FISHERY BULLETIN: VOL. 73, NO. 4 



frequently took 2 wk or longer owing to the large 

 volumes of plankton collected. Dried samples were 

 pulverized and an aliquot(s) of the powder used to 

 determined carbon in either a Perkin-Elmer No. 240 

 or a Hewlett Packard No. 185 B carbon, hydrogen, 

 nitrogen analyzer. A number of exceptions to this 

 procedure are evident in Table 1. In some cases, 

 wet weight was not measured; in others, carbon 

 was not determined. 



All data presented below were standardized to 

 biomass per cubic meter and then logarithmically 

 transformed (base 10) before use in the regression 

 analyses. 



RESULTS 



Several regression lines can be used to express 

 the relationship between pairs of variables (Ricker 

 1973). The appropriate one is determined by the 

 frequency distribution of the parent population as 

 well as the nature of the error sources in the 

 measurements (natural or measurement error). 

 Since the biomass measures are all subject to na- 

 tural variability and measurement error and since 

 the observations presented cannot be assumed to 

 be a random sample from a bivariate normal 

 population, the "geometric mean (GM) estimate of 

 the functional regression of Y on X" (Ricker 

 1973:412) is appropriate. As Ricker points out, this 

 regression line minimizes the sum of the products 

 of the vertical and horizontal distance of each 

 point from the line. Thus, the GM regression lines 

 of F on X and XonY are identical. Given the GM 

 regression equation: 



where Y' = log (Y) and X' = log {X), one can 

 determine both an X given Y or Y given X. 

 Although Ricker's (1973) paper should be consulted 

 for an in depth discussion of the assumptions and 

 computations, we note that the slope, v, is given 

 by: 



V = 



r V 2 



nij'-Y)'' 



^{x'.-xy 



(4) 



where b is the slope of the predictive regression of 

 Y' on X' and r is the correlation coefficient. The 

 Y'-axis intercept, u, is easily determined by: 



= Y'- vX'. 



(5) 



Y' = u + vX', 



(3) 



Plots of the values used in the GM regressions 

 are given in Figures 3-5. The equations are listed 

 in Table 2. All equations have slopes significantly 

 different from zero (P<0.001). As indicated above, 

 in the case where ^of Equation (1) {v of Equation 

 (3)) is equal to 1.0, one biomass measure is a 

 straight percentage of another. The only regres- 

 sions with a V approaching 1.0 compare dry weight 

 to carbon and displacement volume to wet weight. 

 In these cases, predicted carbon varies from 31 to 

 33% of zooplankton dry weight and predicted wet 

 weight varies from 72 to 73% of displacement 

 volume. In all other regressions, a variable bias is 

 present which causes v to deviate from 1.0. We 

 believe that a large portion of the bias is caused by 

 the interstitial water present in displacement 

 volumes and wet weights. This bias is inversely 

 proportional to the sample size; i.e., a small sample 



Table 2.— Functional (geometric mean) regression equations for pairs of biomass measures. 

 Carbon: C; dry weight: DW; wet weight: WW; displacement volume: DV; Be et al. (1971) and Be 

 (footnote 5) wet weight: BWW; Be et al. (1971) and Be (footnote 5) displacement volume: BDV; 

 Be et al. (1971) and Be (footnote 5) dry weight: BDW; Piatt et al. (1969) dry weight: PDW; Piatt 

 et al. (1969) carbon: PC. Logarithms to the base 10. 



'Note that biomass data used to determine equations 1-10 were standardized to per cubic 

 meter while the data used to dete>mine equations 11-13 were not standardized. 



780 



