Regional Population 

Monitoring of the Marbled 

Murrelet: Field and 

Analytical Methods

Martin G. Raphael, Jim Baldwin, Gary A. Falxa, Mark H. Huff, 

Monique Lance, Sherri L. Miller, Scott F. Pearson, C. John Ralph, 

Craig Strong, and Chris Thompson

United States 

Department of 

Agriculture

Forest Service

Pacific Northwest 

Research Station

General Technical Report

PNW-GTR-716

May 2007

DEPAR TMENT OF AGRICULT URE
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Authors

Martin G. Raphael is a research wildlife biologist, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, 3625 93rd Avenue SW, 

Olympia, WA 98512-9193; Jim Baldwin is a statistician, U.S. Department of Agriculture, Forest Service, Pacific Southwest Research Station, P.O. Box 245, Berkeley, 

CA 94701; Gary A. Falxa is a wildlife biologist, U.S. Fish and Wildlife Service, 

Arcata Fish and Wildlife Office, 1655 Heindon Rd., Arcata, CA 95521; Mark H. 

Huff was a wildlife biologist and branch chief of science support, U.S. Fish and 

Wildlife Service, 911 NE 11th Avenue, Portland OR 97232. Huff is now North 

Coast and Cascades Network Monitoring Coordinator, National Park Service, 333 

SW First Ave., Portland, OR 97208-3623; Monique Lance is a fish and wildlife 

biologist, Washington Department of Fish and Wildlife, 7801 Phillips Road SW, 

Tacoma, WA 98498; Sherri L. Miller is a wildlife biologist, and C. John Ralph

is a research wildlife biologist, U.S. Department of Agriculture, Forest Service, 

Pacific Southwest Research Station, 1700 Bayview Drive, Arcata, CA 95521; Scott 

F. Pearson is a research scientist and Chris Thompson was a research scientist, 

Washington Department of Fish and Wildlife, 600 Capitol Way N, Olympia, WA 

98501; Thompson is now senior associate, Environment International, Ltd., 5505 

34th Ave. NE, Seattle, WA 98105; Craig Strong is a consulting biologist, Crescent 

Coastal Research, P.O. Box 2108, Crescent City, CA 95531, Crescent City, CA.
Raphael, Martin G.; Baldwin, Jim; Falxa, Gary A.; Huff, Mark H.; Lance, 

Monique; Miller, Sherri L.; Pearson, Scott F.; Ralph, C. John; Strong, 

Craig; Thompson, Chris. 2007. Regional population monitoring of the marbled 

murrelet: field and analytical methods. Gen. Tech. Rep. PNW-GTR-716. Portland, 

OR: U.S. Department of Agriculture, Forest Service, Pacific Northwest Research 

Station. 70 p.

The marbled murrelet (Brachyramphus marmoratus) ranges from Alaska to California and is listed under the Endangered Species Act as a threatened species in 

Washington, Oregon, and California. Marbled murrelet recovery depends, in large 

part, on conservation and restoration of breeding habitat on federally managed 

lands. A major objective of the Northwest Forest Plan (the Plan) is to conserve and 

restore nesting habitat that will sustain a viable marbled murrelet population. Under 

the Plan, monitoring is an essential component and is designed to help managers 

understand the degree to which the Plan is meeting this objective. This report 

describes methods used to assess the status and trend of marbled murrelet populations under the Plan. 

Our monitoring plan is specifically designed to estimate marbled murrelet 

density, population size, and population trend in each of five geographic areas (conservation zones) between the northern tip of Washington state and San Francisco, 

California. Within each zone, we defined an offshore boundary denoting the extent 

of the target population. We then divided the shoreline into 20-km segments (primary sample units, denoted as PSUs) and drew a stratified random sample of about 

30 PSUs for each zone. For each PSU survey, observers in small boats followed a 

prescribed at-sea transect line and recorded perpendicular distances to all murrelets 

observed from mid-May to the end of July when murrelets detected on the water are 

most likely locally breeding birds. We use distance sampling methods to compute 

density and population estimates for the target population each year. This sampling 

design was implemented during the 2000 field season and sampling has continued 

each year thereafter. This report describes our sampling design, survey methods 

and analysis methods. To help illustrate our methods, we present results from the 

2005 field season. The total population estimate that year was approximately 20,200 

murrelets with a 95 percent confidence interval ranging from 16,000 to 24,500 

murrelets. We emphasize that this is the first systematic sampling protocol applied 

throughout the murrelet’s listed range. Because these methods have not been used 

in the past, our current population estimates are not directly comparable to past 

estimates from other researchers.

Keywords: Brachyramphus marmoratus, distance sampling, line transect, 

marbled murrelet, Northwest Forest Plan, population monitoring.

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Introduction

Marbled murrelets (Brachyramphus marmoratus) range from Alaska to California 

and are federally listed under the U.S. Endangered Species Act as threatened in 

Washington, Oregon, and California (USFWS 1997). Recovery of the murrelet 

depends, in large part, on conservation and restoration of breeding habitat on 

federally managed lands. Conservation of murrelet nesting habitat was one of the 

major objectives of the Northwest Forest Plan (hereafter the Plan). Under the Plan, 

the goal was to conserve and restore nesting habitat on federally administered 

lands that will sustain a viable murrelet population (FEMAT 1993). Monitoring is 

an essential component of the Plan and is meant to help managers understand the 

degree to which the Plan is meeting this objective. This report describes the methods used to assess the status and trend of the marbled murrelet in the portion of its 

range covered by the Plan. 

Madsen et al. (1999) developed an approach for marbled murrelet effectiveness 

monitoring under the Plan that recommended assessing population trends at sea 

under a unified sampling design and standardized survey methods. Inland, the goal 

was to establish a baseline estimate of suitable nesting habitat. The trends in population abundance and nesting habitat would be tracked over time. The ultimate goal 

was to model population trends based on the amount and distribution of nesting 

habitat. If that modeling effort is successful, then managers might monitor nesting habitat as a surrogate to monitoring murrelet populations over the long term. 

However, until this relationship is established, population monitoring will be the 

primary murrelet monitoring tool. This report provides an overview and application 

of current population monitoring methods. 

In 1998, the U.S. Fish and Wildlife Service named a team leader and assembled 

a team of experts to design and implement a population monitoring protocol. The 

population team members were Naomi Bentivoglio, Team Lead, U.S. Department of the Interior, Fish and Wildlife Service; Steven R. Beissinger, professor, 

University of California, Berkeley; Jim Baldwin, statistician, U.S. Department of 

Agriculture, Forest Service, Pacific Southwest Research Station, Tim Max, statistician, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research 

Station; Sherri L. Miller, wildlife biologist, U.S. Department of Agriculture, Forest 

Service, Pacific Southwest Research Station; Ken Ostrom, GIS/database specialist, 

U.S. Department of the Interior, Fish and Wildlife Service; C.J. Ralph, research 

wildlife biologist, U.S. Department of Agriculture, Forest Service, Pacific Southwest Research Station; Martin G. Raphael, research wildlife biologist, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station; Craig 


GENERAL TECHNICAL REPORT PNW-GTR-716

Strong, consulting biologist, Crescent Coastal Research; and Chris Thompson, 

research scientist, Washington Department of Fish and Wildlife.

