Most aquatic animals spend part or all of their lives in groups. Nektonic biomass in coastal oceans is often dominated by aggregations of pelagic and demersal fish. Describing distributions, abundances, and structures of biological aggregations is a common theme among fisheries researchers and is often accomplished using acoustic technologies. Backscatter models that include behavior can be used to augment laboratory or field measurements by simulating echoes from individual fish within aggregations. Large numbers of echoes can be grouped in probability distribution functions (PDFs) to quantify the magnitude and variance of echo amplitudes. Echo PDFs of similar or varying sized individuals can then be used to construct a PDF for an aggregation of fish.

Effective target strength is the predicted or measured target strength of an aggregation that includes variability due to fish behavior. We define behavior as the spatial orientation of an animal due to its tilt and roll angles relative to the sound source. At this time we tabulate tilt and roll angles as independent, normally-distributed PDFs. We do not have data to suggest the use of a joint tilt and roll PDF.

Distributions of tilt and roll angles can be tabulated from laboratory observations or generated using random number generators.

A total of 2000
random tilt and roll angles were used to tabulate these tilt and
roll PDF's for Namibian pilchard.
Both distributions were centered on 90^{o} and had a spread
of one (roll) or three (tilt) standard deviations. This represents
an aggregation of fish swimming horizontally. Increasing the mean
tilt angle above 90^{o} simulates fish migrating upward
while mean angles less than 90^{o} simulate downward migration
by fish.

Effective target strengths are calculated by weighting the predicted echo amplitude from KRM models by the tilt and roll angle probabilities. The effect of tilt and roll is examined by comparing predicted target strengths from KRM models to those that incorporate tilt and roll PDF's in target strength tabulations.

Generate your own Effective
Target Strength Curve (coming soon!) |

The
left pane plots the predicted (black line; 90^{o}
tilt and 90^{o} roll) and effective
target strength (green line; 70^{o}
- 110^{o} tilt and 80^{o}
- 100^{o} roll) of pilchard as a function
of fish length at 38 kHz. The predicted and effective target strength
curves are similar from 10 to 15 cm. For pilchard greater than 15
cm, effective target strengths increased over predicted KRM
target strengths. Explanation for the divergence can be seen the
in the right pane. Backscatter KRM models were constructed for 32
lengths from 10 to 25 cm at 0.5 cm increments (10 cm black curve
- 25 cm red curve). Backscatter curves between 10 to 15 cm (light
blue) have roughly equal reduced scattering length values (i.e.
echo amplitudes) above and below the value at 90^{o}
(intersection of black vertical and horizontal lines). As fish get
bigger (see red curve), a larger percentage of reduced scattering
length values are larger than the value at 90^{o}
(pink horizontal reference line). Higher backscatter amplitudes
over a range of tilt angles results in larger predicted target strengths
than at 90^{o} and a larger effective target strength.

What happens if fish are migrating toward the surface?

If we shift
the mean tilt angle to 98^{o} then the effective target
strength pattern changes. Effect target strengths of fish less than
22 cm (green line; 86^{o} -110^{o} tilt and 80^{o}
- 100^{o} roll) are less than predicted target strengths
that don't incorporate behavior (black line). On the right pane,
you can see how a large proportion of reduced scattering lengths
among smaller fish with a mean of 98^{o} are much less than
values predicted at 90^{o}. Only large fish (>22 cm)
have effective target strengths greater than those at 90^{o}.

Can you guess what will happen when a fish aggregation migrates toward the bottom?

The
mean effective target strength was shifted to 82^{o}. Since
most backscatter response curve values for fish at all lengths are
greater with a mean of 82^{o} compared to those at 90^{o},
effective target strengths are larger than predicted for all fish
lengths in this example.

This example illustrates the effect of behavior on calculations of target strength to length relationships. Abundance estimates of fish could be over or underestimated depending on what the fish are doing when the survey is conducted.

**Relevant Publications**

Jech, J.M. and J.K. Horne 2000. Incorporating behavior in target strength | |

predictions of fish schools. ICES FAST working group manuscript. |