Rooper: An ecological analysis of rockfish assemblages in the North Pacific Ocean 
5 
Figure 2 
Theoretical distribution of three species along an environmental gradient ( K ). In this 
study, K was depth, temperature, or distance. The value w is the standard deviation 
of the resource utilization curve for a single species and d is distance between the 
weighted means for two species along a resource continuum. Reproduced from May 
(1973). 
(depth, temperature, and position) was computed as 
Mean = 
where f t - the CPUE of each rockfish species group in 
tow i; and 
x t = the value of the environmental variable at 
tow i. 
The weighted standard deviation (SD) was then com- 
puted as 
X(/>,) 
It 
(I 
A?) 
\ 
M 
*mean 2 j 
i (i> 
i - 1 
These calculations yielded the niche dimensions for each 
species group defined along each of the three environ- 
mental gradients. 
The overlap of each species group across each envi- 
ronmental gradient (A) can then be calculated as 
A v = C,j exp 
where the normalization constant (CL) is calculated by 
C v = 
2W:W , 
1 J 
2 , 2 
Wj +Wj 
where d = the distance between means for a pair of 
species i and j; 
w t = the standard deviation (SD) for species i; 
and 
W: = the SD for species j (Murawski and Finn, 
1988). 
Overlap indices for each variable were calculated for 
each species and within each species, by the groupings 
of males, females, and juveniles. The overlaps between 
males and females were first examined and if the overlap 
index was greater than 0.9 across all three environmen- 
tal gradients, these males and females were combined 
and the means and SDs for each environmental gradi- 
ent were recalculated. The resulting groupings (adults 
and juveniles) were then compared and, again, where 
the indices exceeded 0.9, the catches for the entire spe- 
cies (all size and sex classes) were combined and the 
means and SDs for each environmental gradient were 
recalculated. 
Finally, the overlap indices were compared to de- 
termine the amount of separation among both species 
and the remaining groupings by size and sex. The 
multinomial intersection in the overlap indices across 
the three environmental gradients was calculated by 
multiplying the individual overlap coefficients together. 
This was used as a measure of the relative similarity 
in environmental preferences computed for each pair of 
species subgroups and resulted in a matrix of overlap 
coefficients for all species-group pairs. The matrix was 
then clustered into assemblages with similar distribu- 
tions across environmental gradients by using Primer 
Analysis software (PRIMER-E Ltd., Plymouth, UK). 
The combined overlap index was used as a measure of 
similarity and the average cluster linkage method was 
used to determine the species composition of rockfish 
