(3) Next we used a method outlined by 

 Gushing (1968), but more fully described by 

 Beverton and Holt (1957). The equation is 



Z = log e -= . I place the greatest amount 



N t+1 

 of reliability in this estimate because the latter 



authors explained that with a continuous fishery, 

 a much better estimate could be expected 

 from the mean abundance of a year or molt 

 class during 1 year of life when related to the 

 same year or molt class and mean abundance 

 1 year later. This method also has shortcomings 

 (other than our assumptions regarding length 

 frequencies) in that the total mortality should 

 be approximately the same in each of the two 

 years considered. This shortcoming can be 

 compensated for, to some extent, by a cor- 

 rection factor or picking one month (May, in 

 the case of the lobster fishery) in each of two 

 years as described by Paloheimo (1961). 



We made this estimate with two different 

 types of effort, (1) trap-haul-set-over-days and 

 (2) trap-hauls. With the first effort term the 

 estimates are: 94.5% (»i/»2 between May 1968 

 and May 1969) and 94.2% (n 2 ln 3 for the same 

 time period); 94.4% (niln 2 between May 1969 

 and May 1970) and 94.6% (n 2 ln 3 for the same 

 time period). With the second effort term the 

 estimates are: 94.1% (»i/m 2 between May 1967 

 and May 1968) and 94.3% (n 2 ln 3 for the same 

 time period). 



(4) Beverton and Holt (1957) described an- 

 other method of estimating total mortality from 

 the combination of (1) parameters from the 

 von Bertalanffy Growth Equation and (2) the 

 mean length and the size when lobsters are 

 fully vulnerable in the commercial fishery. The 



equation is Z = 



kjloo-r 



I-r 



-. The estimates by 



year are 88.9% (1967), 90.1% (1968), 88.9% 

 (1969), and 77.6% (1970). 



(5) Again Beverton and Holt (1957) described 

 a method which involved the use of the total 



mortality estimates from Z = log e - plot- 



N t+ 1 



ted against the effective fishing effort (in this 

 case trap-haul-set-over-days). Because we col- 

 lected these effort data from 1968 on, it is only 



possible to use three years of data. The authors 

 caution that we should have a long series of 

 years; nevertheless, we estimated an annual 

 natural mortality of 7.7% for lobsters of com- 

 mercial size. 



(6) Ricker (1958) presented a detailed dis- 

 cussion on the use of "catch curves" along 

 with the methodology. For use in this method, 

 we organized the length frequencies of the 

 commercial and prerecruit sizes of lobsters 

 into either 14% groupings or numbers at se- 

 lected modes from the probability paper deter- 

 minations, all within years. A plot of the natural 

 logarithm of the frequency of numbers of pre- 

 recruit and commercial sizes with effort reveals 

 a dome-shaped curve with a somewhat sinuous 

 descending right limb (Fig. 17). In addition 

 to the contributive causes for this type of curve 

 described by Ricker (1958), we must add our 

 technique of estimating the assumed age or 

 molt groups by 14% increments or by proba- 

 bility modes. It then follows that the descending 

 right limb which is concave suggests that the 

 fishing mortality has increased on the larger 

 sizes (positively the case from prerecruit to 

 recruit sizes), but variable recruitment from 

 shedding frequencies might affect these esti- 

 mates, as could a changing natural mortality 

 or vulnerability to the trap in association with 

 SOD. The latter consideration seems plausible, 

 but then we should expect either larger sizes 

 in the population to be readily apparent or a 

 good carry-over of commercial sizes of lobsters 

 from December to May of the following year. 

 The conclusion from sampling the natural popu- 

 lation with different types of gear, including 

 scuba observations, refutes this carry-over 

 contention; therefore, it appears that either 

 a decreasing natural mortality (some of our 

 estimates indicate this is true) or as Ricker 

 (1958) pointed out, the shape of the curve 

 could also be affected by the assumed age 

 or molt groups not being uniform in size in- 

 crements. In this case the probability modes 

 between and within years do not lend support 

 to this premise, at least for the commercial 

 sizes. 



While we included in Table 9, under the 

 catch curve section, only the total annual 

 mortality estimates from the number of lobsters 

 at consecutive probability modes, we also 



45 



