Practical considerations

7.6.4 Practical considerations

This completes the description of the Extended Survivors Analysis. The calculation of reciprocal catchability and survivors is of course carried out iteratively, with a new VPA at each step, so there is always a current estimate of cum Z for use in equa- tion (7.36). The algorithm may be summarized by the following pseudo-code:

Pseudo-code for Extended Survivors Analysis

Read data Set prior weights, etc. Set terminal Fs (e.g. to 1.0)

ln - ln ( - [ )

Begin iterative loop Do VPA (or cohort analysis) Calculate Z, ECZ, etc. For each fleet and age

calculate weighted mean reciprocal catchabil-

ity (7.33) and variance thereof Next fleet and age Adjust weights (using estimated variance of r) For each fleet, age and year

calculate estimated population (equation

7.34) Next fleet, age, and year For each cohort

calculate weighted mean survivors (equation

7.36) Next cohort Repeat loop Print results, residuals, diagnostics, etc.

In fact, it turns out that, as usual, catchability on the oldest age is extremely ill determined, and some restriction must be imposed. In practice it is usual to assume that catchability for each fleet is constant above a certain age, so that the values estimated for that age are used for all subsequent ages, in estimating the populations. This removes the need to make an ad hoc assumption about fishing mortality on the oldest ages, but may lead to rather extreme estimates for these F values. A further technical detail is that, since surveys are carried out at different times of the year, and com- mercial fleets may catch fish mainly during one season or another, it is desirable to relate the CPUE/survey indices to the population estimates at the appropriate time of year. The most conve- nient way to do this is in fact to correct the indices to the beginning of the year using the appropriate proportion of Z. This is, however, almost an unnecessary refinement, since these adjustments would otherwise be allowed for in the calibration of the catchability values.

A more substantial refinement is to allow a more complicated model for the catchability on the youngest recruiting ages. As discussed by Shepherd (1997), there is good evidence that CPUE is not lin- early proportional to eventual year-class strength for these youngest age groups. This is easily

Dynamic Pool Models I: Interpreting the Past

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Chapter 7

allowed for in this method, since any procedure, The results are also illustrated in Figs. 7.12 and such as a regression, which permits population to

7.13. From these it can be seen that the XSA inter-

be estimated from CPUE may be substituted for the pretation differs in important details from those use of the simple weighted mean. The calibration presented before. Firstly, it indicates a moderate regression procedure described by Shepherd (1997) reduction of fishing mortality rates over the is fully compatible with this, and may be used for period, particularly on the 2-year-old fish, which any desired range of ages, provided that the oldest are among the most important age groups for this age is less than that above which one wishes to set stock. The mean F on ages 2 to 6 is in fact also esti- catchability to be constant. All the technical re- mated to have fallen from 0.93 to 0.81. Secondly, finements proposed by Shepherd (1997), such as the estimated abundance of the survivors at age 3 shrinkage to the mean, setting minimum vari- is much higher than for either of the other two ances, forecast/hindcast variance inflation, etc., credible analyses given above using the JAM and may also be incorporated without difficulty.

separable VPA methods. This is because both survey indices indicate a high abundance for these