FISHERY BULLETIN VOL 77, NO 



Table 2.— Estimation of the number in each component (iV, ) and the annual instantaneous total mortality rate iT ) from the 

 1976-77 weighted seasonal size-frequency distribution of male New Zealand rock lobsters from the Gisbome local area using 

 Method iv of Bhattacharya 1 1967). 



into the fishery, so these smaller size classes were 

 not included in the analysis. Moreover, only the 

 first three components were used because the 

 small number of individuals of larger sizes in the 

 sample made it difficult to accurately distinguish 

 any further components. Assuming that each 

 component approximates an individual year class, 

 the annual instantaneous total mortality rate be- 

 tween components 1 and 3 is 1.06. 



Estimates of the annual instantaneous total 

 mortality rate were also derived from the six 

 monthly samples (see Table 5). These estimates 

 ranged from 0.00 to 1.15, with a weighted mean 

 (weighted by the proportion of the seasonal land- 

 ings taken during the month) of 0.49 and 9.5'; 

 confidence limits of 0.06 and 0.92. 



The model used by Van Sickle ( 1977) describes 

 the exact shape of the size distribution of a sta- 

 tionary or steady state population, with the shape 

 expressed as a function of size-specific mortality 

 and growth rates. His Method 2 requires com- 

 prehensive growth and size-frequency data to es- 

 timate mortality on a size-specific basis. However, 

 it does not require the explicit determination of 

 the age distribution nor a fitted gi-owth curve, 

 which is advantageous for this species. 



The size distribution was divided into size class- 

 es (indexed by,/), and it was assumed that the 

 mortality rate ( /x, ) was the same for all individuals 

 in size class,/. The size classes can be of any width, 

 but the growth rate and number density must be 

 known at the boundaries of each class. 



Using the terminology of Van Sickle ( 1977), let 

 ./stand for the size interval (^,,2,.l). If the growth 

 ratesgiz, ),giz, . i ) and the number dnesitiesN, (2,), 

 A^^(2,.,) at the boundaries plus N, *, the total 

 number or proportion of organisms in classy are 

 known, then /x^ is calculated from his equation 8: 



Estimates of the annual instantaneous total 

 mortality rate applying Method 2 of Van Sickle 

 ( 1977) to the seasonal size distribution of Table 1 

 are shown in Table 3. The growth rate of 4.8 mm 

 used at the boundaries is an initial estimate of the 

 average annual growth increment of males in the 

 Gisbome local area, and was based on the molt 

 increment of 204 tagged rock lobsters recaptured 

 during 1976-77. The tagged individuals were all in 

 the size range 80-106 mm, due to difficulties ex- 

 perienced in obtaining larger animals for tagging, 

 so growth estimates were not available for the 

 upper part of the size distribution. However, ini- 

 tial growth information from other areas indicates 

 it is not unreasonable to assume a constant molt 

 increment for males between 80 and 115 mm 

 carapace length. 



Some difficulty was experienced in determining 

 the lOO/; retention length for rock lobsters using a 

 carapace measure because the minimum legal size 

 is based on a tail length measure (Annala 1977). 

 The carapace length class from 100.0 to 100.9 

 mm had the highest proportion of any single mil- 

 limeter class in the size-frequency distribution 

 ( Table 1 , Figure 2 ) and was therefore chosen as the 

 smallest size class fully represented in the land- 

 ings. The size-frequency distribution was then 

 partitioned into 4 mm and 5 mm size groups, be- 

 ginning with the 100 mm size class, to bracket the 

 average annual growth increment of 4.8 mm. The 



T..\BLE3.—E.stimation of the annual instantaneous total mortal- 

 ity rate I /i, ) from the 1976-77 weighted seasonal size-frequency 

 distribution of male New Zealand rock lobsters from the Gis- 

 bome local area using Method 2 of Van Sickle ( 1977). 



Size 

 grouping |z,,.2, .,1 W ' IgU,). 9(f ■)) M,(yr ) 



1 



g{Zj)NAz,)-g(^,+ iWj^,+ i) 



474 



