LESTKK KT Al..; I'AKASITKS OK SKUMACK Tl'NA 



from head length using the formula 7.8 + 2.75 x 

 (head length) for heads under 14.5 cm and - 1.7 + 

 3.3 X (head length) for larger heads (from measure- 

 ments of 80 and 83 fish, respectively). Prior to 

 dissection, fish were thawed overnight at 6°C. In 

 general, all viscera parasites were counted whereas 

 gill parasites were counted on one side only and the 

 numbers doubled in the final tables. A didymozoid 

 capsule was counted as one parasite though most 

 contained two individuals. Representative parasites 

 were fixed and stored in 10% Formalin"* except for 

 nematodes which were fixed and stored in 70% 

 alcohol. 



An additional set of data on the abundance of the 

 larval cestode Tentacularia coryphaenae was col- 

 lected at sea by SPC and NZ fisheries officers. They 

 recorded the number of Tentacularia visible through 

 the peritoneum in the wall of the body cavity of 1,529 

 fish. 



Besides some summary statistics, two types of 

 statistical analysis were done: 1) investigation into 

 the similarities and dissimilarities of the parasite 

 fauna between the various areas sampled, and 2) a 

 study of school integrity. 



The similarities and dissimilarities between areas 

 were examined using a series of cluster analyses and 

 multivariate canonical analyses (Mardia et al. 1979). 

 Strictly speaking, canonical analyses require data 

 which are normally distributed and which have a 

 common variance. However, the frequency distribu- 

 tions of the parasites were not normal. They showed 

 considerable differences from one parasite to 



^Reference to trade names does not imply endorsement by the Na- 

 tional Marine Fisheries Service. NOAA. 



another and most appeared to have two components: 

 one which could be adequately approximated by a 

 negative binomial distribution; and a second compo 

 nent consisting of a disproportionately large zero 

 category, presumably arising because some schools 

 had not been exposed to infection. Precise trans- 

 formations to normalize the data would thus have 

 been complex and of doubtful accuracy considering 

 the small size of the samples from each school. A 

 single transformation for all species was therefore 

 used: the natural logarithm of the number of 

 parasites plus 1.0. 



To avoid possible biases due to associations be- 

 tween parasite numbers and fish length, such as that 

 shown in Figure 2, the transformed counts were 

 then adjusted for fish length. This was done for each 

 species by regressing log (parasite number + 1.0) on 

 fish length, for all Pacific tropical fish (489), to esti- 

 mate the magnitude of any relationship. This was 

 used to adjust the transformed parasite numbers, ex- 

 cept where this was zero, to that expected for a fish 

 of a standard length of 50 cm. (This length was very 

 close to the overall mean length of the fish.) The 

 method could not be trusted to eliminate all effects of 

 length, so, as an added safeguard, only fish 39.5 to 

 57.5 cm were used in the multivariate analyses (83% 

 of the total). These are likely to have been 1 yr old 

 (Uchiyama and Struhsaker 1981; Wankowski 1981). 



In a few instances a parasite was absent from all 

 fish in one area. To allow matrix inversion in the 

 canonical variate analyses, a random number be- 

 tween -0.005 and -1-0.005 was added to the data. 

 This did not influence the outcome. The results of the 

 canonical variate analyses were displayed graphi- 

 cally as plots of the first versus the second canonical 



25- 



20 



15 



10 



5- 



30 



\ Total tropics (1017 fish) 

 k New Zealand (512 fish) 



AO 



50 60 



Fish length, cnn 



Figure 2. -Relationship between 

 number of T. coryphaenae and fish 

 lenjrth. Mean ±2 SE. Each mean from 

 minimum of 19 fish. In the tropics the 

 number increased with length but this 

 was not reflected in the New Zealand 

 samples. 



345 



