a multiple linear regression between the measured coordinates and Log(weight). This gave a multiple R of 0.82. The shape change associated is shown below. Small fish have a relatively bigger head and smaller tail.
Hockaday, S, Beddow, T.A., Stone, M., Hancock, P. and Ross. L.G. Using truss networks to estimate the biomass of Oreochromis niloticus, and to investigate shape characteristics. Journal of Fish Biology 57:(4) 981-1000, 2000.