

VARIABILITY IN TRAWL CATCHES 



151 



variance 7 were calculated for each classification. 

 The data for depth zones are presented in tables 

 15a and 15b. Direct comparisons of pairs of 

 values of the indices were made considering dif- 

 ferences greater than twice the standard error of 

 their difference to be significant. Since many 

 comparisons are possible, one must remember that 

 about 1 in 20 of such comparisons may be signifi- 

 cant at the 5-percent level. 



None of witbin-year and between-year compar- 

 isons of indices of diversity by depth zones were 

 significant, so that one may conclude that in 

 "richness of species" the depth zones do not differ 

 significantly either within or between years. This 

 does not mean that the species composition does 

 not vary with depth zone but rather that the 

 relation of the variety of species to the total 

 number of fish in each depth zone and in each 

 year is about the same. 



A measure of the differences in species composi- 

 tion which exist among depth zones may be ob- 

 tained by combining data for the various depth 

 zones under consideration. If no differences exist, 

 the resulting index will be about the same as those 

 for the depth zones from which the combined 

 sample was taken. If the depth zones differ com- 

 pletely in species composition, the resulting index 

 will be the sum of the individual indices. The 

 depth-zone data combined in this way show in- 

 creases in the indices of diversity, but they are 

 rather small (table 14). It is evident that there 

 must be many species common to all depth zones 

 with fewer species restricted to one alone. This 

 is borne out by the observed depth distribution of 

 the various species. 8 



Bottom samples were attempted at each station 

 where trawls were made. These data were com- 

 pared with and supplemented by data from Coast 

 and Geodetic charts and classified into four general 

 types: sand, mud, mud and sand, and stony. 

 Indices of diversity were calculated for each bot- 

 tom type in each depth zone for each year and 

 also for the three years combined. The indices 

 were compared in the usual way, the difference 

 being divided by the standard error of the 

 difference. 



Only one difference significant at the 5-percent 



' See appendix C for tbe formula used in calculating the variance. 



' The statistical significance of the increase in the index through combining 

 cannot be determined by comparing the difference with the standard error 

 of the difference, since the variates compared are no longer independent. 

 254646—53 2 



level was found. Since 30 comparisons were 

 made, we may expect at least one significant 

 d-fference to appear by chance. These tests do 

 not, then, reveal any evidence of significant dif- 

 ferences in the diversity of species either between 

 bottom types within depth zones, or between 

 depth zones within bottom types. 9 



DISTRIBUTION OF SPECIES PER TOW 



In the logarithmic series, the distribution of the 

 number of species, S, is Poisson (Anscombe 1950). 

 We may, therefore, further examine the trawl 

 data to find whether the observed distribution of 

 species per tow conforms with theory. 



In table 15 the number of species per tow and 

 the number of tows are presented for the years 

 1948-51. The data for all tows in the Georges 

 Bank area are tabulated in column A. In col- 

 umn B, the first three tows of each cruise and the 

 first three tows following a change from the port 

 to starboard trawl net, or vice versa, have been 

 eliminated. 



Data for 1949a and 1950a may be fitted with 

 Poisson distributions with probabilities somewhat 

 greater than 0.10 and 0.80, respectively. The 

 data 1948a and 1951a are fitted with probabilities 

 so low that the hypothesis of a Poisson distribution 

 must be rejected. 



Data for 1949b, 1950b, and 1951b are fitted 

 with Poisson distributions with probabilities 

 greater than 0.30, 0.80, and 0.30, respectively. 

 Data for 1948b does not give a satisfactory fit. 

 The observed and expected values are presented 

 in table 16, together with 2x 2 (n—2 degrees of 

 freedom) . 



There is no reason to reject the hypothesis that 

 the distribution of number of species per tow is 

 Poisson. It is apparent from table 16 that fac- 

 tors are operating in the sampling procedure which 

 tend to result in tows with a small observed num- 

 ber of species. The greatest number of these 

 tows occur in 1948 and 1951; 1948 was the first 

 year of the census sampling. In 1951 a different 

 vessel, the Delaware, was used. One is inclined, 

 then, to suspect that factors affecting the efficiency 

 of operation of the trawl net are the cause of a 



• Preliminary analyses of variance of the transformed catch-per-tow data 

 Indicate consistent significant differences in the distribution of particular 

 species by bottom type. The distribution of species by bottom type may 

 be studied by analysis of variance or by x '-contingency tables, after a 

 square-root transformation of the number of species per tow. 



