BARKLEY: SELECTIVITY OF TOWED-NET SAMPLERS 



net radius R' (identical with r in Figure 2), 

 Gilfillan arrived at the following equation: 



where present notation has been substituted for 

 the original and the equation slightly simplified. 

 Clearly Gilfillan's equation is an approximate 

 form of equation (6) for the case where Ue can 

 be neglected compared to U; which is to say, 

 for animals which move much slower than the 

 net. This approximation is good to within 5% 

 as long as Ue is less than 30% of U. 



It is not obvious that xqUb should in general 

 be a constant, even for a single component of 

 the plankton or nekton. Constancy of the prod- 

 uct XoUe implies that either (1) reaction distance 

 and escape speed individually are constant, (2) 

 animals deficient in one of these survival traits 

 can compensate for this by excelling in the other, 

 or (3) animals given an unusually long time to 

 react by faulty net design — such as a bridle or 

 other conspicuous obstruction some distance 

 ahead of the mouth— fail to take advantage of 

 this warning. The first alternative is perhaps 

 too much to expect; the second and third seem 

 unlikely. Nevertheless, Gilfillan obtained nearly 

 constant values for /f in a series of field trials 

 with different nets towed at various speeds, 

 where catches of Calanus spp., Euchaeta japon- 

 ica, and euphausiids were enumerated (Clutter 

 and Anraku, 1968). 



There is great practical value to knowing that 

 A" is a constant for any particular component of 

 a sample, because this constant fully specifies 

 the avoidance behavior of that component. If 

 K is constant, it is possible to calculate proba- 

 bilities of capture without making measurements 

 of either Xo or Ue, as long as U is known to exceed 

 Ue by a factor of three or more. 



Numerical values of K can be estimated, as 

 Gilfillan suggested, from tows made at two dif- 

 ferent speeds, Ui and U2, or by using two other- 

 wise similar nets with openings of radii Ri and 

 R2, while holding other factors constant: 



K 



m' 



where C1/C2 is the ratio of catches of individual 

 components in the samples taken under each of 

 the two different conditions. Equation (8) is 

 approximate; the exact form can be obtained 



V 



by substituting ■•/ U^n — u^e for C/„. 



RiUi 



R2U2 



m 



Vz 



(8) 



Holding "other factors" constant is obviously 

 a problem, since the same net towed at different 

 speeds, or different size nets towed at the same 

 speed, may have widely different noise levels, 

 mesh losses, hydrodynamic behavior, etc., which 

 would tend to invalidate the comparison. 



RESULTS 



Although definitive tests of the theory devel- 

 oped above must await knowledge of avoidance 

 and mesh escape behavior of at least some com- 

 ponents of the plankton and nekton, a few in- 

 formative comparisons can be made now be- 

 tween theory and catches obtained with various 

 towed nets. 



Equation (5) is presented graphically in Fig- 

 ure 3, where Pc, the minimum probability of 

 capture (ordinate) is plotted as a function of 

 the ratio Ue/U, the escape speed relative to the 

 net's speed, for various values of the ratio Xo/R, 

 the reaction distance relative to the net's radius. 

 The linear graph shows the complete theoretical 

 solution; it is used to provide a check on results 

 obtained using the semilog format. In practice 

 the semilogarithmic graph is more useful for 

 analyzing catch data because it simplifies graph- 

 ical calculations. Either of these graphs, as well 

 as equations (5), (6), and (7), can of course 

 be used to determine Pc, Ue, or Xo if any two of 

 these variables are known, along with R and U. 

 For example, a 1-m net {R = 0.5 m) towed at 

 100 cm/sec should catch at least one-third 

 (Pc = 0.33) of all those organisms in its path 

 which react at a distance of 1 m and can swim 

 20 cm/sec {iie/U = 0.2, Xo/R = 2). 



A more interesting application is the use of 

 Figure 3 to analyze size-frequency data from a 

 tow, or set of tows, made with one sampler at 

 one speed. To illustrate this application, sup- 

 pose that the population in question is a species 

 for which mesh losses are negligible beyond some 



803 