Because of the murrelet’s crepuscular activity and cryptic nature in its nesting habitat high in forest canopies throughout much of its range, there is general 

consensus that populations are best assessed at sea (Becker and Beissinger 1999, 

Becker et al. 1997, Madsen et al. 1999, Huff et al. 2006). Members of the population 

team identified the target population for monitoring as those birds in the nearshore 

waters (generally within 8 km of shore) from the Canadian border to San Francisco 

Bay, the area associated with the Plan. The team divided the target population into 

the marbled murrelet conservation zones identified in the marbled murrelet Recovery Plan (USFWS 1997, fig. 1). The isolated subpopulation found in San Mateo and 

Santa Cruz Counties (Conservation Zone 6) was not included in monitoring as no 

federal lands associated with the Plan are found there. 

Methodological tests (e.g., evaluation of distance estimation techniques, efficacy of single versus double observers) were conducted during the 1998 and 1999 

field seasons. Those baseline data, as well as data on the offshore distribution of 

murrelets obtained from earlier surveys, permitted the team to reach consensus 

on the methods and sampling design for a pilot project in the 2000 field season. 

Table 1 and the following discussion describe the agreed-upon sampling design 

and the population monitoring program. This report is an expansion of an earlier 

publication (Miller et al. 2006) and is intended to provide additional detail to more 

fully describe our methods and analytical procedures. Miller et al. (2006) provided 

results of our population surveys for the years 2000 through 2003.

Sampling Design 

Spatial Target Population

The marbled murrelet Recovery Plan (USFWS 1997) identified six conservation 

zones, five within the Plan area. The recovery plan states that when populations 

within four of six zones have stable or increasing numbers, murrelets may 

have reached recovery status. For this reason, we designed our sampling frame 

to permit a separate population trend estimate for each of the five zones. The 

target population is contained within Conservation Zones 1 through 5 (fig. 1). 

The northern boundary is the U.S.-Canada border and the southern boundary is 

approximately San Francisco Bay. Within this area, we targeted the ”nearshore” 

waters, 8 km or less from shore. The inshore boundary was defined by the closest 

possible navigable distance from the shore outside the surf zone (i.e., away from 

the surf, rocks, and kelp). The offshore boundary varied within and among 

Because of the 

murrelet’s crepuscular 

activity and cryptic 

nature in its nesting 

habitat high in forest 

canopies throughout 

much of its range, 

there is general 

consensus that 

populations are best 

assessed at sea.
Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Table 1—Population sampling design overview

Conservation zone

Attribute Stratum 1 2 3 4 5

Area of inference (m from shore) 1 300–5000 350–5000 350–5000 350–3000 350–3000

2 100–2000 350-8000 350-5000 350-3000 350-3000

3 100–2000

Centerline distance (m from shore) 1 1500 1500 1500 2000 2000

2 500 1500 1500 2000 2000

3 NAd

Total PSUsa available 1 9 8 7 14 8

2 42 6 10 8 8

3 47

 Total 98 14 17 22 16

Number of unique PSUs sampledb 1 5 8 7 14 7

2 20 5 10 7 5

3 5

 Total 30 13 17 21 12

Total PSUs sampledb c 1 10 21 `12 16 10

2 40 5 16 15 5

3 10

 Total 60 26 28 31 15

Total km surveyedb 1 105 299 438 602 653

2 1398 354 564 891 139

3 197

 Total 1700 653 1002 1493 792

Total area of zone (km2)

b 1 840 724 661 739 442

2 1196 926 935 427 442

3 1459

 Total 3494 1650 1596 1165 885

a

PSU = primary sample unit, an area of ~20 km in length along the coast and 2000 m, 3000 m, 5000 m, or 8000 m in width off the coast. 

b

Sample sizes refer to the 2005 field season; sample sizes in other years vary slightly.

c

Total number of PSUs sampled, including repeated samples from the same PSU.

d

In Stratum 3 of Zone 1, we do not distinguish the inshore and offshore subunits and follow a zigzag transect throughout each PSU.

conservation zones and portions of zones. This distance was approximated for 

each zone or for each stratum (geographic areas with different densities of 

murrelets—see below) within the zones by using available data on the relative 

abundance of murrelets in relation to distance from shore. We do not foresee a 

consistent long-term increase of birds beyond our offshore boundaries. However, 

if evidence from other studies suggests a change in distribution further offshore, 

extending the offshore boundary may be necessary. 
GENERAL TECHNICAL REPORT PNW-GTR-716

Figure 1—Forest Plan and marbled murrelet recovery plan conservation zones.

Temporal Target Population

Mid-May through mid- or late-July is the time of year when breeding birds at sea 

are likely to be associated with inland nesting habitat in the Plan area (Nelson 

1997). As a result, we established 15 May through 31 July as our population 

sampling period.


Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Stratification

Within each zone, researchers identified large geographic areas along the coast, 

designated as strata. See fig. 2 for an example and Miller et al. (2006) for a more 

detailed map of each stratum within each zone. In Zone 1, Stratum 1 is the Strait 

of Juan de Fuca, Stratum 2 is the San Juan Islands and selected portions of Puget 

Sound, and Stratum 3 is the remainder of Puget Sound. In the other zones, Stratum 

1 is the northern portion of the zone and Stratum 2 is the southern portion. Strata 

were selected to distinguish areas of coast with differing densities of murrelets 

(based on available data from previous surveys or existing literature). Sampling 

Figure 2—Sample layout of strata and primary sample units, numbered 1–17, for one conservation 

zone.

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Marbled Murrelet 

Conservation Zone 3

Stratum 1

Zone 3

Stratum 2

o 20 0 20 40 60 Kilometers
GENERAL TECHNICAL REPORT PNW-GTR-716

occurred within each geographic stratum; however, a separate population estimate 

was not made for each of these strata. In general, strata with low densities of 

murrelets received less sampling effort, strata with high densities received greater 

sampling effort, and all those data within a zone were used to obtain the population 

estimate for that zone. In this way, greater precision and lower variance in 

population estimates would be achieved for the strata with higher murrelet density.

With additional sampling, separate density estimates with adequate precision 

could be obtained for a geographic stratum within a zone. This could help refine 

information about at-sea populations and the amount and distribution of inland 

habitat at scales smaller than an entire conservation zone. Our budgets did not 

allow for this during the pilot year (2000) with the exception of Zone 4. In Zone 4, 

the Pacific Lumber Company implemented a Habitat Conservation Plan under the 

Endangered Species Act that included a murrelet monitoring component (Pacific 

Lumber Company 1999). This funded additional surveys and a separate population 

estimate in the southern portion of that zone for the years 2000 to 2003 (Miller 

et al. 2006). 

Primary Sample Unit

A primary sample unit (PSU) is a roughly rectangular area along approximately 

20 km of coastline. The width of the PSU is the distance between the inshore and 

offshore boundaries (fig. 3); width varied by zone and stratum. The PSUs meet end 

to end along shore without any gaps. Each PSU consists of one inshore and one 

offshore subunit (divided by the “centerline”), and we sampled approximately 30 

PSUs per zone, totaling 93 selected from a total of 167 PSUs over all zones (see 

below). 

