1 - 



(F + M) (i-e-^+Af+feJX) + b(b-l) (b-2) (ft-3) _-«(*' -fc,)l; 



(F+M+k) (l- e -( F+M )^) 



X e- k (fp-t ) 



The values are: 



F + M 



too 



ft 



f P 

 t„ 



2.4700 

 266.77 

 0.04785 

 7.0 

 -0.77250 



The estimate of this mean length is: 

 Ly = 85.58 mm carapace length. 



This value is close to the estimates of mean 

 length calculated from the length frequencies 

 in the cluster samples of the commercial catch 

 (Table 7). 



Of course this similarity does not indicate 

 that any or all of the calculated parameters are 

 correct. Certainly, I feel more confident with 

 these estimates due to the favorable comparison 

 of mean lengths by this method and those from 

 the cluster samples. 



YIELD ESTIMATES 



The primary objective of the preceding analy- 

 ses was to estimate parameters that can be 

 used in a yield equation so that we might deter- 

 mine the biological minimum size for maximum 

 sustainable yield. 



We have calculated yield estimates from 

 the simple yield equation of Beverton and Holt 

 (1957) by two methods of expansion: 



(1) bionomial, as outlined by Norman J. 

 Abramson (personal communication), California 

 Department of Fish and Game: 



' w/r = W^Fe-mp 

 . b(b-l) 



f- 1 -- 



2(F+M+2k) 



IF+M F+M+k 

 e-2k(f p -t ) 



e- k (t p t ) 



_ b(b-l)(b-2) 3k{t } 

 6(F+M+3k) e K P °> 



(2) cubic, as described by Gulland (1965): 



w/r 



= Fe -M(t c -t r ) WooZ 



3 C/„e-" fe ( f c- f o) 



F+M+nk 



The symbols in each of the preceding equa- 

 tions are defined as follows: 



F 



M 



Woe = 



instantaneous fishing mortality 

 instantaneous natural mortality 

 maximum expected weight 

 constant proportional to catabolic 

 rate 



hypothetical age at zero length 

 assumed age at first capture 

 assumed age at recruitment 



= t 



t'n 



C T 



assumed age when first on fishing 



grounds 



assumed exploited ages offish 



= f 



<-p ■ 



It is inherent in the cubic expansion that 

 growth is isometric or that b from the weight- 

 length relationship is "3." If this value were 

 significantly different from "3," then it should 

 affect the yield estimates from this type of 

 expansion. 



On the other hand, the binomial expansion 

 uses the actual value of b so that these yield 

 estimates are not affected by this assumption 

 on growth. 



It follows then that we should use the binomial 

 expansion for lobsters (b = 2.8283 ± 0.0167). 

 We must reiterate that the commercial sizes 

 did yield a slope value (6 = 3.10584 ± 0.13224) 

 not significantly different from "3." Therefore, 

 we included the methodology by Gulland for 

 this reason and the fact that his method is 

 much more comprehensive than the binomial 

 expansion by Abramson. That is, we can deter- 

 mine yield values not only for different as- 

 sumed ages at first capture {t c ) of the same 

 assumed age or molt class but also for different 

 instantaneous fishing mortalities (F). There- 

 fore, if we use both methods, we should be 

 able to determine how much the value of b 

 influences the yield estimates and whether the 

 more inclusive method has any application. 



50 



