# 8.18 PRODUCTION MODELS (EQUILIBRIUM) - SCHAEFER

(6.7.1)

The following table presents the annual total catch Y, (t) and mean biomass , (t) for the fishery of the Iberic stock (Div. VIIIc and IXa) of sardine, Sardina pilchardus, between 1977 and 1996, used by the Working Group of ICES (ICES, 1998a).

 Year Y (t) 1977 125750 750289 1978 139990 759192 1979 153441 763313 1980 191682 804765 1981 214133 842091 1982 204504 802573 1983 181139 713376 1984 202686 794856 1985 204107 810539 1986 180606 679808 1987 168825 547179 1988 158540 481295 1989 137126 431719 1990 139157 368099 1991 127756 316365 1992 126054 453161 1993 138795 539096 1994 132800 416842 1995 121384 368158 1996 111431 246037

GROUP I

1. Calculate Fi corresponding to each year i.

2. Calculate the biomasses, Bi, at the beginning of each year. (Use the procedure proposed by Schaefer, that is, the biomass at the beginning of a year is approximated by the arithmetic mean of the mean biomasses of the previous and the following year).

3. Calculate the equilibrium catches, YE, which would correspond to the observed values of F.

4. Calculate the equilibrium mean biomasses, E, which would correspond to the observed values of F.

5. Draw the graph of E against Fi.

GROUP II

The Schaefer model was adjusted and the following parameters were estimated:

k = 1562851 t

r = 0.426 year-1

1. Calculate the equilibrium biomasses and the equilibrium catches corresponding to the fishing levels observed in each year, using the Schaefer model.

2. Draw, in the graph of Group I point 5, the equilibrium biomasses calculated with the Schaefer model.

3. Calculate FMSY, BMSY and YMSY

4. Calculate F0.1, B0.1 and Y0.1.