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Fishery Bulletin 115(3) 
was then calculated from the 3 coordinate velocity vec- 
tors as 
S g =sqrt(XJ 2 x +U 2 y +U 2 z ). (2) 
Swimming polarity, which is a measure of the align- 
ment in swimming direction of individuals relative to 
that of the group, was calculated as the mean of the an- 
gular deviations (0;) between the individual velocities 
(Vj) and the group velocity (U) (Viscido et al., 2005): 
W 
(3) 
where is the vector dot product; and “ | j” is the ab- 
solute value. 
The individual swimming polarities were then convert- 
ed to a nondimensional mean value to simplify inter- 
pretation (Viscido et al., 2004) as: 
o = 
(90° -0j) 
90° 
(4) 
In this notation, fish swimming directions become in- 
creasingly parallel as <£> approaches 1.0. 
Nearest neighbor distance Nearest neighbor distance of 
each individual fish to other group members is defined 
in the following manner (Viscido et al., 2005): 
NND i = m . ..d j>p ), (5) 
where dj k = the distance between the j th fish and each 
of the p remaining fish. 
Nearest neighbor distance of the group is the mean 
over the p + 1 members of the group. 
The above metrics of group behavior were calculated 
identically for both the disturbed and undisturbed pe- 
riods, but the use of those descriptors differed between 
these periods. For the disturbed period, we were inter- 
ested in the temporal change of the metrics in response 
to the tow vessel and camera vehicle. In contrast, for 
the undisturbed case, we used the metrics to set a ref- 
erence level to use as a baseline for comparison with 
the disturbed case. We assumed that the values of each 
metric were relatively constant over the 10-s interval 
and that they characterized the undisturbed state of 
each metric as its mean and standard deviation. 
Results 
The response of the vermilion snapper to the vessel, 
tow cable, and camera vehicle can be considered from 
the perspective of individual behavior, but, because 
this is a schooling species, response can also be con- 
sidered from the perspective of the group behavior of 
the school. First, we considered the movement attri- 
butes of individual fish. These attributes are best seen 
as a time series of mean swimming vectors, which, 
in Figure 3, are represented by the mean speed and 
direction and were projected separately on the hori- 
zontal plane (x- and y-axes) and vertical direction (z- 
axis). At the moment that the tow vessel passed the 
camera (£=0), the mean horizontal swimming direction 
was aligned with and almost directly away (180°) from 
the tow direction; however, the swimming direction 
abruptly changed to 270° at 11 s, so that the fish were 
swimming perpendicular to the tow path, and again at 
20 s to approximately 315°, so that they were swim- 
ming obliquely away from the towed camera. Hori- 
zontal swimming speed, indicated by the lengths of 
the movement vectors in Figure 3, increased at 11 s 
and again at 20 s in accordance with the directional 
changes. Therefore, as expressed on the horizontal 
plane, there were 2 changes in swimming speed and 
direction that essentially partitioned the time series 
into 3 distinct periods. 
Vertical swimming speed and direction changed in 
a similar pattern. The vertical swimming direction 
is initially slightly upward until 10 s, when it shifts 
abruptly downward for 1 s before a horizontal shift in 
direction (Fig. 3). The downward shift in vertical swim- 
ming direction was also accompanied by an increase in 
swimming speed. 
These changes in vertical swimming speed led to 
changes in the mean distance of the fish from the 
bottom (Fig. 4). The initial upward speed of the fish 
resulted in a gradual increase in distance off bottom. 
However, synchronously with the changes in horizontal 
and vertical swimming direction, the distance off bot- 
tom rapidly decreased from a maximum of ~4 m at 8 
s after vessel passage to ~1 m at 22 s. Perhaps the re- 
duction in vertical swimming speed seen in the last 2 s 
of the series (Fig. 3) is the result of the school reaching 
this close proximity to the bottom. 
Next, we considered the descriptors of group behav- 
ior: group speed; individual speed; and swimming polar- 
ity. These descriptors also displayed a temporal pattern 
with 3 distinct periods. Group speed (i.e., movement 
of the school itself), over the entire period after vessel 
passage, was elevated considerably above its value dur- 
ing the undisturbed case, and 2 distinct increases were 
observed, one starting at -11 s and another starting 
at -18 s (Fig. 5A). These changes in group speed are 
related to changes in individual speed and swimming 
polarity, but the relative influence of each factor chang- 
es over time. Mean individual swimming speed (now 
expressed in 3 dimensions) was barely elevated above 
its value in the undisturbed case and increased only 
gradually during the first 17 s after vessel passage, 
but the rate of increase distinctly accelerated start- 
ing at -18 s (Fig. 5B). In contrast, swimming polarity 
(i.e., the alignment of individuals) was elevated greatly 
above its value in the undisturbed case over the en- 
tire record and a distinct rate of increase was observed 
at -11 s (Fig. 5C). Therefore, changes in group speed 
(i.e., movement of the school) were primarily deter- 
mined by changes in swimming polarity until the last 
few seconds when individual swimming speed greatly 
increased. 
