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<br />
<br />Appendix 1: Calculation of Detection Efficiencies
<br />
<br />The formulae below show how we calculated
<br />detection efficiencies (which we equate to probabilities
<br />of detection) for our 3 X 2 PIT tag interrogation system.
<br />The 3 X 2 system consisted of a serial arrangement of
<br />three arrays of two antennas each, which we labeled
<br />(from upstream to downstream) as arrays A, B, and C.
<br />A PIT -tagged fish that passed the system and was
<br />detected could have one of seven array detection
<br />histories. The fish with the different array detection
<br />histories were summed (S) as follows:
<br />
<br />Sa = fish detected only on array A
<br />Sab = fish detected on both array A and array B
<br />but not array C
<br />Sac = fish detected on both array A and array C
<br />but not array E
<br />
<br />Sabc = fish detected on array A, array E, and array
<br />C
<br />Sb = fish detected only on array E
<br />Sc = fish detected only on array C
<br />She = fish detected on both array B and array C but
<br />not array A
<br />
<br />To calculate the detection efficiency of array A, four
<br />values were required. These were generated from the
<br />numbers of fish within each an'ay detection history as
<br />follows:
<br />
<br />NA = fish detected on array A (Sa + Sab + Sac +
<br />Sabc),
<br />NABC = fish detected on array A and at least one
<br />other array (Sab + Sac + Sabc),
<br />
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