The inshore boundary, adjacent to the coast, was defined by the physical 

features of the shoreline that affected navigation. In some PSUs, these physical 

features are permanent obstructions, such as submerged rocks or islands. In other 

PSUs, these features are not permanent, such as kelp beds that shrink or expand 

depending on storm conditions or other environmental factors. Tidal fluctuations 

and swell height also affect navigation, especially near shore. Some areas that can 

be surveyed during high tides may be inaccessible during low tides. Although boats 

stayed a safe distance from shore, observers were able to thoroughly survey the 

area within about 50 m of the boat. Therefore, the area of inference (from which we 

calculated densities and population estimates) extends up to 50 m inshore of 

the transect lines.

A primary sample 

unit (PSU) is a roughly 

rectangular area along 

approximately 20 km 

of coastline.
Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

5 km, Segment A

5 km, Segment B

5 km, Segment C

5 km,Segment C

5000m

5 km, segment A

5 km, segment B

1500 m Centerline

5 km, segment C

5 km, segment D

5000m m

Inshore

subunit

1500 m Centerline

Inshore

subunit

Offshore

subunit

o

Figure 3—Marbled murrelet primary sample unit with inshore and offshore subunits showing 

parallel and zigzag transects. The inshore subunit is divided into four equal-length segments 

(approximately 5 km each) and four equal-width bins (bands parallel to and at increasing 

distances from the shore). One bin is selected without replacement (depicted in red) for each 

segment of transect.
GENERAL TECHNICAL REPORT PNW-GTR-716

Temporal definition of PSU—

We only used PSU surveys completed in 1 day. In many areas, afternoon winds 

increase in intensity and make it impossible to continue surveys. Partial surveys 

(where less than 75 percent of the transect length was completed) were not used 

for analysis. If a crew completed more than one PSU in a day, all survey data were 

used in analyses.

Sample size per zone—

Each conservation zone had a target sample size of 30 PSU surveys. We based this 

target on an analysis that demonstrated reasonably low coefficients of variation as 

total transect length approached 600 km (fig. 4), and 30 PSU surveys resulted in a 

total shoreline length of about 600 km.

0

0.2

0.4

0.6

0 200 400 600 800 1000

Transect length (km)

Coefficient of variation

Figure 4—Coefficient of variation in encounter rate of marbled murrelets in relation to transect length.

Method of selecting PSUs—

We segmented the entire coastline into approximately 20-km PSUs (n = 167, table 

1). Within each zone, we randomly selected a sample of PSUs. Some PSUs were 

selected more than once to achieve the desired sample size (about 30). Although 

the selection of PSUs was initially random, field sampling was subject to logistic 

constraints, such as location of ports, weather, mechanical difficulties, etc. These 

logistics sometimes resulted in some temporal and spatial clustering. We conducted 

a bootstrap analysis, accounting for these clustered observations, to estimate 
Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

the variance (and 95 percent confidence intervals) of our density estimates (see 

“Analysis” section for details).

The set of PSUs that we selected during the initial (year 2000) field season was 

and will continue to be resampled each year. Resampling selected PSUs will reduce 

variance in our estimate of population trend. Of 167 PSUs available throughout the 

target area, we sampled 93 PSUs. As mentioned above, this total includes some 

individual PSUs that might be sampled two or more times (table 1); total numbers 

of PSUs that we sampled each year from 2000 to 2005, including these repeated 

samples, varied from 160 to 198 (see table 1 for an example of sample sizes of 

unique and repeated PSUs from the 2005 field season).

Transect layout within PSUs—

We used georeferenced parallel and zigzag transects to sample PSUs: parallel 

transects were used in the inshore subunit and zigzag transects were used in the 

offshore subunit (fig. 3). We used parallel transects for the inshore subunit to take 

advantage of the higher density of murrelets in that area and thus to increase the 

encounter rate. We used zigzag transects in the offshore subunit to cut across the 

gradient of declining murrelet density in that subunit while giving all areas of that 

subunit an equal probability of being included in the sample. In all cases, we placed 

transects to avoid overlapping sampling effort close to the centerline between the 

two subunits. See appendix 1 for a detailed description of methods used to lay out 

transect lines.

Within the inshore subunit, we divided the length of the PSU (approximately 

20 km) into four segments that were approximately 5 km long and parallel to shore. 

We then divided the width of each subunit into four bins parallel to shore and of 

equal size. One transect was randomly placed within each bin (without replacement) ensuring that transects were distributed spatially at different distances from 

shore (fig. 3). Within the bins, we selected the transect segments in increments of 

100-m distances from shore (app. 1).

Within the offshore subunit, we delineated a zigzag transect so that it traversed 

the entire width of the subunit (fig. 3) and a portion of the PSU’s length, or in some 

cases the entire length. Length of the zigzag was calculated to be proportional to 

the average density of murrelets in the offshore versus inshore subunits. We determined a zigzag transect’s starting point from a random point. We approximated the 

length of the zigzag transect in each zone from a formula based on the total area 

of inshore and offshore subunits and murrelet densities (from previous data; also 

see Rachowicz and Beissinger 1999) as follows: Each PSU consists of two subunits 

labeled inshore and offshore with areas (km2) a1 and a2, respectively. We assumed 

We used parallel 

transects for the 

inshore subunit to take 

advantage of the higher 

density of murrelets in 

that area and thus to 

increase the encounter 

rate. We used zigzag 

transects in the 

offshore subunit to cut 

across the gradient 

of declining murrelet 

density in that subunit 

while giving all areas of 

that subunit an equal 

probability of being 

included in the sample. 
10

GENERAL TECHNICAL REPORT PNW-GTR-716

that the number of birds observed in each collection of subunit transects followed a 

Poisson distribution with mean densities d1 and d2 (in birds per km2). Therefore, the 

ratio (r) of inshore to offshore transect length is given by:

r = × a1

a2

d1

ƅd2

This ratio (r) is simply the product of the area ratio and the square root of the 

density ratio. Given a 20-km transect in the inshore subunit, this equation was 

solved for the length of the transect within the offshore subunit within each stratum 

of each zone (see app. 1 for additional details).

Line Transect Sampling

The line transect sampling method was used to estimate murrelet density (number 

of murrelets per unit area per day), and ultimately, population size. We recorded the 

perpendicular distance of each murrelet observation (or group of murrelets) from 

the transect line for use in the software program DISTANCE (Buckland et al. 2001, 

versions 3.5 and later 4.1), which selects a mathematical function to describe the 

effect of distance on numbers of groups of birds detected.

This method makes some important assumptions, including objects near the 

line are not missed and objects have not moved away from the line in response 

to the observer prior to being detected. If objects are missed or move away from 

the line, density will be underestimated. We examined these assumptions. Brennan (2000) tested the assumption that all murrelets on or near a transect line are 

detected. She found that on average, birds moved prior to detection by the observer, 

but not large distances (x < ~10 m) and that some birds were missed because they 

dove or flew away. Evans Mack et al. (2002) evaluated the effects of observer, number of observers, and other covariates on the likelihood of detecting birds on the 

transect line and showed that some proportion of birds on the transect are missed 

and that each of these covariates has some effect on detection rates. We are continuing to examine the potential effect of these behaviors on our estimates.

