MORGAN ET AL.: STOCK AND RECRUITMENT RELATIONSHIPS IN PANl'UltUS CYdNI'S 



tionship between puerulus settlement and the 

 subsequent spawning stock will inevitably be 

 confused by the effects of variable amounts of 

 fishing pressure on the commercial stocks be- 

 tween the time the rock lobsters are recruited to 

 the fishery as whites and the time that they be- 

 come mature. In addition, the mature females 

 will be subjected to fishing pressure when they 

 are not carrying eggs. When they are carrying 

 eggs, the fishermen are required by law to re- 

 turn these mature females to the sea. 



This fishing pressure on the mature and im- 

 mature stocks will lead to a reduction in the 

 abundance of the spawning females compared 

 with their potential abundance if there was no 

 fishing pressure. Moreover, the degree of reduc- 

 tion will be a function of the fishing effort (/) 

 since 



Nt = N e {M "> f)t 



where N t = numbers present at time t 

 No — numbers present at time 

 M = instantaneous natural mortality 



rate 

 q = catchability coefficient. 



If the growth rate of P. cygnus is considered 

 (Morgan 1977), it will take approximately 1 yr in 

 coastal areas north of lat. 30°S for female rock 

 lobsters to grow from the legal minimum length 

 of 76 mm to the average size of a mature female 

 of 92 mm (Table 1) and approximately 2 yr in 

 areas south of lat. 30°S to grow from 76 mm to the 

 average size of a mature female of 105 mm. 

 Therefore, as a first approximation and neglect- 

 ing the apparently small influence of the Abrol- 

 hos Islands area, it will be assumed that female 

 P. cygnus are subjected to fishing pressure for an 

 average of 1.5 yr during their life in the fishery. 

 The indices of abundance of the spawning stock 

 for all areas (Table 1) can now be adjusted to take 

 into account the probable effects of fishing pres- 

 sure by assuming the index for any year, i, is not 

 only a result of puerulus settlement in previous 

 years but has been reduced by the effect of fish- 

 ing effort in year (i - 1) and one-half the fishing 

 effort in year {i — 2). 



Using the effective fishing effort data given by 

 Morgan (1979) and Hancock (1981), a relative 

 index, R.I., for later years can be calculated so 

 that it takes into account the effects of fishing 

 effort prior to maturity. This will be given by 



R.I. (/) = I.A.S.(i)/exp (-</(/(/' 

 + 0.5 f(i - 2))) 



1) 



where f(i -- 1) 

 f(i ~ 2) 

 I.A.S.(i) 



fishing effort in year i 1 

 fishing effort in year i — 2 

 index of abundance of the 

 breeding stock in year i. 



Using the values of fishing mortality rate F 

 and effective effort,/, given by Morgan (1977) a 

 value of q may be calculated from 



f 



This gives an average value of q for the period 

 1967-73 of 1.4 X 10" 7 . 



Using the above formula and value of q, rela- 

 tive indices of abundance have been calculated 

 and are shown in Table 8. 



The spawning stock will inevitably comprise a 

 number of year classes each of which is the result 

 of puerulus settlement some 6 yr earlier. How- 

 ever, at the high levels of fishing effort which 

 have been characteristic of the fishery in recent 

 years (Morgan 1979) the breeding stock will be 

 dominated by the younger year classes. Using 

 the value of q of 1.4 X 10" 7 and the value of the 

 natural mortality rate Mof 0.226 (Morgan 1977), 

 it can readily be shown that during the 1978-79 

 season, the total instantaneous mortality rate Z 

 was about 1.54. At this level of mortality, only 

 about 21% of spawning females may be expected 

 to survive for a second year's spawning and about 

 5% for a third year. 



The relative indices of the spawning stock 



Table 8.— The relative index of the breeding stock (R.I.) calcu- 

 lated from the index of abundance of the breeding stock 

 (I.A.S.), and adjusted for fishing effort. The method of calcula- 

 tion is explained in the text. NA = not yet available. 



483 



