Hanrahan and Juanes: Estimating the school size of Thunnus thynnus thynnus 
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A schematic representation of the configuration of the video equipment used for our analyses. 
Data analysis 
School size Groups of tuna were considered to be schools 
and were included in the analyses if they were a polarized 
group (multiple individuals maintaining lateral proximity 
to neighbors and actively maintaining the same direction 
of travel during an observation period). The total number 
of fish in each school was counted and the frequency distri- 
bution of school size was determined. Because the obser- 
vations were assumed to be independent and the total 
sample size was less than 2000, the normality of the dis- 
tribution was tested by using the Shapiro-Wilks W-test. 
Least-squares regression was then used to evaluate the 
relationship between school size (TV.) and each environ- 
mental variable. 
Predicting number of fish in school from surface counts 
Our video footage was filmed at an oblique perspective 
to the upper boundary of schools occurring within two 
meters of the water’s surface. Measurement of school 
characteristics in body lengths or meters was not pos- 
sible because of the camera angle or because of poor 
image resolution due to low light or high turbidity level. 
The total number of individual fish (N s ) was determined 
and the distribution of individuals within the school was 
described in terms of five depth intervals (Fig. 3). The 
surface interval included fish that were at the immedi- 
ate surface of the school or fish that overlapped other fish 
at the surface on the horizontal plane. Each of the four 
subsequent intervals encompassed 25% of the remaining 
depth of the school. The number of fish per interval was 
designated as N : ( ; =the number of tuna in the z th depth 
interval). Fish positioned at an interval boundary were 
assigned to the interval in which the greater portion 
of their body volume was positioned. Analysis of covari- 
ance (ANCOVA) (Sokal and Rohlf, 1995) was employed to 
detect differences in the slopes of each of the regressions 
of Nj on N s in order to determine whether the distribution 
of individuals into school depth intervals changed in pro- 
portion to school size. 
Three individual least-squares regression models were 
used to predict school size. The relationship between the 
number of individuals in the surface interval (Ny, inde- 
pendent variable) and the number of individuals in the re- 
mainder of the school (N s \ dependent variable) was first 
explored using simple least-squares regression (Sokal and 
Rohlf, 1995). The distribution of N s given N t was het- 
eroscedastic necessitating the use of a weighted least- 
squares regression model by using a weight of 1/variance 
(Kleinbaum et ah, 1988). A similar-weighted multiple-lin- 
ear-regression relationship between N v N 2 (independent 
variables), and N s (dependent variable) was developed be- 
cause fish below the immediate surface of the school are 
sometimes seen and counted in photographs. 
