APPENDIX/ANNEXE

I. LIST OF PARTICIPANTS/LISTE DES PARTICIPANTS

II. GUIDELINES FOR SARDINELLA AGE ESTIMATION/DIRECTIVES POUR L’ESTIMATION D’ÂGE DE LA SARDINELLE

The Workshops developed the below criteria, based on the experiences gained. These criteria are preliminary and are to be further developed and validated in the next Workshops. Before the Workshops, a sampling programme will have been put into place and a new exchange of otoliths carried out between all of the institutions in the sub-region.

1. The date of birth adopted is 1 January.

2. One year is equivalent of a pair of opaque and translucent rings.

3. In general, the width of the first annual ring varies depending on the month of “birth” (date of spawning) (Figure X, Appendix X).

4. The basic characteristics to be taken considered for the annual rings are the width and continuity. In general, the ring width decreases in the first two years of life and if one ring is discontinued it is considered false.

5. If the sardinella is caught in the first quarter with a translucent ring on the otolith edge the age assigned will be equal to the number of annual rings observed.

6. If the sardinella is caught in the second quarter with a translucent ring on the otolith edge the age assigned is equal to the number of annual rings observed, but if this ring is very narrow the ring is formed this year and should not be considered (N-1).

7. If the sardinella is caught in the third and fourth quarter with a translucent ring on the otolith edge the age assigned is equal to the number of annual rings minus one.

Figure. Example of age interpretation (Op - opaque; T - translucent)

III. SURPLUS PRODUCTION MODELLING/MODÈLE DE PRODUCTION EXCÉDENTAIRE

by Pedro Barros

The stocks in the area were assessed using a non-equilibrium production model based on the Schaefer (logistic) population growth model.

The model uses four basic parameters: Virgin Biomass K, population intrinsic growth rate r, initial depletion D (starting biomass relative to K) and catchability q. All other parameter estimates are derived from these four.

Given the best parameter estimates, the model calculates the MSY, B_MSY and F_MSY reference points. It also calculates the reference points B_Ratio, (the ratio between the estimated biomass for the last year in the data series and B_MSY), and F_Ratio, (the ratio between the effort actually exerted on the stock in the last year of the data series and the effort that would have produced the sustainable yield in the same year).

The absolute values of F_MSY, B_MSY and even K must not be considered, since the model provides more accurate estimate for F_ratio and B_ratio.

Trends of these ratios and whether or not they are above/below 100% provide useful information for management purposes.

B_Ratio, indicates the current status of the stock biomass in the last year of the data series B_Cur, relative to the biomass that would produce MSY, B_MSY. Values smaller than 100% indicate a stock abundance below B_MSY, while values larger than 100% indicate a stock abundance larger than B_MSY.

F_Ratio, measures the fishing effort in the last year of data available, as a proportion of the fishing effort that would have been necessary to extract the sustainable catch at the Biomass levels estimated for the same year. The value of this ratio is the same as the Yield ratio Y_Ratio, the current yield as a proportion of the sustainable yield at the current stock biomass level, . Values below 100% indicate that the catch currently being extracted is lower than the natural production of the stock, and so stock biomass can be expected to increase, while values above 100% suggest that the catch exceeds the production from the stock and so this will decrease next year.

Incorporation of environmental variability

Pelagic stocks are known to be significantly affected by environmental variability. Years with exceptionally favourable environmental conditions will see an above-average set of growth conditions of the stock, while years with exceptionally poor environmental conditions will be associated with large decreases in stock biomass or at least in stock growth rate. The evolution of the stock biomass in these periods cannot be explained solely by the dynamic of the catches or the average stock growth conditions. The model with constant parameters cannot describe the evolution of the pelagic stocks under these circumstances. Therefore, a modification of the model to include environmental variability was made during the Working Group meeting.

An environmental quality index was introduced for each point in the data series, and the r and K parameters of each year were considered to depend on the corresponding value of the index.

The stock growth parameters in each year I, K_i and r_i, were defined as

where K and r are the overall base level of the carrying capacity, and of the intrinsic growth rate of the stock, respectively, E_i is the value of the environmental quality index for this stock in year i, and a is a constant defining the intensity of the environmental effect on the population growth parameters.

Implementation

The model and its fitting were implemented in an MS Excel spreadsheet, modified from the spreadsheets distributed by FAO under the BioDyn package. The minimisation algorithm used was the Newton-Raphson algorithm implemented in the Solver add-in in MS Excel. Given that the different parameters have different orders of magnitude, automatic scaling of the parameters was chosen.

The basic data used for each stock was total yearly catch estimates, and a series of abundance indices. The fitting of the model was based on fitting the series of observed abundance indices, assuming an observation error model. The objective function minimised was the sum of the squared residuals between the logarithms of the observed and predicted indices.

Given the limitations in the data, it was decided not to combine different abundance indices series in any single assessment. Accordingly, a single abundance index series was used in each model run, using the abundance indices series considered by the researchers involved as having the best probability of actually reflecting the changes in underlying stock abundance.

When more than one candidate abundance index series was available, a separate run of the model was done for each of them. Care was taken to ensure that the start (seed) values of the parameters were the same for all abundance indeces series considered.

The four parameters of the model, r, K, q and D, are strongly correlated, a well-known problem in non-linear model estimation. For example, given the same data series, a larger intrinsic stock growth rate estimate is necessarily linked with a smaller carrying capacity and/or a larger catchability.

In order to reduce this difficulty, the initial depletion D was fixed from knowledge of the fishery in the years preceding the start of the data series. When there were doubts about this ratio, the model was run several times with different values of the ratio, and the results compared.

The other three parameters, r, K and q, were estimated using the non-linear minimisation algorithm.

Initial (seed) values and constraints

The minimisation algorithm is in general very sensitive to the starting (seed) values for the parameters. The following procedure was adopted:

1. A start value, B₁, was estimated for the average stock biomass during the period analysed, from external knowledge about the fish stock;

2. The initial value for q, q1, was calculated dividing the average value of the abundance index during the period, , by B₁, ;

3. The initial value for K, K₁, was estimated taking the average value of the abundance indices for the two first years, dividing it by q₁ to obtain a first estimate of the initial Biomass B₁, and dividing it by the value established for initial depletion D

4. The initial value for r was taken to be 0.5 for slow-growing long-lived species like horse mackerel, and 1.0 for faster-growing, short-lived species like e.g. sardine or chubb mackerel.

In the estimation, K and q were constrained to be between half and twice the initial values,

,

r was only required to be positive.

Abundance indices used

Theoretically, any abundance index that is supposed to be correlated with stock abundance can be used to fit the model. In the case of the stocks evaluated during this Working Group, two sets of abundance indices were used, commercial CPUE series and series of acoustic abundance estimates from the December surveys carried out by R\V DR. FRIDTJOF NANSEN, the longest series of fisheries-independent abundance indices available. The commercial CPUE series were allocated to the year they were collected in, while the acoustic estimates, collected in December, were allocated to the following year.

Other forms of using the abundance indices, e.g. considering the average abundance of two consecutive December surveys as index of abundance for the year between the surveys, should be explored, and possibly used in future assessments.