54 



Fishery Bulletin 100(1) 



time series, standard regression models, including survey 

 date but excluding effects of environmental covariates, 

 were used to examine seasonal patterns and trends. We 

 believe the exclusion of other covariates during statistical 

 modeling had little effect on trend estimates because sur- 

 veys were conducted consistently over years and over 

 the entire year interval, resulting in large sample sizes 

 (?! = 1134 surveys conducted; range among years 1974- 

 96: 45 to 52 surveys/year). It is unlikely that population 

 trend estimates were confounded by changes in environ- 

 mental conditions because no obvious annual trends in 

 environmental conditions over the 22 years of the study 

 (weather and tide data were collected daily [at 1000 hours] 

 at Southeast Farallon Island) were apparent, except for a 

 potential increasing annual trend in sea surface tempera- 

 ture (PRBO. unpubl. data^). 



Seasonal abundance patterns To examine seasonal abun- 

 dance patterns, polynomial regression (Kleinbaum et al.. 

 1988) was used to fit a cui-ve to counts pooled over years, 

 1974 to 1996. Data from 1971 to 1973 were excluded 

 because survey methods were not standardized until the 

 end of 1973. We fitted the regression model by first con- 

 verting Julian date to orthogonal polynomial variables 

 (linear combinations of the natural polynomial variables 

 that contain the same information as the natural polyno- 

 mial variables but are uncorrelated to each other) to avoid 

 problems of multicollinearity when using higher-order 

 terms (POeinbaum et al., 1988). Higher-order terms were 

 then added sequentially until the last term was not signif- 

 icant in the model (forward stepwise procedure, P>0.05). 

 We then added year as a variable to the model and tested 

 the year x date interaction to determine if the seasonal 

 pattern varied significantly among years. To examine sea- 

 sonal patterns by sex and age class, polynomial regression 

 curves were fitted separately to counts of adult females, 

 males (adults and subadults pooled), and immature indi- 

 viduals as described above. We excluded surveys in which 

 not all individuals were identified by sex and age class (i.e. 

 all surveys before 1977). 



Annual abundance trends Because high-order polynomial 

 models were used to address seasonal haulout patterns, 

 annual abundance trends were examined in a separate 

 analysis to simplify results. Seasonal variability in abun- 

 dance was accounted for in annual trend models by using 

 residuals from the regression of Julian date on counts. 

 Assuming e.xponential rates of change, we log-transformed 

 (log^,) the residuals (centered about the mean count) and 

 regressed the transformed residuals against the variable 

 year. Annual rates of change were calculated as el\-^,^^ - 1 

 X 100%, where Pycar 's ^^^ regression coefficient for annual 

 trend (Caughley, 1977). The following groups were ana- 

 lyzed: 1) all animals, by pooling data over all 12 months 

 and sex and age classes; and 2) each sex and age class, by 

 pooling over a) all months, and b) two periods when peaks 

 in counts were observed for some age classes (the breed- 

 ing [May-July] and late fall through early winter [Sep- 

 tember-December] seasons). Nonlinearity in trend was 

 assessed by using orthogonal polynomials as described 



earlier in this article. Assumptions of the regression model 

 were verified by visual inspection of residuals. 



Trends In pup production, reproductive rate, and adult sex 

 ratio during the breeding season We used linear regres- 

 sion to test if the decline in maxnnum pup counts during 

 sui-veys presented in Sydeman and Allen (1999) was sig- 

 nificant. We used only data after 1977, when counts by 

 age class were conducted consistently. Only data from sur- 

 veys conducted from June to July were included because 

 during the fall, the ability to distinguish young-of-the year 

 from immature individuals was difficult and because an 

 influx of nonnative pups may have occurred. For example, 

 in November 1978, five times the number of pups known 

 to have survived the breeding season and an increased 

 number of adult females were observed (PRBO, unpubl. 

 data^). The origin of these young-of-the-year is unknown, 

 but the nearest known pupping areas are Aiio Nuevo Island 

 and the North Farallon Islands. Although Steller sea lions 

 are present at Point Reyes, no pups have been obsei-ved 

 there in the past two decades (Sydeman and Allen, 1999). 

 To examine averages and trends in adult sex ratio and 

 reproductive rate, we used maximum counts of adult fe- 

 males, adult males, and pups during June and July in each 

 year and linear regi'ession to test for annual trends. Re- 

 productive rate was calculated as the maximum count of 

 pups divided by maximum count of adult females. Because 

 not all pups born were observed during surveys, we in- 

 creased the maximum count of pups by 57%, the average 

 amount that maximum pup counts underestimated true 

 pup production from 1973 to 1986 (range: 33-90''^ among 

 years). This average was determined from unpublished 

 data of pup production as determined from daily observa- 

 tions of breeding areas (Huber et al.'^). 



Results 



Seasonal abundance patterns 



When data from all sexes and age classes were pooled, 

 the seasonal abundance pattern was bimodal; one peak in 

 numbers occurred before and during the breeding season 

 (April-July) and another peak occurred from late fall 

 through early winter (October-December; Fig. 2A). The 

 regression model was complex with significant date and 

 higher-order terms (variables date- through date'^); all 

 P<0.001; adjusted r-=0:28. ;i = 1134); the variable date-' 

 was not significant (P>0.65). Counts varied significantly 

 with year (P<0.001) and the seasonal pattern varied sig- 

 nificantly among years (datexyear through date^xyear; 

 P<0.001; adjusted r-=0.61 ). Total numbers during the peak 



'^ Huber, H. R., D. G. Ainley, R. J. Boekelheide, R. R Henderson, 

 and T. J. Lewis. 1988. Annual and seasonal variation in num- 

 bers of pinnipeds on the Farallon Islands. California (Table 

 3). Final report to the National Marine Mammal Laboratory, 

 National Marine Fisheries Service. Seattle, WA, 3.5 p. [Avail- 

 able from Point Re.yes Bird Observatory, 4990 Shoreline Hwy., 

 Stinson Beach, CA 94970.1 



