FISHERY BULLETIN: VOL. 79, NO. 2 



6 



no — 0)0)  



I I I 



~^ ""80 100 120 140 



CARAPACE LENGTH (mm) 



100 



Gjjgia nPioiiiigiagKDgigiiDgig i 



80 100 



CARAPACE LENGTH (mm) 



120 



Figure 5. — Percentage of male (upper) and female (lower) 

 Lithodes couesi classified adult as a function of size. The size of 

 50% maturity was estimated by first fitting a logistic equation to 

 the data, then determining the size (shown by dotted lines) 

 corresponding to 50% mature. 



P. camtschatica (Haynes 1968), L. aequispina 

 (Hiramoto and Sato 1970), and L. antarctica (Guz- 

 man and Campodonico 1972). 



An attempt was made to develop an appropriate 

 functional relationship to describe the fecundity 

 and size of L. couesi. To determine whether or not 

 this relationship should be curvilinear, the fit of a 

 second degree polynomial was statistically com- 

 pared with that of a straight line. The coefficient of 



o 

 o 

 o 



CO 



O 

 O 



LLI 



DC 

 LU 

 00 2 



80 90 100 110 



CARAPACE LENGTH (mm) 



120 



Figure 6. — Fecundity o^ Lithodes couesi as a function of size. 

 An asymptotic curve was fit to the data using methods described 

 in the text. Three specimens ( shown by circles) had conspicuously 

 fewer eggs. Although these females did not appear to be 

 damaged, their fecundities were excluded from the analysis. 



the squared term of the polynomial was highly 

 significant (F = 12.23, P< 0.001), indicating that 

 the polynomial fit the data better than a straight 

 line; however, a second degree polynomial was not 

 a good relationship because the predicted fecun- 

 dity did not increase monotonically with size. 

 Since it is unlikely that fecundity reaches some 

 maximum and then diminishes with size, an 

 asymptotic curvilinear relationship was consid- 

 ered. The chosen equation is E = E^ - Ae~ , 

 where E is egg number, L is carapace length, E^ 

 is a parameter representing the theoretical maxi- 

 mum number of eggs that can be carried, and A 

 and B are parameters controlling the rate at 

 which the maximum egg number is achieved. 

 Using nonlinear regression, the best fit was ob- 

 tained when E = 4,329 - 3.19 x 10^ ^-0172^ 

 (Figure 6). 



If the number of eggs a female could carry were 

 limited either by the length of the pleopods or by 

 the volume of the brood chamber enclosed between 

 the abdomen and the sternum, then fecundity 

 should increase in proportion to the carapace 

 length raised to a power of one or greater, that 

 is, fecundity should be an upwards concave func- 

 tion of size. The best fitting equation is concave 

 downwards, which indicates that some other 

 mechanism limits fecundity in L. couesi. One 

 possible explanation is that the low oxygen con- 



264 



