Andrew and Chen: Estimating size structure and mean size of Haliotis rubra 
405 
Number of days per zone 
Number of abalone per day 
115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 
Length (mm) 
Figure 2 
Summary statistics from the NSW abalone fishery for 1993 
and 1994: (A) Frequency distribution of the number of days 
per zone, (B) Frequency distribution of the number of aba- 
lone per diver-day calculated from known average weights 
per abalone, (C) Frequency distribution of the mean length 
of abalone caught per diver-day. Sample sizes indicated 
are the number of diver-days. 
3 Sample a fixed number of abalone randomly from 
diver-days selected randomly. 
Of the three strategies, the third is the most logis- 
tically and financially reasonable. There is consider- 
able unpredictability in where and when divers will 
work both because of weather conditions and a re- 
luctance by divers to specify where they will work on 
a given day. These facts conspire to make it difficult 
to sample in a truly random manner. Nor is it practi- 
cal to stratify appropriately across either divers or 
days because the population of diver-days to be 
sampled can be determined only in retrospect. For 
these reasons we have used a “diver-day” as the unit 
of stratification. Three sources of variation are con- 
founded in “diver-day.” Differences among divers, as 
a result of their fishing behavior (e.g. experience and 
ability) could not be separated from the variation in- 
herent in where they fished, and therefore in the aba- 
lone caught. The third source of variation pooled into 
diver-day is the day itself (e.g. weather and sea con- 
ditions). Although these sources of variation were in- 
separable within the present study, the inferences 
drawn about a representative sampling scheme are 
not confounded. Strategy 1, although desirable, 
would limit the number of diver-days that could be 
sampled given a fixed total sampling effort. Strat- 
egy 2 represents the “ideal” sampling scheme and is 
used as a standard from which the remaining, more 
realistic, schemes are judged. 
Parameters of the simulation 
Parameters were determined for the simulations by 
using information collected during the 1993-94 fish- 
ing years. We assumed that there is as much vari- 
ability in parameters among diver-days within a zone 
as among zones. Sampling schemes for zones or 
groups of zones and for the whole fishery were as- 
sessed by varying the total number of diver-days in 
the “fishery” per year. We therefore ran simulations 
by using up to 600 diver-days to determine sampling 
schemes for zones and groups of zones and simulated 
a 4,000-d fishery to determine a sampling scheme 
for the fishery as a whole. 
Step 1 (determination of the number of abalone 
caught per diver-dayj Based on previous sampling 
(Fig. 2B), the numbers of abalone caught in all diver- 
days were grouped into different catch groups rang- 
ing from the midpoint of 20 to 760 abalone, with the 
interval of the catch groups being 20. Thus, the total 
number of catch groups is 38 (i.e. (760-20)/20 + 1 = 
38). The frequency of the number of abalone caught 
per diver-day was then estimated. Based on these 
frequencies, the total catch per diver-day was deter- 
mined by multinominal sampling described as fol- 
lows. Let Pj = probability of the number of abalone 
harvested in a diver-day in catch group J, where J = 
1, 2, ..., 38. The catch of diver-day i was determined 
by generating a random number R between 0 and 1 
based on the uniform distribution and by assigning 
this number to one of the catch groups. The catch 
was assigned to catch group J if the random number 
followed 
