212 J. A. GULLAND 



by the use of some theoretical formula. The use of some formula, such as 

 assuming that mortality is linearly related to density, viz. 



M=m-\-kS, 

 where 5 is measured either in terms of number or weight, may be incor- 

 porated into the various equations with but moderate mathematical difficulty. 

 It is more difficult to determine the values of m and k. Some steps towards 

 doing this can be made if natural mortahty is split up into its component 

 parts, e.g. disease, parasitization and predation in some proportion, i.e. 



The values of a, b and c are in the first instance estimated (i.e. guessed) from 

 a general impression of the biology of the species concerned. Then reasonable 

 assumptions are 



Mjjis DO proportion of diseased individuals in the stock. 

 MpAR X proportion of parasitized individuals in the stock. 

 MpRED DO abundance of predators. 



All these factors could be directly estimated for any short period. 



The equation relating to mortahty and stock abundance may now be 

 more usefully written in terms of some average or standard conditions, 

 where M = M, S= S, and becomes 



M- M , J S- S 



M 

 which reduces to M = k^ M/S S - M {i - k"). 



In this form there is essentially only one constant to be estimated, k^, which 

 gives the percentage change in M for a given percentage change in the stock. 

 In particular k^ -= o gives constant mortahty and fei = i mortahty pro- 

 portional to abundance. 



In this form the various components of mortality, or numbers pro- 

 portional to them, can be directly related to population abundance, viz. 



Mpis - Mpis _ y. S- S 



^Dis ^^^ ^ etc-' 



and hence the relation of the total natural mortahty given in this form where 

 ^1 = akl^^ + bkl^^ + ck\^ED 



