Analytical correction for 

 oversampled Atlantic mackerel 

 Scomber scombrus eggs collected 

 with oblique plankton tows 



Denis D'Amours 

 Francois Gregoire 



Division de la Recherche sur les Peches 



Minist^re des Peches et des Oceans, Institut Maurice-Lamontagne 



C.P. 1000, Mont-Joli, Quebec G5H 3Z4, Canada 



Atlantic mackerel Scomber scom- 

 brtLS is a pelagic species spawning 

 on both sides of the North Atlantic 

 ocean. In the east, mackerel spawn 

 off the British Isles and in the North 

 Sea (as reviewed by Lockwood 1988 

 and Daan et al. 1990). In the west, 

 mackerel spawn in the Middle At- 

 lantic Bight (Berrien 1978) and in 

 the Gulf of St. Lawrence (Ware 

 1977). Atlantic mackerel is a mod- 

 erately prolific species (Bigelow 

 and Schroeder 1953); its fecundity 

 has been estimated at 255,000 eggs 

 for a medium-size female (30 cm 

 FL) in the northeast Atlantic (Lock- 

 wood et al. 1981), and at 243,000 

 eggs for a similar-size female in 

 the Middle Atlantic Bight (Morse 

 1980). 



Mackerel eggs are concentrated 

 near the surface when the water 

 column is thermally stratified dur- 

 ing spawning (Coombs et al. 1983, 

 Ware and Lambert 1985). Sette's 

 (1943) data from the Middle Atlan- 

 tic Bight indicated that 80% of 

 mackerel eggs were in the top 10 m. 

 In the North Sea, Coombs et al. 

 (1981) reported that 91% of mack- 

 erel eggs were above 26 m, and that 

 more than 85% were between and 

 16 m. In the Gulf of St. Lawrence, 

 deLafontaine and Gascon (1989) in- 

 dicated that 89% of mackerel eggs 

 were within 15 m of the surface. The 



Manuscript accepted 9 December 1991. 

 Fishery Bulletin, U.S. 90:190-196 (1992). 



distribution of mackerel eggs is thus 

 characteristically non-homogeneous 

 in the vertical plane. 



In the Gulf of St. Lawrence and 

 Middle Atlantic Bight, mackerel 

 eggs are routinely surveyed for 

 stock assessment purposes (e.g., 

 Castonguay and Gregoire 1989, Ber- 

 rien 1990). Surveys are carried out 

 with oblique plankton tows, with 

 bongo nets as described by Posgay 

 and Marak (1980). However, accu- 

 racy of oblique plankton tows is 

 known to be sensitive to nonhomog- 

 eneous vertical distribution of the 

 sampled organisms (Smith and Rich- 

 ardson 1977). Ideally, there should 

 be no hesitation at the surface when 

 retrieving the net, as it would lead 

 to a severe oversampling of the sur- 

 face layer where the eggs are con- 

 centrated (Posgay and Marak 1980, 

 Smith et al. 1985). In practice, it is 

 difficult not to drag the plankton 

 net at the surface for at least a few 

 seconds; when the net is retrieved, 

 it reaches the surface several meters 

 behind the block, and is dragged at 

 the surface until directly under the 

 block, where it can be lifted out. 

 During such dragging at the sur- 

 face, the mouth of the net is typical- 

 ly nearly all submerged and samples 

 the surface layer. It is usually as- 

 sumed that such oversampling at 

 the surface leads to a negligible bias 

 in estimates of abundance. 



In this paper, the bias caused by 

 an oversampling of surface water 



on the calculated abundance of 

 mackerel eggs is analyzed. An ana- 

 lytical correction for this bias is de- 

 rived and applied to empirical data 

 from a mackerel egg survey held in 

 the Gulf of St. Lawrence in 1990 to 

 reevaluate the annual production of 

 eggs. Also, some potential effects 

 of oversampling surface water are 

 evaluated when computing total 

 abundance and mortality rates of 

 near surface organisms. 



Bias in computed egg 

 abundance caused by 

 oversampled surface 

 water 



Distribution 



of macl<erel eggs 



Concentrations of mackerel eggs 

 are highest near the surface and 

 decrease rapidly with depth. Sund- 

 by (1983) reported that under as- 

 sumptions applicable in the present 

 study, a negative exponential model 

 (as Eq. 1, below) was appropriate to 

 describe the vertical distribution of 

 mackerel eggs. Ware and Lambert 

 (1985) also concluded that the ver- 

 tical distribution of mackerel eggs 

 was best described by a negative ex- 

 ponential model. Data on the ver- 

 tical distribution of mackerel eggs 

 presented by Sette (1943) and by 

 deLafontaine and Gascon (1989) 

 were fitted to negative exponential 

 models; in both cases, over 90% of 

 the variance in the egg distribution 

 was explained. Therefore, a nega- 

 tive exponential model is appropri- 

 ate to describe the distribution of 

 mackerel eggs in the vertical plane. 



Sampiing macl<erei eggs 



Let the abundance of a population 

 of eggs in a body of water decrease 

 from the surface following an ex- 

 ponential model: 



dN(z) 

 dz 



= - kN(z) 



(1) 



190 



