FISHERY BULLETIN: VOL. 75, NO. 3 



vessels whose catch data are to be collected 

 adequately. 



If the fleet is large, a part of the fleet is appointed 

 as sampling vessels while the effective fishing 

 effort of unappointed vessels should be estimated. 

 The sampling surveys should follow one another 

 with no intervening time periods within a group 

 of surveys. The durations of the surveys may vary 

 from one survey to another or kept constant if 

 the total fishing effort varys from survey to 

 survey. The total effort exerted on the population 

 should vary from one survey to another. 



ASSUMPTIONS 



1 . A fish population has a constant area of distri- 

 bution and a constant uniform distribution of 

 fishing relative to fish concentration so that the 

 instantaneous fishing mortality is proportional to 

 fishing effort. 



2. The population is subjected to a sequence of 

 n sampling surveys grouped into M groups repre- 

 senting M seasons with constant population 

 parameters. The duration of the &th survey is 

 denoted by T k . The catchability or percentage of 

 available fish captured by a standard unit of fish- 

 ing effort during the kth survey is denoted by q k . 



3. The commercial and sampling vessels exert 

 a constant fishing effort per unit time during the 

 &th survey denoted by f kc and f ks respectively, 

 so that the efforts exerted become 



noted by N . The number of fish present at the 

 start of the £th survey is N k0 while the number of 

 fish present at the end of the kih survey or the 

 start of the (£ + l)th survey is A^,^ + 110 . 



6. The instantaneous natural mortality rate per 

 unit time during the Mh survey is M k . The instan- 

 taneous natural mortality during the £th survey 

 is 



M h  Ty = Mi. 



(1.8) 



7. The instantaneous recruitment rate per unit 

 time during the kth survey relative to the number 

 of fish present is R k - The number offish present 

 at the end of the kih survey or the start of the 

 (k + l)th survey when recruitment is acting solely 

 is 



Af 



(/t + l>0 



N k0  exp(R k  T k ) 

 N k0  exp(R' k ), 



that is. 



Rb Ty — R'y 



(1.9) 



(1.10) 



where R' k denotes the instantaneous recruitment 

 rate during the /eth survey. 



8. The instantaneous rate of change offish abun- 

 dance per unit time during the kth survey relative 

 to the number of fish present is "Ay" which is 

 the "instantaneous abundance coefficient" so 

 that 



where f' kK , f' kc , and f' k represent the total fishing 

 effort exerted by the sampling, commercial ves- 

 sels, and the whole fleet, respectively, during the 

 £th survey. 



4. The instantaneous fishing mortalities per 

 unit time by the sampling, commercial, and total 

 fleet in the Mh survey are denoted by F ks , F kc , 

 and F k , respectively. The instantaneous fishing 

 mortalities during the £th survey (F' ks , F' kc> and 

 F' h ) are evaluated as 



F ks  T k --- Fy[ s ---- q k  flu 



Fkc  T k = Fk c = Qk ' fkc 

 F k  T k = F' k = q k  f' k . 



(1.5) 

 (1.6) 



(1.7) 



5. The fish population has an initial size de- 

 562 



(1.11) 



In other words, A k • T k = A' k and A' k denotes the 

 instantaneous change of abundance during the 

 Mh survey. 



According to previous assumptions we have 



A' k ---- R' k - M k ' - F^ ---- (R k - M k - F k )T k (1.12) 



and 



N.*n>o = N ko  exp(A^) 



= N k0  exp(Rk - M k ' ~ F^). (1.13) 



9. If the sampling surveys (&- 1), k, and (k + 1) 

 belong to the same season, 



#*-i == Rk = Rk + \ = Rj (1.14) 



M k -i --= M k = M k + 1 --= M k (1.15) 



