FISHERY BULLETIN: VOL. 72, NO. I 



Table 4. — Comparison of king crab mating ability, slopes and slope contrasts for relative fullness of brood chamber and 



percent of eggs fertilized. 



Relative fullness of brood chamber 



Percent of eggs fertilized 



Male class 



Slope 



Standard 

 deviation 

 of slope 



F Value for 

 Test of slope = 



Slope 



Standard 

 deviation 

 of slope 



f Value for 

 Test of slope = 



Old-shell vs. 

 new-shell -1.028 



b\ + h2 — h^— hi 



Large vs. small -0.450 



hi + hs — b2~ hi 



0.329 



0.329 



9.80 P = O.OOI 



f = 1.9 



P = 0.17 



-0.585 



-0.482 



0.287 



0.287 



f = 4.1 P = 0.04 



F = 2.8 P = 0.10 



mating ability of the males in that particular 

 group. A test of the hypothesis of equality of 

 slopes {bi = b2 = b^ = 64) yields an F ratio of 

 4.1 for relative fullness of brood chamber and 

 11.7 for percent of eggs fertilized, significant at 

 the 1 and 0.01 percent level respectively. In or- 

 der to determine the significance of the size shell- 

 age classifications, contrasts of old-shell versus 

 new-shell and small versus large were computed 

 as shown in Table 4. These contrasts indicate 

 that the major contribution to the inequality in 

 slopes comes from the difference in shell age. 

 Size did not appear to be a significant factor as 

 is indicated by P values of 0.17 and 0.10 respec- 

 tively for relative fullness of brood chamber and 

 percent of eggs fertilized. Within the shell-age 

 contrast, the small old-shell males contribute 

 the most in the form of a more negative slope, 

 indicating that these males have much less 

 mating ability than the other three groups. 



The data pre.sented thus far give a comparison 

 of the mating abilities of the four size shell-age 

 groups. A linear approximation was assumed 

 for each group and, although this procedure is 

 not exact, it is sufficiently close for comparative 

 purposes. Graphs of the curves for mating abil- 

 ity versus number of matings indicate that small 

 old-shell and large new-shell males have the 

 least linear relationship of the four groups. The 

 points i)lotted in Figures 1 and 2 are the means 



of the transformed variables for each successive 

 mating. A point may represent as few as one or 

 as many as ten observations, as shown in Tables 

 2 and 3. The original to 100 scale is attached 

 to the graphs to make them easier to read; thus 

 after the means are computed, they are trans- 

 formed back to the original scale. 

 The slopes of the functions were approximated 

 by computing the means of the transformed 

 measurement variables for each x and fitting 

 empirical curves to the data points. Figures 1 

 and 2 show the relationship between percent of 

 eggs fertilized and relative fullness of brood 

 chamber respectively and are presented primar- 

 ily as an aid to fisheries management. The 

 results, however, are quite consistent with those 

 given in Table 4. The graphs show a marked de- 

 cline in the mating ability of small old-shell 

 males after approximately the seventh mating 

 and a decline in the ability of large new-shell 

 males after the tenth mating. Figure 2 indicates 

 that partial clutches result from mating with 

 small old-shell and large new-shell males which 

 had mated several times previously. 



The least squares regression lines for large 

 old-shell males and small new-shell males are 

 also plotted in Figures 1 and 2. These groups 

 show little decrease in mating ability as the 

 number of matings increases, particularly for 

 the percent of eggs fertilized. The slope of the 



176 



