GROWTH OF THE ADULT MALE KING CRAB 



65 



The simplest inetliod of estiiimtiiifi the average 

 growtli rate would appear to be a stepwise accu- 

 mulation of the average annual growth incre- 

 ments. For example, using the 1958 data (fig. 9) 

 and assuming that the growth increments repre- 

 sent growth potential in terms of length, crabs 

 110 mm. in length at some single age N would, on 

 the average, increase in size by 15.4 mm., result- 

 ing at age ^V-l-l in an average size of 125.4 mm. 

 The average annual increment for 125.4 mm. crabs 

 can then be added to determine the size at age 

 :V-l-2, etc. It can be seen that the average annual 

 increment is the average amount of growth for all 

 crabs of a size, and that the proportions used are 

 made up of crabs that have, and those that have 

 not, molted. The resulting relation of size with 

 time by this accumulating process is, therefore, 

 in terms of average size against average age. 



To avoid the use of double averages, a method 

 was developed to express the growth rate in terms 

 of average size at a particular age. The method 

 utilizes a model which we believe represents the 

 growth of the eastern Bering Sea king crab stock, 

 and depicts the advancement of a size group 

 through 6 years. 



We will examine a hypothetical group of 10,000 

 male crabs under the assumption that the attained 

 sizes of several year classes in one year are repre- 

 sentative of the growth of one year class from 

 year to year. Basic inferences derived earlier in 

 the report from tagging and from the sampling 

 data for 1958 are utilized in a hypothetical model. 

 These are : (1) when male king crabs 110 mm. and 

 larger molt, the carapace length increases by 16 

 mm., and (2) the proportion molting by 16 mm. 

 intervals (fig. 8) are: at 110 mm. carapace length, 

 the proportion molting, P is 0.96; at 126 mm. 

 P=0.87; at 142 mm. P=0.65 ; at 158 mm. P=0.37; 



and at 174 mm. P=0.03. Since there were no 

 crabs larger than 195 mm. taken in 1958, we as- 

 sume P at 190 mm. to be 0.02, allowing for a slight 

 decrease in molting frequency. 



The smallest size considered in the model is 110 

 mm., a size generally common to the progressions 

 of modes described previously. Since most, if 

 not all, crabs less than 110 mm. molt at least an- 

 nually, and the modes in size frequency distribu- 

 tions of these sizes are quite definite, we assume 

 that 110 mm. crabs in the model are all of one age 

 class at .V years of age. The sizes, numbers, and 

 average size present in each of the successive years 

 from age iV to age X + 5 are calculated and shown 

 in table 3. At the end of the first year, since 96 

 percent of the 110-mm. crabs molt and 4 percent 

 do not molt, the age group has been segregated 

 into two size classes with an average length of 

 125.4 mm. The following year the crabs are of 

 age .V-l-1, and the 110-mm. crabs (.V=:400) and 

 the 126 mm. crabs (A'=9,600) are calculated to 

 be distributed in varying numbers in three size 

 classes consisting of 16 crabs remaining at 110 

 mm., 1,632 crabs at 126 mm., and the remaining 

 8,352 advancing to 142 mm. In this manner, at 

 the end of the year of age N + 5, five size classes 

 are represented, the average length of the year 

 class being 167.8 mm. 



The 1956, 1957, and 1959 data are treated in the 

 same manner, and the average lengths for each 

 age for all years are tabulated in table 4. The 

 growth curves based on the average sizes for each 

 age are shown in figure 10. Both the table and 

 tlie figure include an extension below 110 mm. to 

 ages .V— 1 and A — 2. The extension is the mean 

 of the means of the progression of modes in the 

 size frequency distribution discussed earlier. 



618363 O— 62 



