Zeppelin et al.: Sizes of walleye pollock and Atka mackerel consumed by Eumetopias lubatus 



513 



Results 



Regression formulae 



A total of 517 pollock and 191 Atka mackerel samples 

 were used to develop the regression equations of bone 

 and otolith measurement to fork length. The sample size 

 and range of fish lengths used for the regressions varied 

 between species and cranial structures (Table 1). No 

 clear indications of sample size required for regression 

 analysis are currently provided in the literature; how- 

 ever, Owen and Merrick (1994) recommend a minimum 

 sample size of 30-40. Sample sizes used to develop equa- 

 tions presented here ranged from 44 to 508. 



In general, linear models were used for regression 

 equations; however, several cranial structures were 

 best fitted with a quadratic model. For both species, 

 all structures were strongly related to fork length (r 2 

 range: 0.78-0.99; Table 1). The regressions encompassed 

 the majority of sizes of bones and otoliths found in Stell- 

 er sea lion scat samples for this study. However, a small 

 proportion of walleye pollock bones from scats were 

 larger than those used to develop the regressions. 



Frost and Lowry (1981) developed otolith linear re- 

 gression equations for walleye pollock from the Bering 

 Sea using a double-regression approach that produced 

 an inflection point at 10 mm. We examined the double 

 regression approach but found a higher degree of corre- 

 lation using a quadratic regression model. We compared 

 the results of our model with Frost and Lowry 's (1981) 

 model and found that estimated fork lengths of walleye 

 pollock differed less than 2 cm across the length range 

 in our samples. 



Estimation of size of walleye pollock and Atka mackerel 

 consumed by Steller sea lions in the Bering Sea 

 and Gulf of Alaska 



A total of 714 scats from 39 sites contained 3646 selected 

 cranial elements from either walleye pollock or Atka 

 mackerel. Of those, 212 scats contained 666 walleye 

 pollock cranial elements with a condition grade of either 

 "good" (ft =236) or "fair" (n = 430). The minimum number 

 of individual pollock per scat ranged from 1 to 18 with 

 a mean of 1.6 (SD = 1.7). For Atka mackerel, 379 scats 

 contained 1685 skeletal elements with condition grade 

 of either "good" (;?=755) or "fair" (rc=930). The minimum 

 number of individual Atka mackerel per scat ranged 

 from 1 to 14 with a mean of 1.9 (SD = 1.6). 



The mean fork length of walleye pollock consumed by 

 Steller sea lions in the Bering Sea and Gulf of Alaska es- 

 timated from uncorrected otoliths found in scats was 23.7 

 cm (SD=12.0; « = 88). Application of the DCF increased 

 the mean estimate to 28.4 cm (SD=14.75; rc=88). The size 

 distribution estimated from corrected otoliths had three 

 modes: a major mode around 32 cm and minor modes 

 around 5 cm and 13 cm (Fig. 2A). Confidence intervals for 

 all grade-corrected estimates can be found in Table 1. 



The mean fork length of walleye pollock estimated 

 from all seven structures was 39.8% greater than the 



mean estimated from otoliths alone. The uncorrected 

 mean was 33.1 cm. Applying the DCF increased the 

 mean length of walleye pollock by 18.7% to 39.3 cm 

 (paired t test, ? 665 =37.9, P<0.001). Mean grade-corrected 

 size estimates for cranial structures other than otoliths 

 ranged from 34.5 cm (PHAR) to 47.2 cm (HYPO) and 

 95% confidence intervals ranged from 25.2 to 50.6 cm 

 (Table 2). The condition-specific DCFs increased length 

 estimates between 6.8% (HYPO) and 28.3% (DENT). 

 The size distribution estimated from all grade-corrected 

 structures had three modes: a major mode around 44 cm 

 and minor modes around 5 cm and 15 cm (Fig. 2A). 



The mean fork length of Atka mackerel consumed by 

 Steller sea lions in the Bering Sea and Gulf of Alas- 

 ka estimated from uncorrected otoliths was 30.3 cm 

 (SD=4.0; n=117). Application of the DCF increased the 

 mean estimate to 34.7 (SD = 4.8; n=U7). 



The mean fork length of Atka mackerel estimated 

 from all structures (30.7 cm; SD = 5.9 cm, corrected 

 32.3 cm; SD = 5.9 cm, rc=1685, paired t test, f 1684 =39.1, 

 P<0.001) was similar to the mean estimated from oto- 

 liths (6.9% less without a DCF and 1.3% less with a 

 DCF; Fig. 2B). Mean grade-corrected size estimates 

 for structures other than otoliths ranged from 26.6 cm 

 (QUAD) to 34.2 cm (INTE) and 95% confidence inter- 

 vals ranged from 24.0 cm (DENT) to 35.0 cm (INTE; 

 Table 2). Use of the condition-specific DCFs increased 

 length estimates between 2.1% (INTE) and 24.0% 

 (DENT). Fork length estimates for all structures did 

 not include PHAR because too few were recovered in 

 scats in the feeding studies of captive Steller sea lions 

 to develop a correction factor. 



When mean prey size was calculated by using MNI, 

 the mean corrected and uncorrected size estimate of 

 both walleye pollock and Atka mackerel differed by less 

 than 0.2 cm from estimates derived by using all struc- 

 tures. There was little difference in the standard devia- 

 tions or distributions when MNI estimates were used 

 compared with all structures (Table 2). Unsurprisingly, 

 the use of MNI estimates did substantially reduce the 

 sample size (336/666 for walleye pollock and 722/1685 

 for Atka mackerel). 



Spatial and temporal variation in size of pollock and 

 Atka mackerel consumed by Steller sea lions 



No statistical difference was found in the proportion of 

 pollock stage classes among years on summer rookery 

 sites (P=0.29, ^ 2 = 4.9, df=3) or winter haul-out sites 

 (P=0.10; Fisher's exact test). Scats were collected only 

 on summer haul-out sites during 2000. Although sample 

 sizes were limited, we found significant differences in 

 the proportion of pollock stage classes between summer 

 rookery and haul-out scats (P=0.02; Fisher's exact test) 

 and between summer and winter haul-out sites (P=0.018; 

 Fisher's exact test) for year 2000. A greater proportion 

 of juvenile pollock were found on summer haul-outs 

 (64%' juveniles, n=ll scats) than on summer rookeries 

 (9% juveniles, n = 132 scats) or winter haul-out sites (3% 

 juveniles, n = 69 scats, Fig. 3). No statistical difference 



