Accurate conversion of acoustic data to estimates of organism size, distribution, and abundance requires quantification of variability associated with acoustic measurements. Measurements of target strength have been widely used to relate fish length to backscatter amplitude. Variability in backscatter amplitude is traditionally treated as noise. We used KRM backscatter models to quantify variance in acoustic backscatter and to estimate the probability of discriminating targets in two species aggregations.
We start with two fish species that you will unlikely see together in any aquatic environment  Atlantic cod and brook trout.
Atlantic
Cod

Brook
Trout

Gadus
morhua

Salvelinus
fontinalis

Individual KRM backscatter models of nine cod and ten brook trout were used to calculate mean (lower surface) and standard deviation (upper contour plot) reduced scattering lengths for each species. See the Predicting backscatter page for an explanation of the backscatter response surfaces.
Backscatter
response surfaces for 9 Atlantic Cod and 10 Brook Trout


Atlantic
Cod

Brook
Trout

General features of the mean backscatter response surfaces were similar between the two species. The influence of aspect angle (q) is reduced at low fish length to acoustic wavelength ratio (L/l) values. As L/l values increase, aspect angle increases in importance. Small deviations from near horizontal result in dramatically reduced echo amplitudes in both species. Mean reduced scattering lengths peaked when swimbladders were orthogonal to the acoustic wave front and decreased as the aspect angle deviated from approximately 85^{o}. Along the ridge of maximum scattering, constructive and destructive interference between the swimbladder and fish body resulted in small peaks and valleys. An increase in variance with increasing frequency occurred over a narrower band of aspect angles in trout compared to variances observed in backscatter from cod.
The mean and standard deviation reduced scattering lengths can be combined in a standardized ratio to a indicate speciesspecific signal to noise values at each combination of fish aspect, fish length, and acoustic wavelength. Areas of extreme (negative or positive) deviation indicate combinations of physical and biological factors that maximize the ability to discriminate cod echoes from brook trout echoes. 
This idea can be extended by estimating the probability of discriminating between the two species based on a paired ttest of the mean reduced scattering length values. A total of 2653 (62.8%) mean reduced scattering lengths were significantly different (p<0.1, df~17 adjusted for variance in each cell) between cod and brook trout. The number of significantly greater cod reduced scattering lengths (white) cells exceeded the number of larger amplitude trout (black) cells. Grey cells indicate no significant difference between backscatter means. 
If something is known about the behavior (i.e. tilt) and length distributions of fish species in a community, then a suitable choice of acoustic frequency will maximize the probability of detecting and discriminating between two species.
Relevant Publications
Horne, J.K. and J.M. Jech. 1998. Quantifying intraspecies variation in acoustic  
backscatter models. In Proceedings of the 135th Meeting of the Acoustical Society of America, Seattle, 2026 August 1998. pp. 18211822. 