FISHERY BULLETIN: VOL. 82, NO. 1 



routine was BMDP program P3R, nonlinear regres- 

 sion (Dixon and Brown 1979). The function with the 

 smallest residual mean square was selected to repre- 

 sent the relation between camera range and horizon- 

 tal visibility, and was employed in estimating camera 

 range at a depth on a sampling date. 



Data Analysis 



We reduced data into two general forms: densities 

 (number or biomass per unit volume) in different 

 strata, and abundances integrated throughout the 

 entire water column. The first was used to examine the 

 vertical distribution of individual species or of the 

 entire assemblage and to compare the relative abun- 

 dances of species in a stratum. The second was used 

 to estimate the overall abundance of the assemblage 

 and to compare the overall abundances of different 

 species. In both cases, the final point and interval 

 estimates were based on the means and variances, 

 over dates, of daily means. 



The daily estimate of density (per 1 ,000 m 3 ) for each 

 species in a depth stratum was estimated as the mean 

 number or biomass per transect on that day, times 

 the ratio (1,000/transect volume), where transect 

 volume was estimated as above. Biomass of a species 

 on a given transect was estimated by counts of 

 individuals in different maturity classes, converted 

 to wet weights by the key in Table 1. 



Our estimate of a species' density in a depth 

 stratum was calculated as the mean of the daily den- 

 sity estimates in that stratum. Similar estimates were 

 made for the sum of all "resident" teleosts. Excluded 

 from the analysis of total fish density and abundance 

 were elasmobranchs and certain teleosts (silver- 

 sides, jack mackerel, Pacific barracuda, black 

 croaker, and salema) that were rare at SOK, are 

 seasonal visitors to kelp beds, or are not primarily 

 associated with rock reefs and kelp forests (Feder et 

 al. 1974). Species such as white seaperch and barred 

 sand bass often occur in other habitats, but were 

 included in our analysis because they may have at 

 least a marginal association with kelp-rock habitats 

 and were frequently encountered and abundant in 

 our samples. 



By weighting the average density of a species (or the 

 assemblage) in a stratum by the volume of water rep- 

 resented by samples in that stratum, we were able to 

 obtain estimates of abundance integrated from sur- 

 face to bottom (Snedecor and Cochran 1980:444). 

 The sampling day was an integral component of our 

 analysis, but only the above-bottom strata were 

 sampled on the same day at a given site. To obtain 

 accurate estimates of variance for integrated abun- 



dances, then, we assembled our integrated estimates 

 in two stages. We first estimated stratified mean den- 

 sity for the above-bottom strata on each day and 

 averaged these values over days. We also computed 

 mean density (over days) in the bottom stratum. 

 Secondly, we computed stratified mean density (and 

 its standard error) for the above-bottom and bottom 

 strata, using the means and variances calculated 

 above. The stratified mean density estimates for the 

 entire water column were then scaled to represent 

 abundances over 100 m 2 of bottom. 



Samples in each stratum were assumed to represent 

 a range of depths extending to the midpoints be- 

 tween strata, with the 3 m stratum also extending to 

 the surface (Table 2). Weighting factors for the strata 

 were determined from the relative extents of the 

 depth ranges represented. Among the above-bottom 

 strata, relative weighting factors were the vertical 

 ranges of these strata divided by 13. 5 m. For the bot- 

 tom versus above-bottom strata the depth ranges 

 were divided by 15 m. 



Daily estimates of stratified mean density in the 

 above-bottom strata were calculated as 



D m = 2 W h D h , 



where D m was the estimate of stratified mean density 

 in the 3 m, 7.6 m, and 12 m strata; W,„ the weighting 

 factor; and D h , the mean density on that day in 

 stratum h (Snedecor and Cochran 1980). The mean 

 (D wc ) and variance (S 2 U J of these daily estimates were 

 then computed. The mean {D b ) and variance (S 2 6 ) of 

 estimated daily densities on the bottom were also 

 calculated. 



Stratified mean abundance throughout the entire 

 water column was estimated as 



A 



.-( 



1,500 

 1,000 



XW h D 



n 



/!> 



where A st was the stratified mean estimate of 

 integrated abundance over 100 m 2 of bottom, W h was 

 the weighting factor, and D h was the mean density in 

 either the above-bottom strata {D wc ) or in the bottom 

 stratum (D h ). The term in the summation is the 

 estimate of stratified mean density (per 1,000 m 3 ) 

 over all strata, and the ratio (1,500/1,000) converts 

 this value to abundance over 100 m 2 of bottom. 

 The standard error of A st was calculated as 



 4 " v v 1,000 ' h h '' h 



where S 2 h was the variance of daily density estimates 

 in either the above-bottom (S 2 ,,,.) or bottom (S 2 b ) 



42 