Another important assumption of the transect method is that the distance of 

objects from a transect line is accurately estimated. Raphael et al. 1999 (http://

www.reo.gov/monitoring/murrelet/pdf/pnw_atsea.pdf) tested this assumption 

during the 1999 field season by driving a boat through a field of fixed buoys and 

recording the observer’s estimates of either perpendicular distance or radial distance and sighting angle to the buoys and the true distance measured with a laser 

rangefinder. They found that overall there was no significant difference in distances 

when observers estimated (1) a direct perpendicular distance, versus (2) the radial 

distance from the object to the boat and the angle of the object from the transect 
11

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

line (by using a trigonomic calculation to obtain the distance). Although estimates 

were found to be negatively biased, the direct estimate of perpendicular distance 

was more precise. 

Raphael and Laake (2000, available from the senior author on request) 

documented the full set of steps necessary to configure program DISTANCE for 

analysis of data to compute a detectability function using this design.

Observer Methods

We conducted a number of tests to determine whether to use one or two observers 

to record murrelet observations (http://www.reo.gov/monitoring/murrelet/pdf/

pnw_atsea.pdf, Evans Mack et al. 2002). We obtained more accurate results from 

two observers than from one observer, especially when bird density was high and 

in wind conditions that generated wind wavelets. Under these conditions, single 

observers missed a higher proportion of birds close to the line than two observers. 

After having evaluated the results from these experiments, we decided to use two 

observers at all times.

During surveys, each of the two observers surveyed 90° arcs on their side of 

the boat starting from the bow. Observers scanned continually, but more effort 

was expended watching for birds close to the line ahead of the boat (within 45° of 

line) to reduce the risk of missing birds located close to the transect line. Observers 

estimated the perpendicular distance of each murrelet (or the center of a group of 

murrelets) from the transect line (see app. 3 for training methods). Binoculars were 

used for species verification, but not for sighting birds. For most surveys, observers 

recorded information into tape recorders for subsequent transcription to survey 

forms. In surveys conducted in Zone 2, observations were relayed by headset to a 

person in the boat cabin who entered those data directly onto a laptop computer. 

Appendix 2 describes the data fields and codes we used in these surveys.

Observer Training

New observers spend 2 to 4 weeks with an experienced trainer learning techniques 

for bird identification, distance estimation and scanning, as well as navigation and 

boat safety procedures (app. 3). Returning or experienced observers spend 1 to 2 

weeks working with the trainer to renew their skills. Simultaneous surveys are 

conducted by the trainer and observers to help reduce observer variation. Results 

are compared and surveys repeated until results are similar for the two observers. 

Each observer must successfully complete a series of assessment drills to test their 

survey, boating, and safety skills and knowledge. To assure safety of the crews, 

all observers must learn safe boat handling and maintenance. In Zone 1, new crew 
12

GENERAL TECHNICAL REPORT PNW-GTR-716

members are given a 1-day course taught by the Coast Guard auxiliary or equivalent organization. In Zone 2, there is a dedicated boat operator who has a marine 

operator’s license and is Coast Guard certified. In all zones, safety protocols for all 

crew members include instructions and reminders for weather and sea condition 

assessment, boat handling, proper maintenance of the boat and safety gear, rescue 

techniques, and emergency procedures.

Accurate estimates of the perpendicular distance from the transect line to birds 

detected from the boat are key to density estimates made by using line transect 

methods (Buckland et al. 2001). Training in distance estimation is conducted 

first on land, then on the water. Laser rangefinders are used for training and for 

calibration and testing of observers’ distance estimates before or during each 

survey. Distances to stationary buoys, crab pot markers, or a small float towed 

behind the boat are estimated by the observer and the distance then measured 

with the rangefinder when the boat reaches the position perpendicular to the object. 

Each observer completed a minimum of 80 distance estimates during training.

Quality assurance tests were repeated daily or weekly throughout the entire 

survey period where each observer was tested on their ability to accurately 

estimate distances. Observers made a set of 5 to 10 estimates of perpendicular 

distance to targets and the actual perpendicular distance was measured with a laser 

rangefinder. After the first set of estimates, the observer’s results were assessed. 

If estimates were within 15 percent of the actual distance, the trial was complete 

for that observer. If estimates were not within 15 percent of actual or if observer 

estimates showed consistent bias, the observer continued to estimate distances 

until error and bias were less than 15 percent. In addition, one of the project leads 

accompanied the survey crew and observed their overall performance and ability 

to detect murrelets three times during the survey season and completed an audit 

form created by the Murrelet Monitoring Program (Huff 2003, http://www.reo.gov/

monitoring/murrelet/docs-pubs/MAMU02rptfinalver2__9_23_03.pdf). The results 

of the audit were shared with the observers after the survey day was completed 

for feedback and discussion. See appendix 2 for an example of our field training 

protocol.

Zone-Specific Sampling Details

Detailed descriptions of the locations of strata, equipment used, and technical 

issues specific to each zone are beyond the scope of this report, but details can be 

found in the 2000 monitoring report, available at http://www.reo.gov/monitoring/

murrelet/docs-pubs/MAMU_EM_00report.pdf. 

Accurate estimates 

of the perpendicular 

distance from the 

transect line to birds 

detected from the boat 

are key to density 

estimates made by 

using line transect 

methods.
13

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Analysis

Overview

Statistically defensible estimates of average marbled murrelet density (average daily 

counts of birds/km2 for the target time period) for the target population, with associated estimates of precision, were produced for each conservation zone separately 

and also for the entire target population consisting of all zones combined. The 

estimation process integrated design, implementation, and analysis. The sampling 

design was a stratified design, described above. This section describes the analytical methods required to produce the desired estimates.

An estimate of average daily density, with an associated estimate of precision, 

was produced separately within each geographic stratum for each breeding season. 

All zones had two or three strata (table 1). Estimates of precision were produced by 

using bootstrap resampling methods. Estimates for zones and overall estimates for 

the entire target population were produced by using standard methods for stratified sampling (Cochran 1977, Sokal and Rohlf 1981). We used standard methods 

based on total area within each stratum to expand density estimates, and associated 

estimates of precision, to calculate the average total numbers of birds by zone and 

for all zones combined for the target period. The details of these various procedures 

are documented in the remainder of this section.

Estimates of Density Within Strata

Estimating density within a stratum required:

• Accounting for some nonrandom selection of PSUs in space and time. 

• Specifying parameters to be used in the DISTANCE program.

Nonrandom selection of PSUs occurred for two reasons. First, the long distances between boat launch sites necessitated sampling neighboring PSUs either 

on the same day or on successive days. Second, sea conditions were sometimes 

too rough to allow adequate sampling, or those conditions posed safety hazards 

for the boat crews. Both situations resulted in a nonrandom selection of days in the 

season, and some PSUs that were available with adequate sampling conditions were 

selected more often than originally expected.

Two main parameters were required for using the DISTANCE program for 

summarizing the data:

• Specifications for truncating data at large distances from the transect line.

• Selecting the method for determining which detection function was used.

