406 
Fishery Bulletin 95(3), 1997 
. 7-1 j 
*=i k=\ 
After determining the catch group (i.e. J) for aba- 
lone harvested in diver-day i, the number of abalone 
harvested in diver-day i was determined as 
C, ={J- 0.5)20 + 2017, 
where U is a random number between 0 and 1 gen- 
erated from a uniform distribution. Because J in this 
equation has been determined from the previous 
equation, we have omitted the subscript rJ from C. for 
the sake of simplicity. This procedure was repeated 
for all diver-days in each simulation to determine 
the number of abalone harvested in each diver-day. 
Step 2 (determination of the mean length of aba- 
lone caught per diver-dayj The mean length of the 
catch for each diver-day was determined from the 
estimates derived from sampling 102 diver-days in 
1993-94 (Fig. 2C). Lengths of abalone were measured 
to the nearest mm from catches from a range of zones 
and are assumed to be measured without error. The 
estimates of mean size ranged from 116 to 
129 mm. Let Pj = probability of the mean 
length in length interval I (I = 1, 2, ..., 14). 
The mean length for diver-day i was de- 
termined by generating a random number 
R between 0 and 1 based on a uniform 
distribution and by assigning this number 
to one of the length intervals. The length 
was assigned to length interval I if the 
random number followed 
k=i k=i 
After determining the length interval (I) 
for the mean length of abalone harvested 
in diver-day i, the mean length of diver- 
day i was determined as 
L i ■ = I + 115 (mm), 
where 115 mm is the size limit. This pro- 
cedure was repeated for all diver-days in 
each simulation to determine the mean 
length of abalone caught per diver-day. 
Step 3 (determination of length compo- 
sition of abalone caught per diver- 
dayj The size distributions of abalone 
caught in a diver-day may be described by 
exponential distributions with varying 
slope, truncated at the lower limit by the 
legal size limit and at the upper limit by 
the value T, which was determined by ran- 
dom draws from the range of extreme val- 
ues observed in preliminary sampling. The 
density function for such an exponential 
distribution can be written as 
-(g-a) 
P(x) = Ae a , 
where a <x<T, and A and a are to be esti- 
mated. For an exponential distribution 
Zone X 
n = 468 
Zone Y2 
n = 582 
c 
<u 
3 
cr 
Zone Y3 
n = 334 
Zone Z 
n = 982 
115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 
Length (mm) 
Figure 3 
Examples of length-frequency distributions of abalone from four zones 
in the NSW abalone fishery. Data were pooled among diver-days from 
1994. 
