ANNALA: MORTALITY OF ROCK LOBSTER 



105 110 115 



Coropace iengfh ( 



FlGLTRE 2. — Weighted seasonal size-frequency distribution of 

 male New Zealand rock lobsters from the Gisbome local area 

 landed during the 1976-77 season. 



all other components are negligible. Moreover, the 

 class range should be small , and the sample should 

 be of a sufficient size so that the class frequencies 

 are not small in the area of the distribution where 

 the components are being separated. 



If the class intervals are assumed to be constant, 

 direct graphical procedures can be used, as simple 

 differencing reduces the quadratic to a straight 

 line. The midpoints of the size classes were plotted 

 on the abscissa and the logarithmic difference in 

 the frequency between successive classes on the 

 ordinate. Each of the regions on the graph contain- 

 ing straight lines with negative slope corresponds 

 to the separate components of the distribution. 



The natural logarithms of the abundance of 

 each of the 1 mm size classes and the logarithmic 

 differences between successive size classes are 

 also shown in Table 1. The logarithmic differences 

 plotted against the midpoints of the size classes 

 are shown in Figure 3 , as well as the lines fitted by 

 eye through adjacent points. This procedure in- 

 volved fitting a straight line with a negative slope 

 through successive points and required a certain 

 amount of subjectivity when choosing the posi- 

 tions of the lines. However, the line-fitting was 

 aided by using the average annual growth incre- 

 ment as a guide in determining the positions of the 

 lines and by fitting the lines more closely to the 

 points with the larger than the smaller frequen- 

 cies. 



Using Bhattacharya's (1967) terminology, the 

 revelant parameters from Table 1 and Figure 3 

 are: 



h = the class interval = 1 mm 



90.5 95.5 100.5 105.5 110.5 

 Midpoint of class (mm) 



115.5 



Figure 3. — Logarithmic difference in abundance plotted 

 against the midpoints of successive mill imeter size classes from 

 the weighted seasonal size-frequency distribution of male New 

 Zealand rock lobsters landed from the Gisbome local area during 

 the 1976-77 season 



b 

 d 



K 

 K 



Or 



0, 



i^-r 



M, 



the scale of .v = 1 



the scale of v = 20 



the .r-intercept of the rth line 



100.7 



^2 = 105.0 



110.5 



= the angle the rth line makes with the 



negative direction of the .v-axis 

 = 82.0° So = 78.5° «3 = 79.5° 

 (the mean of the rth component) 

 = K + h/2 



= 101.2 M2 = 105.5 As = 1110 

 (the SD of the rth compone nt) 

 = \/ Idh cot 6r/b) - (h^/12) 

 = 1.6513 ^2 = 1-9967 6-3 = 1.9033. 



Using Method iv, and following the steps out- 

 lined in table 8, of Bhattacharya (1967), the 

 number of individuals {N, ) in each of the first three 

 fully recruited components of the seasonal size- 

 frequency distribution from the Gisbome local 

 area was estimated as shown in Table 2. Male rock 

 lobsters less than the carapace length size class 

 from 100.0 to 100.9 mm were not fullv recruited 



473 



