06-Catch2 - THE CATCH PROCESS (continued) In our previous...

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THE CATCH PROCESS (continued) In our previous derivation of the relationship between CPUE and fish abundance we assumed that all the units of fishing were equivalent. Now we explore what happens when they are not. Fishing Power Suppose there are two boats fishing simultaneously on the same grounds, but they are not equally effective at catching fish. For example, one boat might be using a larger net than the other or it might have a more powerful engine so that it can tow at a faster speed. Suppose boat A removes fish at instantaneous rate q A and boat B removes fish at instantaneous rate q B . The following equations apply. They are simple extensions of the differential equations for N and C. dN dt M q A + q B + ( 29 - N = ==> N t ( ) N 0 ( ) exp M q A + q B + ( 29 - t = dC A dt q A N = ==> C A t ( ) q A N 0 ( ) 1 exp M q A + q B + ( 29 - t - M q A + q B + = dC B dt q B N = ==> C B t ( ) q B N 0 ( ) 1 exp M q A + q B + ( 29 - t - M q A + q B + = Let Z = ( M + q A + q B ), and divide the two catch equations by t to get equations for the observed catch rates. Each boat's catch rate is its own CPUE value. C A t ( ) t q A N 0 ( ) 1 exp Z ( ) - t [ ] - Z t = CPUE A t ( ) = q A avN t ( ) = C B t ( ) t q B N 0 ( ) 1 exp Z ( ) - t [ ] - Z t = CPUE B t ( ) = q B avN t ( ) = We can combine the two sets of equations to show the relationship between the observed catch rates. CPUE A t ( ) q A avN t ( ) = CPUE B t ( ) q B = ==> CPUE A t ( ) CPUE B t ( ) q A q B = The ratio of the catch rates will be the same as the ratio of the catchability coefficients. Notice that the catch rates will be different unless q A = q B . If we ignored the differences between the two boats in their inherent fishing abilities, it might appear that the two boats were fishing on different populations. This becomes a special problem when we apply the notion of catch-per-unit-effort to catches by an entire fishing fleet. If the composition of the fleet changes over time, then changes that we observe in the CPUE might be due to changes in the fleet's fishing ability rather than to changes in fish abundance. One solution to this problem is to calibrate the boats against each other and calculate
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06-Catch2 - THE CATCH PROCESS (continued) In our previous...

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