We truncated extreme observations (those beyond some maximum distance 

from the transect) because they have negligible effect on density estimates and can 
14

GENERAL TECHNICAL REPORT PNW-GTR-716

cause unnecessarily complex models of the detection function. For truncating data, 

we eliminated the 5 percent of all observations in each zone that were the greatest 

distance from the boat. Specifically, if there were n distance observations, then 

we chose the distance associated with the k-th observation where k is the nearest 

integer to n multiplied by 0.95 with the data set sorted from lowest to highest distance. That distance was set as the truncation distance in the program DISTANCE. 

This truncation rule was used because when using the DISTANCE parameter that 

removes a proportion of the observations, that same proportion is removed from 

each stratum. Because there were so few observations in some of the strata, we 

removed only 5 percent of the largest distances irrespective of strata. 

We used AIC (Akaike Information Criteria) (Akaike 1973, Burnham and 

Anderson 2002) in DISTANCE to select the detection function curve from two 

model types: half-normal and uniform (see app. 4 for a discussion of our selection 

of models).

Outputs From the Program DISTANCE

From DISTANCE we obtained estimates of the probability of a bird that is present 

being detected on the transect line (f(0)), and the mean number of birds per group 

(E(s)), along with the observed encounter rate (ER = number of groups of birds 

observed per km of transect) for each PSU subunit (inshore and offshore) survey. 

Density (birds/km2) for each PSU subunit survey was estimated with the following 

formula:

with the “hats” over the letters designating estimates. The constant 1,000 was used 

to convert units to birds/km2, and the constant 2 was used to account for the fact 

that we count numbers of birds on both sides of the transect line. Estimates of PSU 

density were constructed as a weighted average of the PSU subunit densities with 

weights being areas of the PSU subunits.

Estimates of Precision Within Strata

Estimating precision within a stratum also required accounting for the nonrandom 

selection of PSUs in space and time. In general, bootstrap resampling methods 

were used to estimate precision. Bootstrapping allowed for adjusting for sources of 

nonrandom selection, as well as incorporating a component of variance associated 

with the model in model-assisted estimation. 

d = 1,000 × f(0) × E(s) × ER

2 ˆ ˆ ˆ
15

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Our sampling universe is the array of PSU×Day combinations and it is the 

mean of the PSU×Day densities that we use to characterize the density within a 

zone during the sampling season. As such, our sampling scheme has both a spatial 

and a temporal dimension.

We divided each zone into two or three strata and in theory we would randomly 

select PSU×Day combinations to survey. But because of the limited travel range of 

boats from their varying starting locations during the season, some PSUs near each 

other needed to be sampled very close in time (usually the same day or within a few 

days) resulting in a lack of independence of PSU×Day selections.

In an attempt to adjust for the lack of complete independence for estimating 

the precision of the estimates of zone density, we delineated clusters of PSU×Day 

combinations that were close in both space and time. It was then assumed that these 

clusters more closely represented independent selections. That was our justification 

for using bootstrapping methods based on resampling the delineated clusters. In 

addition, during the bootstrap process we randomly selected PSU×Day combinations within a cluster. Both levels of resampling were used to produce one bootstrap 

replicate sample. The resulting bootstrap sample was then analyzed by the DISTANCE program, using all the same methods as described in the preceding section.

Note that some PSUs had multiple observations and some days had multiple 

observations. To account for some PSUs being sampled more than others (in some 

instances because of deliberate unequal sampling), we calculated the PSU means 

and then constructed a weighted mean of those PSU means with the weights being 

the area of the associated PSU. In all strata in all zones (except Strata 2 and 3 in 

Zone 1) nearly all of the PSUs were sampled each year, so we believe that using the 

mean of the means for PSUs removed most of any selection bias.

The bootstrap procedure incorporated the program PSU Variance (Laake and 

Raphael 2000, available from Raphael on request) developed to account appropriately for the pairing of the inshore and the offshore PSU subunits for both estimation of density and estimation of the variance of that estimator. 

Estimates of precision were based on 1,000 bootstrap replications (as described 

above). We used SAS (Version 8, 2000) to select bootstrap replicate samples, run 

DISTANCE, calculate the density estimates, and summarize bootstrap results (see 

app. 5).

Variants in Estimation Procedures

During the initial year (2000), we encountered some sampling problems that 

required special analytical procedures affecting Zone 1 Stratum 1, and Zone 

2 Strata 1 and 2. Most of the distances to observed groups of birds throughout 

In an attempt to 

adjust for the 

lack of complete 

independence for 

estimating the 

precision of the 

estimates of zone 

density, we delineated 

clusters of PSU×Day 

combinations that 

were close in both 

space and time. 
16

GENERAL TECHNICAL REPORT PNW-GTR-716

that season were lost in these strata owing to a malfunctioning recording device. 

Because complete information was available for Strata 2 and 3 in Zone 1, which 

was not the case for Zone 2, different estimation approaches were used in the two 

zones.

Zone 1:

(1) All observations with valid distances (and all observations with no birds) 

from strata 1, 2, and 3 were used to estimate ƒ(0) and the densities for strata 

2 and 3.

(2) For Stratum 1, the following process was used:

(a) The missing distances in Stratum 1 were filled in from random selections of the observed distances (this is just to get DISTANCE to run).

(b) DISTANCE (with the same settings as other estimations—remove the 

largest 5 percent of the distance observations, same detection functions, 

etc.) was run to estimate the encounter rate and E(s) just using the 

observations from stratum 1 (a separate Excel spreadsheet was created).

(c) Using the estimates of ƒ(0) from step 1 and the estimates of the 

mean encounter rate and E(s) from 2b, the estimate of density was 

constructed (for the raw data and for each bootstrap run).

Zone 2:

(1) To get DISTANCE to run and produce estimates of the encounter rate and 

E(s), the missing distances were filled in at random.

(2) DISTANCE was run by using the usual settings.

(3) The estimate of ƒ(0) for the raw data was taken as the average of the 

estimates of ƒ(0) for the years 2001, 2002, and 2003 where there were no 

malfunctioning recording devices. For the 1,000 bootstrap runs for 2000, 

one thousand random selections were taken without replacement from the 

complete collection of 2001, 2002, and 2003 bootstrap values of ƒ(0). That 

effectively results in approximately equal numbers of ƒ(0) from each of the 

years 2001, 2002, and 2003. Year 2004 values were not included, as these 

were from a different crew.

• 2002: Zone 2 Stratum 1. The sub-PSUs in PSUs 1 and 2 were not 

always surveyed near in time:

PSU Sub-PSU New label Survey date(s)

 1 Near-shore 50 6/18/2002, 7/4/2002

Far-shore 51 5/31/2002, 7/5/2002

 2 Near-shore 52 6/18/2002

Far-shore 53 5/30/2002, 7/3/2002
17

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

To account for this, those four sub-PSUs were considered to be separate PSUs 

and relabeled as shown in the above tabulation just for the 2002 season.

Zone and Population Level Estimates

Because of the potential of both spatial and temporal non-randomness, a modelassisted approach for estimating density was developed and considered for 

use. If both spatial and temporal non-randomness existed, then the output from 

DISTANCE would be used to estimate density for each PSU×Day combination in 

the sample. Then the density at each PSU×Day combination in the zone would be 

estimated by fitting the following linear model, and a weighted average of predicted 

densities (with weights being the PSU areas) for each stratum would be constructed:

dDay,PSU = α + ( βDay × Day) + (βPSU × PSU) + ( βDay×PSU × Day × PSU) + error

However, despite the known deviations from a completely random selection of 

days, examination of data did not suggest any temporal trends. Because of the lack 

of any indications of temporal trends, we performed no temporal adjustment of 

estimates for strata. 

