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07-Catch3

# 07-Catch3 - 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 fishing units and all the fish were spatially homogeneous. Now we explore what happens when this is not the case. Spatial Effects on CPUE Fish and fishing gear will almost never be uniformly distributed over the fishing grounds. How does this affect the relationship between CPUE and abundance? Suppose there are two fishing areas, A and B, and no interchange of fish between them. The time-averaged abundance for both areas combined is This is a simple extension of the time-averaged abundance that we explored in the Catch1 lecture. avN A_B t ( ) 1 t 0 t u N A u ( ) N B u ( ) + ( 29 d = The integral of a sum is the sum of the integrals. = 1 t 0 t u N A u ( ) d 0 t u N B u ( ) d + = avN A t ( ) avN B t ( ) + CPUE A t ( ) q A CPUE B t ( ) q B + = from CPUE = q·avN If q A = q B = q , then q avN A_B t ( ) CPUE A t ( ) CPUE B t ( ) + = and in general CPUE A CPUE B + C A f A C B f B + = C A C B + f A f B + To combine catch and effort data from different areas we should take the sum of the individual ratios of catch over effort; we should NOT take the ratio of the sum of the catch over the sum of the effort, although that is what people commonly do. Here is a hypothetical numerical example with N A (0) = N B (0) = 1000 that illustrates the point. M 0.1 = /yr q 0.01 = /yr f' A 10 = units f' B 30 = units Suppose that after three months (1/4 yr) of fishing we have the following: Area A: C A 24.4 = f A 2.5 = CPUE A 9.75 = Area B: C B 71.4 = f B 7.5 = CPUE B 9.52 = Combined: C A_B 95.8 = f A_B 10.0 = CPUE A_B 9.58 = The sum of the CPUE values is CPUE A CPUE B + 19.27 = . The sum of the catches (total catch) over the sum of the effort (total effort) is CPUE A_B 9.58 = . The ratio of the total catch over the total effort is equivalent to the weighted average fish density per area, with the "weight" for each area equal to the fishing effort. FW431/531 Copyright 2008 by David B. Sampson Catch3 - Page 44

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Population B Location Fish Density Population A Location Σ C Σ f Σ f C f 1 Σ f = What is a weighted average? We want our measure of CPUE to be proportional to the total time-averaged abundance, not the average (with respect to area) time-averaged abundance. The quantity ( Σ C)/( Σ f) may or may not be proportional to the time-averaged abundance. It will depend on the distribution of fishing effort
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07-Catch3 - THE CATCH PROCESS(continued In our previous...

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