24 



Fishery Bulletin 105(1) 



Length-fecundity relationships 



Length-fecundity relationships and their 95% confidence 

 intervals were computed for potential annual fecundity 

 iFj), batch fecundity (B,), and the number of atretic 

 oocytes (£,) by using nonlinear regression in S-plus 

 (Venables and Ripley, 2002) with the following model: 



Y=aL'' 



(4) 



S-plus) of the predicted values for potential fecundity- 

 at-length and atresia-at-length: 



Var( R, ) = Vari F, ) + Var( E, ). 

 Annual number of batches spawned 



(6) 



The potential number of batches spawned for each speci- 

 men i was estimated from 



where y = F,, S,, E,; 



a and b = fecundity parameters to be estimated; and 

 L = fork length. 



Oocyte atresia 



Occurrence of atresia was divided into high occurrence 

 (more than 10% of oocytes are atretic) and low occur- 

 rence (less than 10% of oocytes are atretric) by exam- 

 ining visually all histological slides. Because incidence 

 of atresia was low in prespawning- and spawning-stage 

 ovaries, it was not quantified further. 



The occurrence of oocyte atresia in spent oocytes 

 or oocytes that had been spawned was determined by 

 counting the number of atretic oocytes present in the 

 tissue sample of whole oocytes. Atretic eggs were eas- 

 ily distinguished from nonatretic eggs by their shriv- 

 eled appearance, dark to almost black coloration, and 

 dense texture. In postspawning fish, it appeared that 

 all oocytes in an advanced stage were atretic and that 

 stage-4 or smaller oocytes were healthy (Fig. 2A). 

 When the histological slides of the same specimen were 

 examined for verification of the oocyte stages, it ap- 

 peared that all atretic oocytes that were counted corre- 

 sponded to alpha and beta atresia stages (Hunter and 

 Macewicz, 1985). The total number of atretic oocytes 

 for each specimen {E^} was calculated by multiplying 

 atretic oocytes per gram of tissue by total weight of 

 both ovaries. 



Realized annual fecundity 



Realized annual fecundity is defined as the number of 

 oocytes actually spawned per fish in a given year. In 

 order to take the occurrence of atresia into account, a 

 predicted realized fecundity-at-length was calculated 

 by subtracting predicted atresia-at-length from the pre- 

 dicted potential fecundity-at-length, by using 



DPOI 



B. 



(7) 



Ri = F,-Ei, 



(5) 



where i?, = estimated realized annual fecundity at length 



/; 



^,= estimated potential annual fecundity at 



length /; and 

 ^i = estimated number of atretic oocytes at length 



/. 



Variance (Var) of the predictions at length was cal- 

 culated as the sum of the variances (estimated with 



where (Df°') = the potential number of batches spawned 



for each specimen i; 



F- = potential fecundity for specimen i, and 

 B, = batch fecundity for specimen i. 



Batch number for realized fecundity for specimen i 

 was calculated by using the predicted proportion of 

 atretic eggs per length category and applying it to each 

 specimen: 



where 



^" = B. 



F, 



(8) 



(9) 



where Z),7°' = the batch number per specimen i at 

 length Z; 

 pf = the predicted proportion atretic at length 



/; 



El = the predicted number of atretic eggs at 



length /; and 

 Fi = the predicted potential fecundity at 



length /. 



The relationship between batch number and length 

 was examined for both potential and realized fecundity 

 with linear regression (S-plus). 



Results 



Data collection 



Nine samples were collected after spawning events in 

 October 1993 in NMFS statistical areas 542 (« = 4) and 

 620 (n = 5) (Table 1, Fig. 1). One hundred-fifty fish were 

 collected from June through August in 1994 in NMFS 

 statistical areas 541 (/! = 57), 542 (n = 49), and 543 (« = 44). 

 Most (130) of these fish were in prespawning condition, 

 i.e., contained no postovulatory follicles, and 20 had 

 spawned at least one batch of eggs. Because the fish were 

 collected during the NMFS Aleutian survey, which sys- 

 tematically moves from east to west along the Aleutian 

 archipelago, all specimens in area 541 (Eastern Aleutian 

 Islands) were considered prespawning fish Spawning 

 commenced in late July in area 542 and by the middle 

 of August all fish collected showed signs of spawning. 