Once estimates of mean density and their associated estimates of precision were 

produced for each stratum, these stratum-level estimates were combined by using 

standard methods for stratified sampling. The methods, as described in Cochran 

(1977), involve proper weighting of stratum-level estimates by using the areas in 

each stratum. This produced estimates of mean density with associated estimates of 

precision for each zone and for the entire target population consisting of all zones 

combined. Precision was estimated from the standard deviation of the results of 

the individual bootstrap iterations. Confidence intervals for density estimates were 

constructed from the central 95 percent of the bootstrap results (also known as the 

percentile method).

Construction of Confidence Intervals for Numbers of Birds

For each zone, a 95 percent confidence interval for the total number of birds was 

constructed by using the percentile confidence interval method (Efron 1992). For 

each of the 1,000 bootstrap replications, we estimated the number of birds in the 

zone by multiplying the estimate of density (birds/km2) by the total area in the 

zone. These estimates were sorted from lowest to highest and the 25th ranked and 

the 975th ranked estimates were taken as the 95 percent confidence interval limits.

We calculated an estimate of the standard error and then added and subtracted 

1.96 times that standard error from the estimate of the total number of birds to 

estimate 95 percent confidence interval limits for birds in all zones as follows:
18

GENERAL TECHNICAL REPORT PNW-GTR-716

Power Analysis 

One of the measures for assessing this monitoring program is the power to detect 

changes of interest with respect to the mean density (and mean number) of murrelets over time. A full description of our methods to estimate power and an example 

of the analysis for the years 2000 to 2003 are given by Miller et al. (2006). For 

example, given the variability in year-to-year population estimates, we estimate 13 

years of sampling would be needed to have 80 percent power to detect a 2 percent 

annual rate of decline and 7 years to detect a 5 percent annual rate of decline. For 

95 percent power, we estimate 15 and 9 years to detect 2 percent and 5 percent 

annual declines, respectively.

Population Summary Across All Zones

Population Estimates

We present population estimates from the 2005 field season to illustrate the 

application of the methods described above. Results from years 2000 through 

2003 are given by Miller et al. (2006). The total population estimate for the Plan 

area during the 2005 field season was approximately 20,200 murrelets with a 95 

percent confidence interval of 16,000 to 24,500 (table 2). 

ai Area of zone i

di Estimate of density for zone i

Estimate of the variance for zone i

Overall estimate of density for the 5 zones: 

Estimate of variance for average density for all 5 zones ( ): 

SE =

2 ˆS i

d

∑ ∑ = =

=

5

1

5

1

/

i

i

i

d aidi a

2 Sˆ

2 ƅSˆ





 



 = ∑ ∑ = −

5

1

2

5

1

2 2 2 ˆ ˆ /

i

i

i

S ai Si a

d

The total population 

estimate for the 

Plan area during the 

2005 field season was 

approximately 20,200 

murrelets with a 95 

percent confidence 

interval of 16,000 

to 24,500. 
19

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Table 2—Estimates of density and population size of marbled murrelets during the 2005 breeding season in 

the area of the Northwest Forest Plan Zone Stratum Density Bootstrap standard error Coefficient of variation of density 

BirdsaBirds lower 95% confidence intervalaBirds upper 95% confidence intervalaSurvey area Transect length Probability of detection f(0)Standard error of f(0)Mean number of birds per group E(s)Standard error of E(s)Truncation distance Standard error of truncation distance

- - Birds/km2- - Percent km2 km - - Meters - - 

1 1 2.5014 0.9507 38.0 2,100 700 3,600 845 420

1 2 2.4255 .6523 26.9 2,900 1,100 4,300 1,194 2,807

1 3 2.0209 .6336 31.4 2,900 1,200 5,000 1,458 394

All 2.2751 .4820 21.2 8,000 4,800 11,600 3,497 3,621 0.0156 0.0021 1.76 0.149 150 12.7

2 1 2.7283 .4965 18.2 2,000 1,200 2,600 724 301

2 2 .5568 .3579 64.3 500 100 1,600 926 257

All 1.5100 .3069 2.3 2,500 1,600 3,600 1,650 558 .0134 .0014 1.41 .052 130 18.1

3 1 .8123 .2594 31.9 500 300 900 661 439

3 2 5.6780 .9715 17.1 5,300 3,200 6,700 935 562

All 3.6624 .5973 16.3 5,800 3,600 7,300 1,595 1,001 .0126 .0012 1.83 .074 150 12.0

4 1 4.4524 1.1175 24.8 3,300 2,200 5,400 734 807

4 2 .8827 .3762 42.5 400 200 900 425 990

All 3.1423 .7316 23.0 3,600 2,700 6,000 1,159 1,797 .0107 .0011 1.51 .040 170 11.8

5 1 .2733 .1201 42.9 100 0 200 441 620

5 2 .3807 .1482 38.9 200 100 300 441 155

All .3270 .0970 29.6 300 100 500 883 775 .0107 .0011 1.51 .040 170 11.8

All — 2.3020 .2476 1.8 20,200 16,000 24,500 8,785 7,822

a

Numbers rounded to the nearest 100 birds.

Allocation of Effort

As part of the monitoring design, greater sampling effort was allotted to areas of 

higher densities of birds in an effort to reduce variability in the population estimates. Along shore, large geographic strata were identified where more PSUs were 

selected within higher density areas. Within PSUs, densities tend to be higher closer 

to shore and taper off with distance from shore (although these distributions shift 

in different years, possibly associated with different prey conditions). Therefore, 

within PSUs, more transect length per unit area was sampled in the generally 

smaller inshore subunits than in the larger offshore subunit. These design decisions 
20

GENERAL TECHNICAL REPORT PNW-GTR-716

were made prior to implementation of the pilot project in the 2000 field season 

based on previous data collected under different sampling designs. On average, 

density of marbled murrelets in the inshore subunit was 6.5 times that in offshore 

subunits (table 3).

Table 3—Mean density estimates in the inshore and 

offshore subunits and zones, 2000–2005

Zone Inshore density Offshore density Ratio in/off

- - - - Murrelets/km2 - - - -

1 4.55 0.90 5.1

2 2.61 1.42 1.8

3 13.84 .83 16.7

4 5.41 .92 5.9

5 .22 .01 22.0

Future Steps

The 2001 and subsequent field seasons proceeded with very few changes in the 

sampling design or methods. In a few instances, the amount of transect allocated to 

the inshore or offshore subunit was changed. In Zone 1, we implemented a zigzag 

layout of transects in the offshore subunits of Strata 2 and 3 rather than the parallel 

layout used in the year 2000 sampling. As the work continues, we expect to further 

modify procedures as we gain further experience and as new issues are encountered. We have developed a centralized database to archive each year’s observations, survey effort, and maps of transect lines. 

