Appendix A. Estimating the population size of Marbled Murrelets with distance sampling.
We conducted surveys from Half Moon Bay to Santa Cruz, California from1999 to 2003 with a 4.5 m inflatable vessel along approximately 100 km “zigzag” transects that were delineated from 200 to 2,500 m offshore (Fig. 1) to estimate the population size of Marbled Murrelets in central California. The area surveyed encompassed >95% of atsea locations obtained from 48 radiomarked murrelets in the breeding season (M. Z. Peery, unpublished data) and we therefore assumed that atsea surveys provided a reasonable estimate of total numbers of murrelets in the central California region. We divided the area surveyed into a nearshore stratum (200 to 1350 m from shore) and offshore stratum (1350 m to 2500 m from shore) and placed approximately three times more effort in the nearshore stratum. Surveys were conducted from June through August with one observer scanning on each side of the vessel. The starting point of each transect with respect to distance from shore was randomized such that a unique transect was followed for each survey. We recorded the number of murrelets observed in each group and their distance from the transect line by estimating the distance and angle of the group from the boat following Becker et al. (1997). Observers were trained to estimate distances and angles using floats placed at known distances from the boat for several days prior to conducting surveys and were periodically tested during the field season.
We estimated the density of Marbled Murrelets from the counts of individuals using program DISTANCE (Buckland et al. 2001). An important component of distance sampling is to model the detection function (g(x)), which describes the probability of detecting a group of individuals as a function of distance from the transect line. A global detection function (i.e., common to all surveys) was modeled for each year because sample sizes were often too small to permit robust parameter estimation for individual surveys. Modeling the detection data separately for each year resulted in different detection functions each year and accommodated detection probabilities that varied among years. We included observer and seasurface condition (Beaufort Scale) as potential covariates in the global detection function to take into account variation in viewing conditions and observer ability. All detections functions were based on a halfnormal key series with a cosine series expansion (Buckland 2001), because previous work indicates that this model fits distance data from atsurveys for Marbled Murrelets well in our region (S. R. Beissinger, unpublished data). We then ranked four competing models for the detection function with various combinations of the covariates (no covariates, observer, seasurface condition, seasurface condition and observer) using AIC values. Surveyspecific estimates of density ( ; birds/km) were obtained using parameters from the model with the lowest AIC score and the following equation
where (0) was the value of the probability density function of perpendicular distances from the transect evaluated at zero distance, was the expected number of groups, was the expected number of birds per group, and L was the length of the line transect (km) (Buckland et al. 2001). Finally, surveyspecific density estimates were multiplied by the area surveyed (104.65 km^{2}) and averaged to obtain annual estimates of population size.
We detected a total of 878 groups of murrelets from 1999–2003. Models for the detection function with no covariates best explained the distribution of detection distances in 1999 and 2000, but models with both observer and viewing conditions ranked the highest in 2001–2003 (Table A1). Using the best model for each year, the population size ranged from 487 to 637, with the largest increase occurring between 2000 and 2001 (Table A2).
TABLE A1. Akaike’s Information Criteria (AIC) values for competing models of the detection function used to estimate the regional population size of Marbled Murrelets in central California from 1999–2003 with atsea surveys. K = number of parameters in the detection function. ΔAIC values represent the difference between the AIC score of the model in question and the highest ranked model (Burnham and Anderson 2002). 

Model 
ΔAIC 
AIC 
K 
Year: 1999 



No Covariates 
0 
1209.92 
1 
Viewing Conditions 
0.40 
1210.31 
2 
Observer 
2.75 
1212.67 
3 
Viewing Conditions + Observer 
3.39 
1213.31 
4 
Year: 2000 



No Covariates 
0 
1619.17 
1 
Viewing Conditions 
1.97 
1621.14 
2 
Observer 
2.46 
1621.63 
3 
Viewing Conditions + Observer 
4.42 
1623.59 
4 
Year: 2001 



Viewing Conditions + Observer 
0 
613.23 
4 
Viewing Conditions 
2.35 
615.58 
2 
Observer 
4.08 
617.32 
3 
No Covariates 
13.30 
626.53 
1 
Year: 2002 



Viewing Conditions + Observer 
0 
1147.31 
5 
Viewing Conditions 
4.42 
1151.73 
4 
Observer 
19.28 
1166.59 
2 
No Covariates 
19.42 
1166.73 
1 
Year: 2003 



Viewing Conditions + Observer 
0 
991.79 
5 
Viewing Conditions 
5.73 
997.52 
3 
Observer 
6.88 
998.67 
3 
No Covariates 
10.21 
1002.10 
1 
TABLE A2. Population size estimates () for Marbled Murrelets in central California using linetransect sampling atsea. (0) = the probability density function evaluated at zero meters from the transect line and n = the number of surveys. 

Year 
Stratum 
CV 
Lower 95% CL 
Upper 95% CL 
(0) 
CV 
n 

1999 
Nearshore 
399 
0.134 
307 
518 




Offshore 
88 
0.706 
25 
307 




Both 
487 
0.105 
333 
713 
0.0152 
0.071 
5 









2000 
Nearshore 
446 
0.186 
311 
639 




Offshore 
51 
0.379 
25 
104 




Both 
496 
0.173 
338 
728 
0.0174 
0.057 
8 









2001 
Nearshore 
610 
0.169 
440 
847 




Offshore 
27 
0.64 
8 
84 




Both 
637 
0.164 
441 
920 
0.0189 
0.054 
8 









2002 
Nearshore 
628 
0.117 
500 
789 




Offshore 
0 
0 
0 
0 




Both 
628 
0.117 
487 
809 
0.0188 
0.051 
9 









2003 
Nearshore 
554 
0.132 
428 
716 




Offshore 
61 
0.492 
24 
132 




Both 
615 
0.131 
463 
815 
0.0182 
0.067 
6 