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Fishery Bulletin 99(3) 
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Number in school (A/ s ) 
Figure 6 
School depth in number of individuals plotted against total school number (N s ). The dotted line is 
drawn to illustrate the increase in the vertical expanse of schools coincident with the maximum 
number of individuals observed in parabola and echelon-shaped schools. The maximum number of 
depth intervals in our analysis was 5. Schools greater than 5 individuals in total depth are described 
by a surface layer and four 25% depth intervals. 
observed that small schools have a strong horizontal as- 
pect, and little vertical expanse. For example, Partridge 
et al. (1983) and Lutcavage and Kraus (1995) observed 
that small ( < 15 individuals) parabola- and echelon-shaped 
schools of noncaptive giant ABT vary little in shape. Inter- 
estingly, parabola and echelon shapes are not observed for 
large (>15) ABT schools, coinciding with changes in inter- 
individual orientation between groups of less than 10 and 
10-20 individuals (Partridge et al., 1983). This difference 
is similar to the shift in the depth of schools that we ob- 
served with approximately 15 individuals (Fig. 6). It is pos- 
sible that Partridge et al. ( 1983) and Lutcavage and Kraus 
(1995) observed small schools in these configurations be- 
cause larger schools expand vertically and adopt the semi- 
conical shape that we describe. These results suggest that 
there may be a critical minimum number of individuals 
that must be present in a horizontal layer before schools 
begin to expand vertically, which would explain the limited 
size of two-dimensional ABT schools. 
It is possible that ontogenetic variation in school struc- 
ture exists, but understanding how such changes occur is 
critical in determining how variability in school structure 
could affect our modeling approach. Because our models 
use numerical relationships rather than distance metrics 
to predict school size, neither ontogenetic shifts in in- 
terindividual spacing or packing density changes related 
to school size should substantially affect the predictive 
ability of our models. However, if ABT schooling behav- 
iors change at a more basic level due to enclosure or 
changing fish size, then our estimation techniques may be 
invalid outside captivity or with larger fish. Basic changes, 
such as vertical distribution of individuals within schools, 
the three-dimensional shape of schools, and strong school 
structure responses in relation to environmental factors, 
could all have serious effects on our modeling approach. 
Further, we feel that schools similar in form to those 
described as “densely-packed domes” by Lutcavage and 
Kraus (1995) could be described well by our models, but 
that numerical estimation of other school types might re- 
quire the application of a different estimation technique. 
Environmental effects on school formation 
The physical environment may play a role in determining 
the vertical position of tuna in the water column (Holland 
et al., 1990; Block et al., 1997) or school structure (Par- 
tridge et al., 1983; Lutcavage and Kraus, 1995). No rela- 
tionship between environmental variables and the shape 
of schools (quantitatively determined) or the vertical posi- 
tion of fish (in qualitative observations) were observed in 
our study, perhaps because of the small range and lack 
of vertical structure in salinity, pH, and dissolved oxygen 
