192 



Fishery Bulletin 90(1), 1992 



Evaluating Eq. 6 for kD»0, 



Nh = 



No Ll 

 k Di 



1 + 



(ka)2 



(7) 



Nt = 



No Ll 

 k D, 



1 + 



(ka)2 



+ Noe-k-'Lc 



1 + 



(ka)2 



(10) 



where L = Lj + L2, and is the total horizontal length 

 of the tow (Fig. 1 A). It can now be seen that when the 

 number of eggs collected in an oblique plankton tow 

 (Eq. 7) is multiplied by the ratio D/L, and when the pro- 

 duct ka is small, an approximation of Eq. 3 is obtained, 

 which is a measure of the local abundance of eggs in 

 number per surface area. The procedure of multiply- 

 ing the total number of eggs collected in the oblique 

 tow (equation 7) by the ratio of its maximum depth to 

 its total horizontal length (D/L), is equivalent to the 

 standardization procedure described by Smith and 

 Richardson (1977). To obtain estimates of abundance 

 in number per surface area, the standardization pro- 

 cedure consists of multiplying the number of eggs 

 collected by the ratio of the maximun depth attained 

 during the tow to the volume of water filtered. This 

 standardization procedure is valid if all depth strata are 

 sampled equally. 



Now assume the same population of eggs, but where 

 the net is dragged at the surface while being readied 

 for recovery at the end of the tow. The length of drag 

 at the surface is represented by Lq in Figure IB. 

 Along Lp, the mouth of the net is centered at depth 

 a, which is equal to its radius a; i.e., oversampling 

 occurs in the layer of water immediately below the 

 surface, as deeply as the diameter of the net. Over 

 Lo, the net will collect a number of eggs (Ng) equal to 



;o + a +\fa'-{z-a)'' 

 \ N(z)dydz, (8) 

 o-a -* - ya- - (z-a)- 



which is approximated by (as in D'Amours 1988) 



Ns = Noe-kaLD 



1 -H 



(ka)2 



(9) 



The total number of eggs (Nx) collected during an 

 oblique tow, where the net is dragged at the surface 

 at the end, will then be equal to the sum of Nh (Eq. 

 7) and Ng (Eq. 9): 



The component Ng will add to the number of eggs col- 

 lected, and its inclusion in the standardization pro- 

 cedure will result in a systematic overestimation of the 

 abundance of eggs per surface area. When Eq. 10 is 

 standardized with Ld included in the total length of 

 the tow (Lx in Fig. IB), and the result divided by the 

 true theoretical abundance of eggs (Eq. 3), an expres- 

 sion is obtained which is the ratio (B) of the biased abun- 

 dance to the true abundance of eggs: 



B = L -H D 



-ko 



1 -I- 



(ka)2 



(11) 



Removal of bias from computed 

 abundance of mackerel eggs 



Assumption of constant filtration efficiency 



In Eq. 11, L and Lq can be replaced by the proportion 

 of the total duration of the tow they represent, under 

 the assumption of constant filtration efficiency. This 

 assumption is required to use tow time as a measure 

 directly proportionnal to amount of water filtered, 

 so as to separate L and L^ in Eq. 11. However, as 

 pointed out by Smith and Richardson (1977), the filtra- 

 tion efficiency of a plankton tow declines typically with 

 the duration of the tow, as the accumulated plankton 

 reduces the porosity of the net. They warned that the 

 diminishing efficiency of a net could result in an under- 

 sampling of surface water. To verify whether such 

 undersampling of surface water occurred, which would 

 offset oversampling at the end of the tow, the time- 

 course of the efficiency of the plankton net must be 

 assessed. 



If filtration efficiency diminishes with time, the vol- 

 ume filtered per unit time will diminish with increas- 

 ing tow duration. The residuals about a straight line 

 fitted on the values of volume filtered against tow dura- 

 tion would then show a decreasing pattern of depar- 

 ture from linearity. The volumes filtered for the tows 

 in the Gulf of St. Lawrence in 1990 were regressed 

 against their respective total duration. The residuals 

 of this regression did not indicate a decreasing de- 



