404 
Fishery Bulletin 95(3), 1997 
been required to provide details of daily catch weight 
and diving hours in each of 28 zones (Fig. 1). Divers 
may catch abalone in any of the zones, which range 
in length of coastline between 7 and 147 km. In 1994 
there was a total of 3,129 diver-days in the fishery 
and an average of 104 diver-days per zone (Fig. 2A). 
Based on estimates of average weight per abalone, a 
catch of between 20 and 760 abalone was landed per 
diver-day (Fig. 2B). The mean size of abalone caught 
per diver-day ranged between 116 and 129 mm, al- 
though the majority were between 117 and 121 mm 
long (Fig. 2C). A minimum size limit of 115 mm has 
been applied to the fishery since 1987. Fishing pres- 
sure in this fishery is intense and the size structure 
of abalone in the landed catch in each zone may be 
described by negative exponential distributions of vary- 
ing instantaneous slope (see examples in Fig. 3). 
Determining a sampling scheme to provide reli- 
able estimates of the size structure and mean size of 
abalone in the landed catch is complicated by differ- 
ences among diver-days. Worthington et al. (1995) 
and Worthington and Andrew (in press) have de- 
scribed large variations in demographic parameters, 
such as growth rate, maximum size, mortality, and 
fecundity, over a range of spatial scales. These stud- 
ies report as much variation in the rates of growth 
and in the maximum sizes of abalone within sites 
separated by 2 km as there was among sites sepa- 
rated by hundreds of kilometers. Sizes of abalone in 
landed catches will therefore depend on how and 
where the diver worked as well as on the 
demographic attributes of the population 
being fished. For example, on any day, a 
diver may work areas where abalone are 
fast-growing and tend to be larger or ar- 
eas where abalone are slow-growing and 
smaller (or both). 
In this study we report the results of 
simulations in order to determine an ap- 
propriate allocation of sampling effort to 
estimate mean sizes and size structures 
of abalone in the landed catch in the New 
South Wales fishery. Sampling is consid- 
ered for groups of zones and for the whole 
fishery. A simulation approach was adopted 
in preference to an analytical solution (e.g. 
Cochran, 1977) because we were interested 
in simultaneously optimizing sampling 
across a number of size classes — all of which 
were nonindependent. The simulation pro- 
cedure allowed an estimation of the devia- 
tion of samples of different sizes from a 
known or true population. Parameters used 
in the simulations were based on prelimi- 
nary sampling in 1993-94. 
Materials and methods 
Simulation study 
A Monte Carlo simulation approach was 
used to estimate the relative efficiency of 
three strategies for sampling abalone: 
Sample all abalone from randomly se- 
lected diver-days; 
Sample a fixed number of abalone ran- 
domly from the catches of all diver- 
days; and 
Figure 1 
Map of the lower half of New South Wales showing zones in the abalone fish- 
ery. The zones are coded alphabetically from north to south. 
