403 
Abstract. ^The fishery for blacklip 
abalone, Haliotis rubra , is one of the 
most valuable in New South Wales, 
Australia. An important part of the 
stock assessment process for this fish- 
ery is to quantify temporal changes in 
mean size and size structure of abalone 
in the landed catch. Variation in aba- 
lone growth over small spatial scales 
in this fishery and differences in har- 
vest strategy among different divers 
result in large variations in sizes of 
abalone landed. Monte Carlo simula- 
tions were used to investigate the in- 
fluence of these sources of variation on 
estimates of mean size and size struc- 
ture. Different sampling scenarios were 
considered — from random sampling of 
all diver-days to a more realistic scheme 
where abalone were subsampled both 
within and among diver-days. For a 
given total number of abalone mea- 
sured, error in estimated mean size and 
size structure declined asymptotically 
with increasing numbers of diver-days. 
By measuring at least 1,500 abalone 
from 100 diver-days, reliable estimates 
of size structure and mean size of aba- 
lone in the catch for the whole fishery 
were produced. This conclusion was 
robust with respect to the number of 
diver-days in the fishery. Estimated 
sampling intensity and probabilities of 
detecting differences based on simu- 
lated variances for the whole fishery 
are provided. 
Manuscript accepted 3 February 1997. 
Fishery Bulletin 95:403-413 ( 1997). 
Optimal sampling for estimating the 
size structure and mean size of abalone 
caught in a New South Wales fishery 
Neil L. Andrew* 
Yong Chen 
NSW Fisheries Research Institute 
PO. Box 21 
Cronulla, New South Wales 2230, Australia 
*E-mail address: andrewn@fisheries.nsw.gov.au 
Sample-size determination remains 
a crucial exercise in all aspects of 
ecology and fisheries biology, and 
the array of analytical tools avail- 
able continues to grow (e.g. Ger- 
rodette, 1987; Kimura, 1990; Peter- 
man, 1990; Thompson, 1992). The 
great majority of these techniques 
are designed to optimize sampling 
for data derived from independent 
samples from a number of hierar- 
chical sources of variation (e.g. 
Schweigert et al., 1985; Sen, 1986; 
Andrew and Mapstone, 1987; Kitada 
et al., 1992; Crone, 1995). Methods 
for determining sample sizes for 
describing size- or age-frequency 
distributions are less common (but 
see Smith and Sedransk, 1982; 
Schweigert and Sibert, 1983; Parkin- 
son et al., 1988; Erzini, 1990). 
Sample-size determination for 
the simultaneous estimation of dif- 
ferent size classes is possible ana- 
lytically only under limited circum- 
stances in fisheries applications. If 
differences among individuals are 
the only source of variation to be 
contended with, then the proportion 
of individuals in each size class in a 
population may be estimated simul- 
taneously by using the methods de- 
veloped by Fitzpatrick and Scott 
(1987) and Thompson (1987), and 
the calculation of the variances of 
these estimates are simple. 
In most situations facing fisher- 
ies biologists, however, there are 
many sources of variation confound- 
ing simple random sampling and 
sample-size determination for esti- 
mating mean size at harvest and 
the underlying size structure. Typi- 
cally, catches come from many boats, 
fishermen, and fishing grounds, and 
samplers are almost always faced 
with far more fish than they could 
possibly measure. Under these cir- 
cumstances there are many sources 
of variation that may bias sampling. 
Not least of these is the likelihood 
of underlying spatial and temporal 
heterogeneity in the fished popula- 
tions and changes in fishing behav- 
ior. Monte Carlo simulations pro- 
vide a relatively straightforward, al- 
though computation-intensive, 
means of determining appropriate 
schemes in these instances. Sample- 
size determination for multistage 
survey designs relies on apportion- 
ing sampling effort to various lev- 
els on the basis of variance or cost 
(or both). 
The fishery and the 
problem 
The fishery for abalone Haliotis 
rubra in New South Wales (NSW) 
is managed by using a combination 
of size limits, closures, and output 
controls. In 1995, each of 37 divers 
had an annual quota of 9 metric 
tons (t). Since 1974, divers have 
