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Fishery Bulletin 94(4). 1996 



Figure 1 



Illustration of the six methods of growth comparison in Table 1 when 

 growth follows the von Bertalanffy equation. In each panel, the cen- 

 tral point, 'o', represents the growth parameters for species Q, 

 (L x , ,k ). Species P is said to grow faster (or slower) than species Q 

 if the point (L m , p ,& p ) lies in the light (or dark) shaded area of the 

 graph. In the unshaded areas, no comparison can be made over the 

 whole life history (so P may be faster than Q at one age lor length I 

 and slower at another). Comparisons are for (A) methods 1, 3, and 

 5; (B) method 2; (C) method 4; and (D) method 6. See Table 1 for 

 definitions of methods. The curved line in panels A and B is L^ = 

 L^,JiJk. ( Details of the derivation of this Figure are available from 

 the author). 



With this assumption, method 6 is fully defined be- 

 cause the parameter A' determines the rate at which 

 the asymptote is approached; the bigger k is, the 

 faster the asymptote is approached. Thus, according 

 to method 6, P grows faster than Q if k p > kg. 



Now, given growth parameters L^,Q,kg for Q, we 

 are in the position to address the question. "What 

 range of values can L , p ,k p take if we are to say that 

 P grows faster (or slower) than Q?". Figure 1 shows 



that the answer to this question depends 

 strongly on which of the six methods of com- 

 parison is used. Methods 1, 2, and 5 give iden- 

 tical answers, but these are very different 

 from the answers from the other methods. 

 Methods 4 and 6 give completely opposite 

 answers. For methods 4 and 6, we can always 

 say either "P grows faster than Q" or "Q grows 

 faster than P" (as long as the growth rates are 

 not identical ). However, for all other methods 

 in Table 1, it will sometimes not be possible to 

 make either of these statements without quali- 

 fication. For example, in the unshaded areas 

 of Figure 1A, P grows faster than Q at some 

 ages (or lengths) and slower than Q at others 

 (according to methods 1, 3, and 5). 



Method 6: A comparison of rates 

 at which the asymptotic size is 

 approached 



I suggest that method 6 is the most "natu- 

 ral" method of growth comparison, in the 

 sense that it produces common-sense results. 

 To see why, consider the question in the title 

 of this paper. Orange roughy, Hoplostethus 

 atlanticus, is described as "very slow-grow- 

 ing" (Fenton et al., 1991) and herring, Clupea 

 harengus, is generally considered to be fast- 

 growing; therefore the answer to this question 

 should be "yes." Given growth parameters for 

 orange roughy (L m , Q =40 cm, £ Q =0.044/yr; 

 Fenton et al., 1991) and any of the sets of her- 

 ring parameters given by Pauly ( 1980 ) ( range: 

 1,^=19.4 - 36.0 cm, k p = 0.21- 0.48/yr), the 

 point (L , p ,k p ) would lie in the right-hand un- 

 shaded space in Figure 1A (and in the cor- 

 responding position in the other panels of 

 Figure 1 ). This means that with methods 1, 2, 

 3, and 5 there would be no clear-cut difference 

 in growth rates between these species and that 

 with method 4 herring would grow slower than 

 orange roughy. Only method 6 reaches the com- 

 mon-sense conclusion. 

 Another reason to prefer method 6 is that 

 it ignores asymptotic size (Lj. It seems to me that 

 comparisons of this parameter determine only 

 whether one species is bigger than another, not 

 whether growth is faster or slower. In other words 

 L describes size, not growth rate. But note that, for 

 the methods covered by Figure 1. A and H. P cannot 

 be judged to grow faster than Q unless L , r > L , ( ,. 

 This confusion between measures of size and growth 

 rate is illustrated by Figure 2. Method 6 ranks curve P 



