# 8.19 PRODUCTION MODELS (EQUILIBRIUM) - ABUNDANCE AND FISHING LEVEL INDICES

(6.7.1 & 6.7.2)

The following table presents the annual total catches and the corresponding total fishing efforts of a shrimp stock in the Arabian Sea during the period 1969 to 1978 (Sparre and Venema, 1992).

 Year Catch, Y (t) Total effort (1000 days) 1969 546.7 1.224 1970 812.4 2.202 1971 2493.3 6.684 1972 4358.6 12.418 1973 6891.5 16.019 1974 6532.0 21.552 1975 4737.1 24.570 1976 5567.4 29.441 1977 5687.7 28.575 1978 5984.0 30.172

GROUP I

1. Draw a graph of the annual abundance index against the corresponding fishing mortality index.

2. The Fox model was adjusted to the data. The following parameters were obtained:

 a = 6.150 b = - 0.028 with a determination coefficient, r2 = 0.78.

a) Calculate and draw the curves of the equilibrium conditions of the abundance index and of the total catch against fishing effort.

b) Determine the target-points MSY and 0.1.

c) Determine the parameters (kq), (r/q) and (kr).

GROUP II

Knowing that the adjustment of the Schaefer model to the same set of data, resulted in the following values of the parameters:

a = 444.454
b = - 8.055
(r2 = 0.77)

1. Repeat the calculations of the previous Group.