# 8.17 Floss AND Fcrash

(5.3.5 & 5.3.6)

GROUP I

During the meeting of the Assessment Working Group (ICES, 1998b) on the Iberic stock (Div. VIIIc and IXa) of hake, Merluccius merluccius, the recruitment (million individuals at age 0) and the spawning biomass (thousand tons) was estimated for the period 1982-1996. The values obtained are shown in the following table:

 Year N (age 0) (million) Spawning biomass (thousand tons) 1982 125 59.8 1983 107 61.4 1984 136 58.8 1985 97 44.1 1986 104 26.4 1987 97 24.2 1988 84 22.8 1989 56 18.9 1990 59 19.4 1991 69 20.5 1992 86 21.5 1993 70 21.0 1994 63 16.5 1995 32 15.2 1996 83 18.0

The Shepherd S-R relation was adjusted to the pairs of values in the table (r2 = 0.71), and the relation parameters are the following:

α = 3.5 Kg -1
k = 64.94 thousand tons
c = 3.52

1. Draw the dispersion graph of the resulting recruitments, against the parental spawning biomasses.

2. Calculate the expected recruitments in each year of the period 1982-1996 according to the Shepherd S-R model and in the previous dispersion graph, draw the respective curve.

GROUP II

1. Calculate the annual catch in weight and the spawning biomass per recruit for the stock of hake, using the mortality and biological parameters estimated by the Working Group for the long-term projections (given in Section 8.15), namely:

 Natural mortality coefficient: M = 0.2 year-1 Fishing mortality in 1996: F96 = 0.24 year-1

Mean weight in the catch (g):

 Age (year) 0 1 2 3 4 5 6 7 8+ 4 37 106 205 358 517 706 935 1508

Maturity ogive (percent):

 Age (year) 0 1 2 3 4 5 6 7 8+ % maturei 0 0 1 6 20 49 76 91 100

Mean relative pattern of exploitation of the period 1994-1996:

 Age (year) 0 1 2 3 4 5 6 7 8+ si 0.001 0.11 0.398 1.3 1.261 1.019 1.473 1.874 1.874

GROUP III

1. Using the results of Groups I and II, calculate biological reference Limit-Points, Floss and Fcrash.