BIOLOGY OF THE ATLANTIC MACKEREL 195 



For the larvae over 22 mm. long there is no evidence to determine whether or not 

 they were caught by the nets in their true proportions. On general grounds, one would 

 expect that they could elude the nets, though the taking of a specimen as long as 51 

 mm. shows that the gear could catch at least some large-sized larvae. Offsetting the 

 probability of undersampling the larger sizes, there is the opposite probabdity of over- 

 sampling them, because the stations were somewhat more closely spaced (see fig. 14) 

 in the area north and east of Nantucket Shoals, where they were found, than south 

 and west of the Shoals, where the smaller sizes were most abundant. Whether or 

 not the loss of large larvae by eluding the nets and the gain by possible oversamplins: 

 as the result of closer station spacing offset each other perfectly is indeterminable 

 from the available data. Hence, the mortality determination is of uncertain reliability 

 for sizes over 22 mm. For those smaller than 22 mm., the determination is reliable as 

 far as collecting methods are concerned. 



Having found little reason to suspect size-connected biases in collecting, excepting 

 possibly for sizes over 22 mm. long, two questions remain: were the hauls themselves 

 sufficiently quantitative to give reliable indices of abundance for each station; and 

 were the stations spaced properly to give a reliable summation of abundance for the 

 entire area? To answer the first question separately would require a study of the 

 variation in series of duplicate hauls, and is precluded for lack of material, but both 

 questions may be answered simultaneously by a study of the relative numbers caught 

 at the various stations in relation to the probable nature of distribution of numbers 

 of individuals in the sea. 



Inspection of charts of egg or larval distribution (fig. 13) suggests that the 

 pattern of concentration has a form closely related to a normal frequency surface. 

 Near the middle of the area in which eggs or larvae occur are one or several stations 

 with very high concentrations corresponding to the mode; surrounding these are 

 more stations with decidedly lower concentrations corresponding to the slopes; and 

 at the periphery are many stations with very low concentrations corresponding to 

 the "tads" of the normal frequency surface. Let us assume, for the moment, that 

 the concentrations of eggs really do form a normal frequency surface. Then the 

 number of a particular stage caught during a particular cruise is a reliable index of 

 the abundance of that stage at that time, provided that: the stations where the 

 catches were made were so located as to give proper relative representation of the 

 various parts of this normal frequency surface, such as the mode, slopes, and tails; 

 and that the catches also were sufficiently reliable to provide the true relative numbers 

 to be found at the various parts of this surface. Therefore, a test as to the conformity 

 of catches to the normal frequency surface would at once indicate whether the above 

 assumption is correct; whether the catch stations were arranged so as to sample 

 adequately the various parts of the distribution; and whether the hauls themselves 

 were quantitatively reliable. 



To translate the normal frequency distribution into a convenient form for making 

 the tests, table 8 has been prepared. 21 It was derived from the curve of the normal 

 frequency distribution where, for unit standard deviation and unit N 



y=0.3989e 2 



11 Buchanon-Wollaston (1935, p. 85) has given a table purporting to give the same statistics, but it appears to represent the 

 results of sampling only along a line passing through the mode, of a normal frequency surface, not the results of sampling over the 

 entire surface. For the latter, account must be taken of the fact that in such a surface, so sampled, the areas of classes of equal 

 range in ordinate height increase as the square of the distance from the mode. 

 525293—44 4 



