FISHERY BULLETIN: VOL. 70, NO. 2 



total diatom population, and 16 additional spe- 

 cies were recorded. Subsequent samples from 

 this region indicated that the major diatom pop- 

 ulation was below the depth range of the sam- 

 pling study. 



METHODS 



At each location a line of stations was posi- 

 tioned with respect to a 10-m drogue. In the 

 Subarctic Pacific, 10 stations were sampled; in 

 the Central Pacific, 11. The stations were spaced 

 at randomly ordered intervals of 0.5, 1.0, and 

 2.0 nautical miles, covering a total distance of 

 10.5 miles. At each station samples were col- 

 lected from depths of 10, 35, and 50 m (wire out) . 



Samples were collected with 3-liter Van Dorn 

 water samplers. The organisms in samples of 

 400 ml were preserved with 10 ml of 10% basic 

 Formalin. Aliquots of 50 or 100 ml were settled 

 for 24 hr and the diatoms identified and enu- 

 merated under the inverted microscope accord- 

 ing to the sedimentation procedure of Utermohl 

 (1931). The species used for the analysis of 

 distributions were those for which experience 

 has shown the problems of identification and 

 enumeration are negligible. In the case of 

 chain-forming species, the statistical analyses 

 were based upon the numbers of chains per 

 aliquot. 



STATISTICAL PROCEDURES 



The variance of the cell counts includes the 

 variability introduced into the data during the 

 preparation and enumeration of the subsample, 

 as well as any spatial heterogeneity. If these 

 are independent, the sums of squares will be 

 additive: 



oototal =^ OOsuhsaniple + OOspatial 



and the total observed variance is given by: 



s^otai = SStotai /degrees of freedom. 



In a brief preliminary study it was demon- 

 strated that, for all species but one, the varia- 

 bility introduced into the data at either the initial 

 or final subsampling stage was no greater than 



random (Poisson) expectation and may be ap- 

 proximated by the mean count. This agrees 

 with the results of other workers (Holmes and 

 Widrig, 1956; Lund, Kipling, and Le Cren, 

 1958). The single exception was Nitzschia 

 turgiduloides, foj which the total introduced var- 

 iability was SbX. 



It has been shown (Venrick, 1971) that the 

 expected total variance of a series of counts 

 from a randomly distributed population is given 

 by: 



cr^ = 



\ (Wal— 1) (Wss) (Upop) (1— 77) ^al 



+ [(Wss— l)(npop)(l— -^) 



X (fal+ ^^al)] 



+ (Wpop-l)[Za, + ^Xa, 



+ 



n. 



f 



'^jf- ^al] f /[Wal) (Wss) (Wpop) — 1] 



where na\, Wss, and Wpop are the numbers of 

 aliquots per subsample, the numbers of sub- 

 samples per sample, and the number of samples 

 collected from each depth; /i is the ratio of 

 sample volume to subsample volume, fi is the 

 ratio_of subsample volume to aliquot volume; 

 and Xa\ is the mean number of cells (or chains) 

 per aliquot. Substituting t?ai = 1, Wss — 1, and 



, 3000 __ ,, . . ,.. ^ 



/i = "400" ~ ' expression simplifies to: 



r2 = X^i + J^ Zal + -73-yr- Xal 



where /2 = 8.0 for 50 ml aliquots and 4.0 for 

 100 ml aliquots. For N. turgiduloides, the ap- 

 propriate expected variance is: 



a^ = 35Xai + n f- J Xni. 



At each depth, the observed variance, s^, may 

 be compared with the expected variance, ar^, and 

 the probability of departure from random ex- 

 pectation determined by means of the ratio 



364 



