783 



Do herring grow faster than 

 orange roughy? 



R.I.C. Chris Francis 



National Institute of Water and Atmospheric Research fNIWA) 

 Box 1 490 1 , Wellington, New Zealand 

 e-mail address c francis@niwa en nz 



In growth studies it is common to 

 find the statement "P grows faster 

 than Q". However, it is much less 

 common to find a clear definition 

 of what the author means by that 

 statement. What is it about two sets 

 of growth parameters, or two 

 growth curves, that should make us 

 conclude that "P grows faster than 

 Q'? In this note I will show that this 

 is not as simple a question as it may 

 seem. There are several plausible 

 ways of answering it and these 

 have very different consequences. 

 Thus, the statement 'T grows faster 

 than Q" is ambiguous and it is im- 

 portant for authors to be specific 

 about what they mean by it. I will 

 also give reasons for preferring one 

 of the possible meanings. 



In what follows it will sometimes 

 be convenient to refer to the two 

 entities being compared as "species 

 P" and "species Q." However, my 

 conclusions are the same whether 

 the growth comparison is made 

 within species (e.g. males vs. fe- 

 males [Horn, 1993; Hostetter and 

 Munroe, 1993; Kitagawa et al., 

 1994; Collins et al., 1995], one time 

 period vs. another [Raspopov, 1993; 

 Collins et al., 1995], or one area vs. 

 another [Horn, 1993; Savard et al., 

 1994]), or between species (Arkhip- 

 kin and Nekludova, 1993; Gorny et 

 al., 1993; Milton et al., 1993; Potts 

 and Manooch, 1995). 



Before proceeding, it is useful to 

 restrict the scope of the question 

 being considered. First, only the 

 mean growth for a "species" is con- 

 sidered; therefore between-indi- 

 vidual variability in growth is ig- 



nored. Second, I will assume that 

 we have perfect knowledge about 

 the growth of P and Q; i.e. statisti- 

 cal uncertainty is ignored. Third, I 

 will consider only unqualified com- 

 parisons such as "P grows faster 

 than Q," comparisons that apply 

 only to a portion of the life history 

 (e.g. "P grows faster than Q up to 

 age 1") are excluded. The purpose 

 of these restrictions is to allow for 

 a simpler presentation. Without 

 them, the picture is more complex, 

 but the results given below will still 

 apply, although not in precisely the 

 same form. 



Six methods of growth 

 comparison 



There are at least six plausible 

 methods for comparing growth 

 (Table 1). With method 1, we would 

 say that P grows faster than Q if 

 L t p > L t g for all t, where L ( p and 

 L t q are the lengths at age t for spe- 

 cies P and Q, respectively. The ra- 

 tionale behind this method is that 

 L t p >L t g implies that P must have 

 grown faster than Q (at least on 

 average) over the period up to age 

 t. Now, rather than comparing av- 

 erage growth rates over a period of 

 time it may be more sensible to 

 compare instantaneous growth 

 rates. This is the reason for method 

 2. However, it may be argued that 

 method 2 makes no sense when L t p 

 is very different from L t „. For ex- 

 ample, a growth rate of 10 cm/yr is 

 fast for an animal of size 20 cm but 

 slow for an animal of size 200 cm. 



There are two ways to deal with 

 this difference: we can either insist 

 that the comparison be made when 

 the animals are of the same size 

 (method 3), or we can standardize 

 the growth rates by dividing by 

 length (methods 4 and 5). (Method 

 5 is included here for completeness, 

 but it is easy to show that it is ex- 

 actly equivalent to method 3.) 

 Method 6 could be appropriate 

 where growth is asymptotic and the 

 asymptotes for P and Q are differ- 

 ent. Here the species that ap- 

 proaches its asymptote faster is said 

 to grow faster. Of course, this method 

 is not fully defined until we specify 

 what we mean by "the rate at which 

 the asymptote is approached." 



To illustrate the difference be- 

 tween these methods we will as- 

 sume that growth is adequately 

 described by the von Bertalanffy 

 equation with ^ = 0, i.e. 



L=L(l-e- k <). 



Table 1 



Six methods for comparing the mean 

 growth of two species or populations. 

 The absolute growth rate is the slope 

 of the length-at-age curve (with di- 

 mension length/time) and the rela- 

 tive growth rate is this slope divided 

 by the length (dimension 1/time). 



Method 1: compare lengths at 

 each age 



Method 2: compare absolute 



growth rates at each 



age 

 Method 3: compare absolute 



growth rates at each 



length 



Method 4: compare relative 



growth rates at each 

 age 



Method 5: compare relative 



growth rates at each 

 length 



Method 6: compare rates at 



which the asymptotic 

 size is approached 



Manuscript accepted 2 July 1996. 

 Fishery Bulletin 94:783-786 1 1996). 



