NOTE D'Amours and Gr^goire: Analytical correction for oversampled Scomber scombrus eggs 



193 



-100 -■ 



200 



400 



600 



800 



TOW DURATION (s) 



Figure 2 



Residuals of a linear regression of volume filtered against tow 

 duration of oblique plankton tows, from a mackerel egg survey 

 held in the Gulf of St. Lawrence in 1990. 



parture from linearity; somewhat unexpectedly, a 

 tendency towards an increasing departure from linear- 

 ity could be detected (Fig. 2). Therefore, it can be con- 

 cluded that no surface undersampling occurred as a 

 result of diminishing filtration efficiency. The apparent 

 increasing departure from linearity can be explained 

 by the fact that long tows (e.g., duration of 10 minutes) 

 are deeper, i.e., well below the stratum where mackerel 

 eggs are abundant. During short tows (e.g., duration 

 of 6 minutes), the net is towed mainly in the stratum 

 were eggs are present, and the filtration efficiency is 

 less, though stationary, than in water devoid of eggs. 

 During long, deep tows, more time is spent below the 

 stratum containing mackerel eggs, and proportionally 

 more free-flowing water is filtered there. 



Correction of survey data 



In Eq. 11, a rate constant k must be introduced to 

 describe the distribution of the sampled organisms in 

 the vertical plane. For the purpose of the demonstra- 

 tion, a rate constant k = 0.1 5/m was selected as repre- 

 sentative of all mackerel egg stages at all stations; as 

 discussed below, this rate constant is a representative 

 value extracted from the literature on mackerel egg 

 distribution. During the mackerel egg survey carried 

 out in the Gulf of St. Lawrence in late-June and early- 

 July 1990, the total duration of each oblique tow was 

 measured, as well as the duration of the period during 

 which the Bongo net was dragged at the surface before 

 recovey (F. Gregoire, unpubl. data). The period of drag 

 at the surface started when the net was visually spotted 

 at the surface and ended when the net was lifted out 

 of the water. From those measurements, values of L 



and Ld were calculated in percent of total tow time. 

 With a rate constant k = 0.15/m, a net radius a = 0.305 

 m, a centered depth a = 0.305 m along Lq, and a mea- 

 sured maximum depth D, a value of the degree of bias 

 B was calculated for each tow as per Eq. 11. The cor- 

 rected abundance of eggs was obtained by multiplying 

 the computed biased abundance by [100%/B]. Using un- 

 corrected and corrected abundances of eggs at each sta- 

 tion, two total annual productions of mackerel eggs 

 were computed for the Gulf of St. Lawrence in 1990 

 following the procedures of Ouellet (1987). The totals 

 were 6.77 xlO^"* eggs with uncorrected abundance, 

 and 5.63 xlO^^ eggs with corrected abundance. The 

 difference of 1.14 x 10^^ eggs, with a mean fecundity 

 of 300,000 eggs and a sex ratio of 1:1, amounted to 

 7.6x10* mature mackerel. 



The parameter D used in the above calculations was 

 measured accurately with a bathymeter mounted on 

 the plankton net. If triangulation had been used, where 

 D is estimated by the amount of wire paid out and the 

 angle subtended at the block, another source of bias 

 would have been introduced owing to the approx- 

 imative nature of the method. Assume a population of 

 mackerel eggs in a body of water where k = 0.15 and 

 No = 750; if sampled to a depth D of 50 m with a net 

 of radius a = 0.305 on a transect where L = 1000 m, a 

 total of 100,000 eggs will be collected (Eq. 7). Standar- 

 dization of this result by the ratio of D to L shows that 

 the abundance of eggs is 5000 eggs/m-. Had D been 

 underestimated by 10% at 45 m, the abundance of eggs 

 would have been underestimated also by 10% at 4500 

 eggs/m-. If the same tow is repeated, but with Ld = 

 75m and a = 0.305m, a total of 153,775 eggs will be col- 

 lected. Standardization of this result vdth D correctly 

 evaluated at 50 m indicates an abundance of 7152 

 eggs/m^; with D underestimated by 10% at 45 m, stan- 

 dardization indicates an abundance of 6437 eggs/m^. 

 These examples show how an underestimation of 10% 

 of D results in an abundance of eggs equal to 90% of 

 the real value, and how a 7% (75m/1075m) oversam- 

 pling at the surface results in an abundance of eggs 

 equal to 143% of real value. Also, they show that when 

 both an underestimation of D and an oversampling of 

 the surface layer occur during a tow, the effects of both 

 biases on the estimate of abundance are opposite, but 

 not symmetrical, with the effect of the oversampling 

 at the surface much more important than that from the 

 underestimation in D. 



A degree of bias (B in Eq. 11) was computed for 

 various combinations of L^ (with L = 100%-Ld) and 

 rate constant k, with a = a = 0.305 m, and D = 50 m (Fig. 

 3A). The degree of bias caused by an oversampling of 

 surface water is a function of the time of sampling at 

 the surface, and of the degree of contagion of the eggs 

 near the surface, as described by the parameter k. For 