This effort represents an important step for the murrelet monitoring program, 

but more is needed. Ultimately the hope is to understand how at-sea population 

size is influenced by the amount and distribution of inland nesting habitat. Efforts 

continue to develop a map of potential nesting habitat and to evaluate how habitat 

affects population size and productivity (Raphael et al. 2006). Radar (Raphael et al. 

2002) and land- and seascape analyses (Miller et al. 2002, Raphael 2006) may be 

possible tools to help gain an understanding of linkages between murrelet populations and habitat conditions, and we are continuing to explore this possibility.

Acknowledgments

We thank several people and agencies that have contributed toward murrelet monitoring. Naomi Bentivoglio and Patrick Jodice provided guidance to the monitoring 

team in earlier years. Tim Max provided statistical advice during the initial stages 

of our protocol design. Jeff Laake developed PSU Variance to help analyze population data under our sampling design and provided many helpful comments to the 
21

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

population team. Bill Hogoboom, USDA Forest Service Pacific Southwest Research 

Station (PSW), provided geographic information system assistance. Population 

monitoring has been funded by Pacific Northwest (PNW) and PSW Research 

Stations, USDI Fish and Wildlife Service, Washington Department of Natural 

Resources, Washington Department of Fish and Wildlife, Oregon Department of 

Fish and Wildlife, the Marbled Murrelet Study Trust, and Pacific Lumber Company. 

We are indebted to our field crews whose hard work and diligence made the collection of these monitoring data possible. We thank Joseph Ganey and Falk Huettman 

for comments on an earlier draft.

English Equivalents

1 kilometer = 2. 47 acres

1 meter = 3.28 feet

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Buckland, S.T.; Anderson, D.R.; Burnham, K.P.; Laake, J.L.; Borchers, D.L.; 

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murrelet/docs-pubs/MAMU02rptfinalver2__9_23_03.pdf. (April 6, 2007).

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Rep. PNW-GTR-650. Portland, OR: U.S. Department of Agriculture, Forest 

Service, Pacific Northwest Research Station. 149 p.
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31–60.

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America, No. 276. Philadelphia, PA: Birds of North America, Inc. 32 p.

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the Pacific Lumber Company, Scotia Pacific Holding Company, and Salmon 

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A. Testing and designing methods for developing an at-sea monitoring strategy 

for the marbled murrelet. U.S. Fish & Wildlife Service. Unpubl. rep. FWS 

agreement # 1448-10110-97-J132 and DCN 10110-7-4000: 46-72. http://www.

reo.gov/monitoring/murrelet/pdf/bbdist.pdf. (February 27, 2007).

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Forest Plan. Conservation Biology. 20: 297–305.

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relationships between abundance of marbled murrelets and distribution 

of nesting habitat. Condor. 104: 331–342.
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Raphael, M.G.; Evans Mack, D.; Wilk, R.J. 1999. Sampling marbled murrelets 

at sea: tests of survey methods and designs. http://www.reo.gov/monitoring/

murrelet/pdf/pnw_atsea.pdf. (February 27, 2007).

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R.D. 2006. Spatially-explicit estimates of potential nesting habitat for the 

marbled murrelet. In: Huff, M.H.; Raphael M.G.; Miller S.L.; Nelson S.K.; 

Baldwin J., tech. coords. Northwest Forest Plan—the first 10 years (1994–2003): 

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Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Appendix 1: Geographic Information System Methods1

Geographic information system (GIS) technology was used to assist the population 

team in developing and implementing the population sampling design. The team 

used GIS as a computer-based orientation and navigation tool to define the extent 

of the primary sample units (PSUs), to generate survey transects within each PSU, 

and to produce hardcopy field maps and field navigation coordinate tables for use by 

the population survey crews. Using GIS facilitated the implementation of the new 

sampling design.

The GIS personnel for the study included Rich Young, USDI Fish and Wildlife 

Service, Beth M. Galleher, USDA Forest Service Pacific Northwest Research 

Station, and Bill Hogoboom, USDA Forest Service, Arcata, California. The GIS 

software from the Environmental Systems Research Institute (ESRI) was used at 

all locations, including ArcInfo 7, ArcGIS 8, and ArcView 3.1.2 Our spatial 

data were in Universal Transverse Mercator (UTM), Zone 10N, NAD27, unless 

otherwise specified. 

The basic GIS tasks performed for the project included:

• PSU delineation.

• PSU subunit breakdown (inshore versus offshore, and inshore segments).

• Generation of inshore parallel transect survey routes.

• Generation of offshore zig and zigzag survey transect routes.

• Random transect selection.

• Generation of navigation waypoint coordinates (latitude and longitude).

• PSU area calculation.

• PSU transect length calculation.

• Hardcopy maps (field survey transect layout maps, zone maps, and other 

visual aids).

PSU delineation

Within each of the five conservation zones, the team members collectively agreed 

upon the PSU boundaries (table 1). The GIS provided the mechanism to spatially 

define the individual PSU boundaries. We used digital data sets (1:24,000 scale) 

from the U.S. Geological Survey (http://gos2.geodata.gov/wps/portal/gos/) to 

define the coastline for the entire study area. After receiving feedback from field 

1

Appendix 1 was developed by Rich Young, GIS analyst, U.S. Fish and Wildlife Service, 

911 NE 11th Avenue, Portland, OR 97232, and Beth M. Galleher, GIS analyst, U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, 3625 93rd Avenue 

SW, Olympia, WA 98512-9193.

2Use of trade or firm names in this publication is for user information and does not imply 

endorsement by the U.S. Department of Agriculture of any product or service.
26

GENERAL TECHNICAL REPORT PNW-GTR-716

survey crews during the first 2 years of the project, we modified these data sets 

by using hand-drawn maps of islands, large rocks, and shallow beach bars that 

were digitized in GIS to exclude nonnavigable areas from the study area. These 

modifications were in place for the 2002 field season.

Ideally, all PSUs would be a standard length of 20 km, as determined by the 

team. To most closely approximate this standard by using real world data, however, 

the actual PSU length was determined by stratum within each conservation zone. 

We used the dynamic segmentation feature of ArcInfo to automatically determine 

PSU breakpoints resulting in standardized PSUs within each stratum that are as 

close to 20 km in length as possible. Boundaries between PSUs were generated 

perpendicular to the coast at these breakpoints.

We created the offshore boundary, or outer extent of the PSU, by buffering the 

coastline to a specified distance, ranging from 2000 to 8000 meters, depending on 

the zone or stratum as determined by the team (table 1). An exception to this exists 

in Zone 1 Strata 2 and 3 where topography sometimes limited the ability to get the 

full distance from shore. An example is two opposing coastlines that are closer 

together than twice the specified PSU width. In these cases, the channel was split 

and the offshore boundary for the adjacent PSUs was created halfway between the 

two coastlines.

PSU Subunit Breakdown

Within each PSU, we used GIS to create the necessary subdivisions, as illustrated 

in figure 3. We created the centerline, the boundary between the inshore and offshore subunits, in all strata except Zone 1 Stratum 3, by buffering the coastline to a 

specified distance based on zone and stratum (table 1). Additionally, we divided the 

inshore subunit into four equal segments, labeled A through D, each approximately 

5 km in length (fig. 3). This was accomplished in much the same manner as the 

creation of the PSUs.

