Yst = 1 A where: Ah V(Ystl = 1 . 1(2 area <strong>of</strong> the hth A the total area str<strong>at</strong>um yh sample mean c<strong>at</strong>ch per tow str<strong>at</strong>um Nh in the hth number <strong>of</strong> tows in the h th str<strong>at</strong>um 2 Sh = sample variance in the hth str<strong>at</strong>um. The minimum trawlable biomass B is calcul<strong>at</strong>ed by summing the biomass values obtained in each individual str<strong>at</strong>um by the swept-area method: B L Bh = L lh.:..!\11h h b where: Bh minimum trawlable biomass in the hth str<strong>at</strong>um b = mean area swept per tow The variance VB <strong>of</strong> this estim<strong>at</strong>e is given by: 2 2 Afl. sh VB = L h b2.Nh The precision <strong>of</strong> the abundance indices (Ystl can be tested by deriving the coefficients <strong>of</strong> vari<strong>at</strong>ion C.V. <strong>of</strong> the weight and number means (r<strong>at</strong>io <strong>of</strong> standard devi<strong>at</strong>ion to the mean). For each species, a particular group <strong>of</strong> str<strong>at</strong>a corresponding to its distribution area has been selected and is used for the calcul<strong>at</strong>ion <strong>of</strong> abundance indices. SOME RESULTS: A DISCUSSION The analysis <strong>of</strong> our results, in spite <strong>of</strong> the lack <strong>of</strong> long series, indic<strong>at</strong>es th<strong>at</strong> the str<strong>at</strong>um variance increases faster than the mean. It appears also th<strong>at</strong> the standard devi<strong>at</strong>ion <strong>of</strong> the c<strong>at</strong>ch per tow is proportional to the mean for the main commercial species (Fig. ?a, ?b, ?c). As mentioned by Taylor (1g53), this is due to the fact th<strong>at</strong> fish are not randomly distributed on the grounds but tend to congreg<strong>at</strong>e in schools. However, the fitting is not good for all species and, for instance, in the case <strong>of</strong> redfish (Fig. ?c), the sc<strong>at</strong>tering <strong>of</strong> the plots indic<strong>at</strong>es important fluctu<strong>at</strong>ions in the C.V. <strong>of</strong> the mean weights calcul<strong>at</strong>ed for each str<strong>at</strong>um. The results also indic<strong>at</strong>e th<strong>at</strong>, on an arithmetic scale, the C.V. <strong>of</strong> the str<strong>at</strong>ified mean for all main commercial species range from 0.11 to o.g6, with an average value around 0.30. The maximum value (0.96) is observed for cod during the autumn <strong>of</strong> 1978 (cruise 782) and is due to one exceptionally large c<strong>at</strong>ch. The values <strong>of</strong> C.V. <strong>of</strong> the str<strong>at</strong>ified mean vary from one species to another. For the most common commercial species (sk<strong>at</strong>es, cod, fl<strong>at</strong>fish ... )the values are distributed around 0.20 but for others (haddock, hake ... )they are higher (0.59 and 0.49 respectively). On a logarithmic scale, the C.V. <strong>of</strong> the str<strong>at</strong>ified mean range from 0.07 to 0.10 for the main commercial species. For a number <strong>of</strong> reasons, these calcul<strong>at</strong>ions provide only an approxim<strong>at</strong>ion <strong>of</strong> the popul<strong>at</strong>ion size. While some factors can be controlled and results be corrected (for instance, selectivity <strong>of</strong> gear), most factors remain uncontrolled, or difficult to control. For instance, the swept-area is assumed to be constant and equal to 0.015 square nautical mile (trawled distance: 2 nautical miles, distance from wing to wing: 13.50 m). But the trawling speed has an effect on the horizontal opening <strong>of</strong> the trawl and it is known th<strong>at</strong> the two parameters vary in the same way, introducing large vari<strong>at</strong>ions in the swept-area. In the same way, physical factors (depth-wire length rel<strong>at</strong>ionship, type <strong>of</strong> bottom, current strength and direction in rel<strong>at</strong>ion to towing direction ... ) may influence the behaviour <strong>of</strong> the gear. Furthermore, due to the herding effect <strong>of</strong> the sweepline and <strong>of</strong> the trawl boards, the actual swept area is probably wider than the distance from wing to wing. The variability in the c<strong>at</strong>chability coefficient (q) is another important cause <strong>of</strong> vari<strong>at</strong>ion in the results. For our biomass calcul<strong>at</strong>ions the value <strong>of</strong> q is assumed to be equal to 1.0, and these comput<strong>at</strong>ions provide the lowest limit <strong>of</strong> the trawlable biomass. For the same trawl, the value <strong>of</strong> q varies from one species to another due to differences in distribution p<strong>at</strong>terns, behaviour towards the trawl and escapement. For instance, echo-sounding records show th<strong>at</strong> large segments <strong>of</strong> some popul<strong>at</strong>ions (redfish, cod, ... )may be unavailable to the trawl because <strong>of</strong> their distribution above the headline. The vari<strong>at</strong>ions in trawling speed which also induce vari<strong>at</strong>ions in the vertical opening, may also strongly influence the available proportion <strong>of</strong> the popul<strong>at</strong>ions. In some cases, seasonal vari<strong>at</strong>ions in the value <strong>of</strong> q are observed. So, during the autumn season, the abundance <strong>of</strong> prey (mostly sand launce) and the presence <strong>of</strong> a strong thermal gradient induce cod concentr<strong>at</strong>ions near the bottom and thus a larger availability to the trawl. All these vari<strong>at</strong>ions in the value <strong>of</strong> q may serve to explain'the gre<strong>at</strong>er tow-to-tow variability observed for some species having a 77
78 200 150 100 50 • • • • • • • • • • 50 • 100 150 Fig.7a_ Str<strong>at</strong>um mean (Yh kgj30mnl versus standard dcvJ<strong>at</strong>Jon(Sh) for haddock in subdivision 3Ps •
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