FISHERY BULLETIN VOL 77. NO 2 



Table 6. — Recaptures of male New Zealand rock lobsters tagged 

 and released in the Gisbome local area in July 1976. efTort 

 expenditure during 1976-77. and the number of recaptures per 

 unit relative effort (v, ). 



S(i _ lyy^ = 41.03(1 - 1) + 55.36(2 - 1) 



+ 20.63(3 - 1) + 29.41(4 - 1) 

 + 17.83(5 - 1) + 8.13(6 - 1) 

 + 17.16(7 - 1) + 13.33(8 - 1) 

 + 2.50(9 - 1) = 513.09 



Sv, = (41.03 + 55.36 + 20.63 + 29.41 

 + 17.83 + 8.13 + 17.16 + 13.33 

 + 2.50) = 205.38. 



Thus, the mean coded age ix) = 513.09/205.38 = 

 2.4982. 



The proportion of tagged individuals remaining 

 free after the last monthly sampling period was 

 too large to be neglected, so the estimate of mean 

 coded age was equivalent to 



Estimates of the survival rate (S) that will 

 satisfy a given value of x for any given J were 

 determined from table 3 of Robson and Chapman 

 (1961). In this examples = 2.4982 and J = 9, so 

 the value of S which satisfied was 0.786. This was 

 a monthly value for S, so an estimate of S for the 

 entire year, assuming total mortality acts 

 uniformly over the 12-mo period, was San^uai = 

 (SmonthLvH^ = (0.786)'2 = 0.0556. Thus, the annual 

 instantaneous total mortality rate (Z) measured 

 over the 12-mo period = 2.89. However, with 

 fishing effort concentrated in the 9-mo period from 

 mid-June to mid-March and with a low initial 

 estimate of instantaneous natural mortality rate 

 {M) of approximately 0.10 (Annala 1977), it was 



assumed that mortality acted primarily during 

 the 9-mo fishing season. An estimate of annual 

 total mortality based on this 9-mo period was 



S.nnual = (S,„„„,hlv)" = (0.786)« = 0.1145, with 



Z = 2.17. 



The results of this analysis, as well as the re- 

 sults of grouping the tag returns bimonthly and 

 quarterly are shown in Table 7. 



Estimates of the instantaneous fishing mortal- 

 ity rate (F) were made using equation 26of Paulik 

 (1963) for grouped observations, whereF = -/j.ln 

 S/(l - §'^), and /i = n.lN, where n. = the total 

 number recaptured over the period of observation, 

 and A^ = the total number of tags released. 



In the example cited above, where tag returns 

 were grouped on a monthly basis from August 

 1976 to April 1977, ii = 223/433 = 0.5381, where 

 the number recaptured in July (11) was subtracted 

 from the number released (444) to estimate the 

 number still at large at the beginning of August 

 (433). Using the monthly value of S = 0.786, the 

 monthly value oi f = -0.5381 x -0.2408/[l - 

 (0.786)''] = 0.1464. On a 12-mo basis, the annual 

 estimate of F = 1.76. However, based on a 9-mo 

 fishing season, the annual estimate oi P = 1.32 

 (Table 7). 



The value of F was also estimated from the 

 equation F = iiZIA , which was derived from equa- 

 tion (1.13) of Ricker (1975), where u = rate of 

 exploitation, Z = instantaneous total mortality 

 rate, and A = actual total mortality rate. 



The value of u was estimated on an annual basis 

 from the equation ;/ = RIM. where/? = number of 

 recaptures during first year after release and M -= 

 number of tags released. 



For the July 1976 tagging, u = 251/444 = 

 0.5653. Thus, for the tag returns grouped on a 

 monthly basis, the annual estimate of F = uZ/A = 

 0.5653 X 2.89/0.9444 = 1.73 over a 12-mo period. 



T.XBLE 7. — Estimates of the annual instantaneous total (Z) and 

 fishing (Fl mortality rates of male New Zealand rock lobsters 

 from the Gisbome local area derived from tag returns of those 

 tagged and released in July 1976. 



'The figures m parentheses are estimates of Z and F taken over 9 mo for the 

 monthly and quarterly groupings and 8 mo for the bimonthly grouping. 



476 



