HENRY: NATURAL AND FISHING MORTALITIES OF CHINOOK SALMON 



(23) is found by iteration, andF2 is calculated from 

 Equation (24). Finally, M^ in Equation (25) is 

 found by iteration andF^ is calculated from Equa- 

 tion (26). 



In developing the computer program to do the 

 above computations, I assigned a beginning value 

 of 0.001 to m, and then computed the smallest m^ 

 possible that would give me nonnegative values 

 for all the M's andF's. For these particular values 

 of mj and m2, 1 then incremented m^ over a range 

 of values as long as Wg <1 ortheM3,M4,F2, andFs 

 values were nonnegative. The program would 

 then go back and increment mg and compute 

 another series of m^ values and dependent 

 parameters. When mj was incremented to a level 

 where mg = 1 or that would no longer give positive 

 values for either M3, M4, F2, or F3, the program 

 would increment m^ and the process would begin 

 again. A sample of the printout for selected values 

 is shown in Table 2. 



COMPARISON OF TWO METHODS 



To assist in comparing the results from: 1) as- 

 suming a given value for M, (natural mortality) or 

 2) assuming given values for each m, (proportion 

 of fish that mature each year), I have listed in 

 Table 3 the results for the 1962 brood data for the 

 general marked fish based on assuming a given m. 

 (Thei?, shown in the table are equivalent to the A'^, 

 discussed in this paper.) One difficulty in making 

 these comparisons is that the results from the two 

 methods appear in quite different form. In Table 3, 

 there are six lines of estimated values for six dif- 

 ferent levels of M. On the other hand, by assuming 

 fixed values of m, for the same data for the fish in 

 the general mark category, the complete printout 

 of results has a total of 48 groups of data, similar to 

 the selected 10 groups shown in Table 2. Of course, 

 the number of groups of data by the latter method 

 is dependent on just how the m,'s are incremented. 



One obvious difference in the two sets of results 

 is that Table 3 (assuming fixed M) was computed 

 using a single constant value for the M,, whereas 

 Table 2 (assuming fixed m,) had separate esti- 

 mates for each M,. Although an exact comparison 

 of the results is not possible since I did not use 

 exactly the same m, as shown in Table 3, many of 

 my results are close enough to make useful com- 

 parisons. For example, for M -= 0.60 in Table 3, 1 

 calculated F3 = 1.275, F2 = 0.698, Fj = 0.410, m^ 

 = 0.761, m^ = 0.262 and mi = 0.006. From Table 2 

 we can select values of m, that are fairly compara- 



ble, i.e., mi = 0.006, m^ = 0.256, m3 = 0.756, 

 which gives Fi = 0.405, F2 =0.669(0.11143 x 6), 

 F3 = 1.177 (0.19614 X 6) (F's are summed over 6 

 mo). 



The major difference between the two sets of 

 results is the natural mortality estimates with M^ 

 = 5.814, M2 = 0.510, M3 - 0.653, and M4 = 0.727 

 (Ml is summed over 18 mo, M2.4 summed over 12 

 mo) from my calculations using estimates for the 

 proportion offish that mature annually compared 

 with the M = 0.60 in Table 3. The comparatively 

 large natural mortality in the first 18 mo of exis- 

 tence is not too surprising; however, the increas- 

 ing values for M from Mg to M4 do not seem 

 reasonable. Since the natural mortality values 

 listed include the loss of "shakers" (fish released 

 by fishermen because they are too small or out of 

 season), one would expect the M^ value to be 

 largest because this is the time these fish would be 

 most vulnerable to shaker losses. Estimates of 

 shaker mortality have ranged from 15 to 45% 

 (Wright^). 



What these increasing estimates of M, indicate 

 is that the m,'s selected in this comparison are not 

 realistic — m , values for which the M,'s are at least 

 equal, or even decreasing with increased age 

 might be better. Although the relation shown be- 

 tween these values will vary depending on the 

 value of m2 (the M^ value computed for a given m^ 

 value decreases as mg increases), at a certain 

 value of m3 or above, M4 ^M^. 



The relationship between the various parame- 

 ters computed are shown more clearly in Figures 

 2-5 for the 1961 brood Spring Creek data. Thus, in 

 Figure 2 is shown the relation between m 1 and Mj . 

 As mj increases, Mi also increases but at a di- 

 minishing rate. In Figure 3 is depicted the relation 

 between Fi and F2 and m^ m2, and m3. Fi is 

 affected by both the mi and mg values selected, 

 whereas F2 reacts to both the m2 and m^ values 

 chosen. Both Fi and F2 increase as m^ increases 

 for a particular value of m 1 or m 3. Also, for a given 

 value of m2, both Fj and F2 increase with increas- 

 ing mj and m^ values, respectively. In Figure 4 is 

 shown the relation between M2 and Mg for selected 

 values of mi, m2, and m^. With increasing m^, M^ 

 increases but M3 decreases. For a given mg, M3 

 increases with increasing m3, and M2 decreases 

 with increasing mi. Finally, in Figure 5 is shown 



3 Wright, S. 1970. A review of the subject of hooking mor- 

 talities in Pacific salmon. Wash. Dep. Fish., Manage. Res. Div., 

 38 p. (Report, prepared for the Salmon Research Staff of the 

 Pacific Marine Fisheries Commission.) 



49 



