COI.EBROOK: FLUCTUATIONS IN BIOMASS OF ZOOPLANKTON 



TABLE 2. — The numbers of samples collected during each of the January (Jn), April ( Ap), July (Jl), and October (Oc) CalCOFI cruises 

 for the years 1955-59 in each of the standard zones (see Figure 1). Annual totals are given in boldface and the grand total is printed in 

 italic. 



has been employed. By this transformation, 

 means corresponding to greater than about 0.2 

 g/1,000 m 3 are virtually on a logarithmic scale 

 while lower means show a progressive transition 

 to an arithmetic scale. 



Quarterly means were calculated by averaging 

 the data for the stations in each zone and then 

 these were averaged to give annual values. For 

 those occasions when less than five stations were 

 occupied in any zone, the station data were 

 ignored and a quarterly mean was interpolated by 

 the following method: 



1. For each taxonomic category the set of overall 

 zone means (the sum of all the observations 

 for all the cruises in each zone divided by the 

 total number of stations occupied in the zone) 

 was calculated. The set of overall quarterly 

 means (the sum of all the observations for all 

 the cruises in each quarter divided by the 

 number of stations in each quarter) was 

 calculated. 



2. For each missing value the sum of the 

 remaining means for the other zones for the 

 cruise and the sum of the corresponding 

 overall zone means were calculated. The 

 latter was weighted by the ratio of the 

 relevant overall quarterly mean to the grand 

 mean and the missing value then calculated 

 as the product of the remaining zone means 

 for the cruise and the weighted sum of the 

 overall zone means. 



From these quarterly means, annual means 



were calculated for each taxon for each of a set of 

 regularly sampled zones (those marked with an 

 asterisk in Figure 1); and principal components 

 analysis was used to extract from these data the 

 main patterns of year-to-year change in biomass. 

 This is a technique of multivariate analysis (see, 

 e.g., Kendall 1957) which generates a sequence of 

 variables known as components with, in this case, 

 values for each year, which are the weighted sums 

 of the standardized data variables, in this case 

 sets of annual means of the taxonomic categories. 

 The sets of weighting factors, with values for each 

 taxonomic category, are the successive latent 

 vectors of the correlation matrix derived from the 

 original data, in this case the table of correlations 

 between the annual variations in abundance of all 

 possible pairs of taxonomic categories. The first 

 latent vector generates a component which has 

 the largest possible variance. The second vector 

 generates a component which has the largest 

 possible variance in relation to the residual 

 following the removal of the variability associated 

 with the first component, and so on. If the original 

 data are coherent to any extent, it is normal for 

 the first few components to account for a large 

 proportion of the variability of the original data 

 array. 



GEOGRAPHICAL DISTRIBUTIONS 



To provide some geographical background to 

 the study of year-to-year changes in biomass, 

 charts of the overall mean for each taxon in each 

 standard zone were prepared. In order to search 



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