Longevity and Mortality Rates of Fish in Nature 173 



The undoubted association between reproduction and 

 death in many species of fish makes it difficult, merely on the 

 kind of evidence we have considered in this paper, to detect 

 whether true senescent processes play a part in determining 

 longevity in fish, as they do, for example, in mammals. The 

 mathematical representation of the characteristic growth 

 pattern in fish which we have adopted here does, of course, 

 imply that growth proceeds towards a finite limiting size, and 

 so is not "indeterminate" in the sense used by Bidder (1932). 

 When the growth of fish is plotted as in Fig. 3 the impression 

 gained is not only that this is a valid interpretation but also 

 that the growth pattern of the long-lived species (including 

 plaice) does not differ qualitatively from that of the short- 

 lived ones in which a limiting size is efPectively reached within 

 the observed range of age. As Comfort (1956) has pointed out, 

 however. Bidder's hypothesis of immortality in fish does not 

 necessarily depend on whether there is a finite limit to their 

 growth or not, and can equally well be maintained if that limit 

 can be shown to be approached asymptotically — and hence 

 reached only after an infinite span of time — as opposed to 

 abruptly, with growth ceasing beyond a certain specific age. 

 To test this latter alternative directly, at least in the slow- 

 growing species, is as difficult as it is to prove whether or not 

 there is a finite Umit to the lifespan of a species which has a 

 constant mortality rate within the observed range of age. In 

 this connexion, it is perhaps worth noting that although the 

 growth equation we have adopted requires an asymptotic 

 approach to a limiting size, high enough values of ^ (as are 

 found, for example, for Labidesthes sicculus) can produce a 

 theoretical growth curve in which the approach to L^ is so 

 rapid that it would be indistinguishable in practice from an 

 abrupt approach, especially when it is remembered that there 

 is usually a seasonal periodicity of growth superimposed on 

 the general pattern. 



Thus we are inclined to the view that further speculation 

 along these lines is unlikely to contribute much to the solution 



