VENRICK: SMALL-SCALE DISTRIBUTIONS OF OCEANIC DIATOMS 



§2/0-2 r= xVdf. For 10 and 11 samples 

 xM0.05)/df values are 1.88 and 1.83 respec- 

 tively. Species for which the s-/a^ ratio exceeds 

 the xVdf value are considered to have aggre- 

 gated distributions. Ratios greater than 1.63 

 and 1.60 respectively were significant at the 

 0.10 level. 



With the small number of degrees of freedom 

 involved, the maximum variance attainable by 

 species with mean counts less than 0.2 is too 

 small to give an ^/a^ ratio significant at better 

 than the 0.10 level. For rarer species, a runs 

 test on presence and absence (Tate and Clelland, 

 1959) was used to give additional information 

 about distribution patterns. 



RESULTS 



The detection of aggregation in a population 

 is influenced by interaction between volume and 

 spacing of field samples and the scale of aggre- 

 gation of the population (Grieg-Smith, 1964), 

 and by the proportion of the initial sample which 

 is ultimately enumerated (Venrick, 1971). Thus, 

 the specific results of this study are strictly 

 pertinent only to this sampling design, and they 

 must be interpreted accordingly. 



The results of these studies are presented in 

 Tables 1 and 2. Within the Subarctic region, 

 8 of the 24 distributions were significantly ag- 

 gregated at the 0.05 level, and two additional 

 species at the 0.10 level. At every depth the 

 species with contagious distributions were the 

 most abundant ones, with the exception of N. 

 turgiduloides at 10 m. It is likely that spatial 

 variability of this species was obscured by the 

 large sampling error. Aggregations of the dom- 

 inant species would result if they had outgrown, 

 in situ, the other species. The fewest aggre- 

 gated distributions occurred at 10 m. This was 

 the only sampled depth within the mixed layer, 

 and presumably, wind-driven turbulence was 

 sufficient to keep all but the most rapidly di- 

 viding species distributed randomly. 



Within the Central Pacific, only 3 of the 20 

 distributions were significantly nonrandom, at 

 the 0.05 level. The runs test, significant at the 

 0.10 level, indicated that five additional species 

 were aggregated. In this region, aggregation 



did not appear to be related to the abundance 

 of the species. 



Concordance tests were used to investigate 

 the agreement of species with respect to fluc- 

 tuations of abundances between samples. At 

 Subarctic Station 23 there was significant con- 

 cordance (P < 0.05) between all species at each 

 of the three depths, indicating that species 

 tended to respond to, or be influenced by, their 

 environment in the same manner. In contrast, 

 there was no concordance between species at any 

 depth at Central Pacific Station 5. 



PRECISION OF SINGLE SAMPLES 

 ESTIMATES OF ABUNDANCE 



If the frequency distribution of organisms in 

 the field can be fitted to a theoretical distribu- 

 tion, confidence limits on single observations can 

 be derived from the variance of that distribu- 

 tion. Some workers (e.g., Winsor and Clarke, 

 1940; Barnes and Hasle, 1957) have success- 

 fully used logarithmic transformations to nor- 

 malize abundance data. This procedure was 

 successful for some of the diatom species under 

 consideration in this study. (Normality was 

 tested with normal-probability paper.) The 

 transformation, however, was not successful for 

 all species at all depths and thus a general use 

 of parametric statistics on log-transformed data 

 was not justifiable. 



The observed frequency distributions of the 

 aggregated species were satisfactorily predicted 

 by the negative binomial distribution (Ans- 

 combe, 1949). Values of k_ (estimated from the 

 expression k = X^/ (s^ — X) for the aggregated 

 species ranged from 0.15 to 13.30. The com- 

 parisons between the predicted and the observed 

 cumulative frequency distributions were made 

 with Kolmogorov-Smirnov tests (Tate and Clel- 

 land, 1959) ; none were significantly different 

 at the 0.10 level. There are available transfor- 

 mations which normalize negative binomial dis- 

 tributions (Anscombe, 1948). However, these 

 transformations depend upon knowledge of the 

 value of k and thus are applicable only to this 

 particular set of data and not to observations 

 of other species or observations from other en- 

 vironments. 



365 



