Ecological Archives A016-051-A1

M. Zachariah Peery, Benjamin H. Becker, and Steven R. Beissinger. 2006. Combining demographic and count-based approaches to identify source-sink dynamics of a threatened seabird. Ecological Applications 16:1516–1528.

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 “zig-zag” 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95% of at-sea locations obtained from 48 radio-marked murrelets in the breeding season (M. Z. Peery, unpublished data) and we therefore assumed that at-sea surveys provided a reasonable estimate of total numbers of murrelets in the central California region.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 sea-surface 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 half-normal key series with a cosine series expansion (Buckland 2001), because previous work indicates that this model fits distance data from at-surveys 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, sea-surface condition, sea-surface condition and observer) using AIC values. Survey-specific 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, survey-specific density estimates were multiplied by the area surveyed (104.65 km2) 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 at-sea 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 line-transect sampling at-sea.  (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




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