Hanrahan and Juanes: Estimating the school size of Thunnus thynnus thynnus 
421 
method has been used to determine the relative abun- 
dance for other pelagic fisheries worldwide, including En- 
graulis mordax (Lo et al., 1992), Engraulis mordax, Sar- 
da chiliensis, Trachurus symmetricus, etc. (Squire, 1972), 
Trachurus decliuis, Katsuwonus pelamis, Arripis trutta, 
Thunnus maccoyii (Williams, 1981), Mugil spp. (Scott et 
ah, 1989), and Squire (1993) has reported aerial survey 
data for Thunnus thynnus oi'ientalis and other species. 
Abundance estimates derived from an aerial assessment 
are based on biomass or number of individuals per unit of 
area. 
Lutcavage and Kraus (1995) concluded that the aerial 
method could provide area-specific minimum abundance 
and distribution data for large medium and giant Atlan- 
tic bluefin tuna under good viewing conditions. However, 
many difficulties associated with aerial photographic as- 
sessment of ABT remain to be resolved. Sea state, light- 
ing conditions, and turbidity all play an important role 
in the ability to detect and produce useful photographs 
of schools (Lutcavage and Kraus, 1995). Rough seas, sun 
glare, and high turbidity may all result in reduced detec- 
tion of schools, limiting the days on which this type of sur- 
vey method is effective. Visual counts of individuals at the 
surface derived from aerial photographs are difficult to in- 
terpret without a verification count and information on 
behavioral factors such as surfacing frequency (Lo et al., 
1992) and the proportion of the school visible at the sur- 
face (Lutcavage and Kraus, 1995). In addition, variability 
in population movements and distribution could lead to an 
inaccurate abundance estimate if an intensive, spatially 
expansive sampling scheme is not employed. 
We propose a technique to address the problem of es- 
timating the number of fish in a school (NFS) from the 
surface characteristics of a school. If the relationship be- 
tween the surface structure or the surface number of fish 
and number fish in total school was known, school sur- 
face counts from aerial photographs or visual observa- 
tions could be adjusted to include an estimate of total 
NFS, facilitating an improvement of area-specific mini- 
mum abundance estimates based on visual or photograph- 
ic data sources. 
Atlantic bluefin tuna are believed to exhibit the most rig- 
idly defined spatial structure of schooling fishes (Partridge 
et al., 1983). Distinct two- and three-dimensional school 
structures have been described by previous authors (Par- 
tridge et al., 1983; Lutcavage and Kraus, 1995). Parabolas 
and echelons are the shapes of commonly observed sur- 
face-oriented two-dimensional schools, whereas the densely 
packed dome is the shape of a frequently observed three- 
dimensional school configuration (see Partridge et al., 1983 
and Lutcavage and Kraus, 1995 for illustrations). The num- 
ber of fish observed in two-dimensional surface schools is 
generally less than 15, whereas three-dimensional schools 
such as those forming densely packed domes usually have 
greater than 15 individuals (Partridge et al., 1983). Al- 
though the three-dimensional component of bluefin tuna 
school structure has been observed (Lutcavage and Kraus, 
1995), quantitative description and analysis is lacking and 
little is known of the relationship between the two-dimen- 
sional surface structure and three-dimensional structure 
(e.g. total count, biomass) of schools (Partridge et al., 1983; 
Lutcavage and Kraus, 1995). In addition, the behavioral 
and environmental factors that may influence tuna school 
structure and dynamics remain poorly described (Mather, 
1962; Clark and Mangel, 1979; Partridge et al., 1983). 
Our study presents a functional relationship between 
the surface characteristics of and the total number of indi- 
viduals in ABT schools. We analyzed video-taped footage 
of 74 incidences of schooling in a group of captive ABT to 
quantify the relationship between the number of fish vis- 
ible at the surface and the total number of individuals in 
the school (NFS), the relationships between school dimen- 
sions (e.g. length, width) and NFS, and to explore the effect 
of environmental conditions within the net-pen enclosure 
on school size and dimensions. We also analyzed the verti- 
cal distribution of individuals within schools across school 
size, and propose a mechanistic explanation for the limited 
size of the two-dimensional schools observed by Partridge 
et al. (1983) and Lutcavage and Kraus (1995). We then ap- 
ply the predictions from one of the resultant models to the 
single open-ocean school size estimate available. 
Methods 
Field methods 
We employed a 30.5-m diameter, 15.3-m deep, cylindrical 
floating net-pen enclosure (Fig. 1) to hold the tuna used in 
our study. This enclosure is similar to those used in tuna 
research and culture operations around the world. Its low 
cost, large internal volume (11,128.5 m 3 ), and its resiliency 
to dynamic and often damaging effects of the offshore envi- 
ronment make this enclosure the most appropriate type 
for observing the behavior of large pelagic fish in captivity. 
The enclosure proved to be very resilient to the damaging 
effects of a close pass of a hurricane and a tropical storm. 
A white, one-inch, straight-hung mesh net constituted the 
vertical walls and bottom of the enclosure. 
The enclosure was anchored 32.2 km offshore of Wacha- 
pregue, VA, on the southwest corner of 20 Mile Hill — a 
bathymetric feature that rises within 33.5 m of the ocean 
surface in deeper surrounding waters. This location is rel- 
atively near shore and close to a temporally and spatially 
reliable aggregation of small (~1 m) Atlantic bluefin tuna 
regularly targeted by recreational fishermen. 
The vertical temperature profile (°C), dissolved oxygen 
(mg/L), pH, suspended solids (NTU), Secchi depth (m), 
and conductivity (ppt) were monitored twice daily inside 
and outside the enclosure at 3-m intervals to a minimum 
depth of 15 m. 
A pattern of seven, single-hook trolling lures were fished 
from a 18. 3-m commercial vessel on 13-kg or 22-kg class 
trolling gear to capture fifty bluefin tuna in the vicinity 
of the study enclosure in June and July 1996. Tuna were 
subdued as quickly as possible and landed in a special- 
ized cloth stretcher. We recorded the fork length (cm), ap- 
proximate weight (kg), and general condition of each fish 
and released the fish into a 2400-liter elliptical transport 
tank. Compressed, bottled oxygen was employed to elevate 