Generation of Inshore Parallel Transect Survey Routes

Our overall objective was to define transect routes so that any point within a 

subunit of any PSU had an equal probability of being included in a survey. Inshore 

transect lines were generated by buffering the coastline in 100-m increments 

beginning 50 m beyond the extent of the designated surf zone (table 1) and ending 

50 m before the centerline. We used 100-m increments based on pilot surveys 

showing that observers detected nearly all birds within 50 m from each side of a 

transect line. Each transect was attributed with its distance (in meters) from the 

coastline. Transects were then overlain on the PSU segment polygons resulting in 

Our overall objective 

was to define transect 

routes so that any 

point within a subunit 

of any PSU had an 

equal probability of 

being included in a 

survey.
27

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

~5-km transect lines in segments A through D. This process was performed once 

during the pilot study, and then modifications were made prior to the 2002 field 

season based upon survey crew feedback. A random selection of these parallel 

transects has been used in subsequent surveys. This selection is accomplished 

in Zone 1 by use of a random number table, and in all other zones by using the 

RANDOM function of ArcGIS.

Generation of Offshore Zig and Zigzag Transect Routes

Surveys in the offshore subunit followed either a zig (Zones 4 and 5 only) or a 

zigzag pattern (fig. 3). Zig pattern surveys consisted of one transect line oriented 

at an angle between the centerline and the offshore boundary, whereas zigzag 

surveys were two or more contiguous transect lines or “legs” that angle away from 

and then toward the shore. Starting points for transects were based upon randomly 

selected points along the centerline for each PSU. For each zone and stratum, the 

team selected a target length for the offshore transect, and a number of “legs” (zigs 

or zigs plus zags). These parameters, along with the width of the offshore subunit, 

determined the orientation of each transect.

To construct the zigzag transects, we used several GIS functions. First, we 

buffered a randomly selected starting point along the centerline to create a circular 

polygon with a radius equal to the leg size (total transect length / number of legs). 

We then intersected this circle with the offshore polygon and drew a straight line 

between the starting point and the outer PSU boundary. This point of intersection 

became the new starting point for the next leg in the transect, the zag, which heads 

back toward the centerline. We repeated this process until all legs were constructed. 

Partial transect legs that became truncated owing to an intersection with the PSU 

boundary were continued at the opposite end of the PSU.

Owing to topographic constraints, such as convoluted coastlines, we modified 

the method for constructing zigzag transects in Zone 1. The starting point, selected 

from a set of points covering the entire offshore area and spaced 100 m apart, and 

initial direction of the transect from the starting point, were randomly selected for 

each PSU and repetition by using a Visual Basic script, randomizer.exe, written 

by K. Ostrom. Transects in this zone differed in length, and we made one or more 

adjustments in orientation to maintain the overall objective of traversing the area 

between centerline and outer boundary. 

For all zones, except Zone 1, the offshore transect routes were generated each 

year for that year’s survey season based upon new randomly selected starting 

points. For the pilot year, parallel transects were used to survey Zone 1 Strata 2 

and 3. In 2001, the design was modified to employ zigzag transects in these strata; 
28

GENERAL TECHNICAL REPORT PNW-GTR-716

however, owing to the complexities involved in constructing transect routes in and 

around Puget Sound and the San Juan Islands, the offshore routes for Zone 1 were 

generated once and then reused in subsequent survey years with the order of use 

randomly selected each year from a random number table. 

Random Transect Selection

For strata where inshore surveys were performed (all except Zone 1 Stratum 3), 

we chose parallel transects to be surveyed each year by using the random number 

generator in ArcInfo or ArcGIS. Within each PSU, we grouped the parallel transects into four bins, each representing a quarter of the total number of transects 

(fig. 3). Random selection without replacement of bins and transect lines produced 

a survey route for each PSU with one ~5-km transect in each of the four segments 

and each bin surveyed only once. This ensured a more even distribution of survey 

effort across the inshore subunit.

Selection of offshore transects, except in Zone 1 as previously described, 

involved randomly identifying a starting point along the centerline to begin construction of the route. Possible starting points were initially generated for each PSU 

and were evenly spaced at 10-m intervals along the centerline. The first starting 

point was positioned along an extrapolated centerline that extended beyond the end 

of the PSU so that no portion of the offshore subunit was excluded from the possibility of being selected to be surveyed.

Generation of Navigation Waypoint Coordinates

As transect routes were selected or newly constructed, beginning points, endpoints, 

and internal vertices were captured as coordinate points in UTM meters. These 

were then converted to a geographic coordinate system (latitude/longitude) and 

provided to the field survey crews for entering into their onboard global positioning 

system (GPS) units as waypoints for navigation (see fig. 5 for an example map and 

set of coordinates). Originally, these coordinates were provided in hardcopy format 

and manually entered into the GPS by field survey personnel. In recent years, 

digital files containing the waypoint coordinates have been created in a format that 

can be easily uploaded to the GPS units.

PSU Area Calculation

We used ESRI GIS software to calculate the area, in km2, of the inshore and 

offshore subunits of each PSU. We did this by using a digital coverage in a UTM, 

Zone 10, NAD27 projection. We provided the area calculations to the team statistician for use in generating population estimates.
29

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

PSU Transect Length Calculation

The team used the length of a transect to calculate encounter rates for density estimates. Transect lengths were recorded by using tracklines produced by GPS units 

during surveys and compared with lengths of transects as mapped by using ESRI 

GIS software. The two measures were similar and we found no bias in any differences between recorded and mapped transect lengths. Therefore, we used the GIS 

estimates in most cases. The GPS tracklines were used to measure transect length 

when the actual course deviated significantly from the planned course.

Figure 5—Sample layout of inshore and offshore subunits for one primary sample unit in Zone 3, along with the coordinates used to 

navigate to each waypoint along the transect lines. Similar maps and coordinates are provided to each field crew at the start of each day’s 

marbled murrelet survey.

March 2005

USFWS Pacific Region

0 1 2 3 4 5 6 7 8 9 10

Kilometers

2005 MAMU Field Survey Way-Point Map

Zone 3, Strata 1, PSU 01

o
30

GENERAL TECHNICAL REPORT PNW-GTR-716

Hardcopy Maps

Maps of each PSU displaying selected transect routes and waypoint coordinates 

were generated in GIS and provided to the field crews for use in planning and 

executing surveys. The waypoint coordinates were output in the same projection as 

the base maps (UTM, Zone 10, NAD27) to a text file. The PCX5 software (Garmin 

1993–1997) was used to convert the UTM coordinates to latitude-longitude decimal 

degrees, WGS84. PCX5 produces a file that can be directly uploaded into the GPS 

units. Hardcopy listings of the coordinates were also provided to field crews as 

backup. Although the points were provided at submeter precision, the ability to 

locate these points accurately in the field was limited by equipment and terrain. 
31

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Appendix 2: Offshore Marbled Murrelet Survey 

Form Instructions

Header

Zone 1 digit

Strata 1 digit

PSU 2 digits

Vessel First 4 letters of boat name

Observer Height Eye height (m) above water where observer is standing

Skipper Initials of boat navigator

Observer 1 3 letters initials of observer

Observer 2 3 letters initials of observer

Date 6-digit date (mo-dy-yr)

Notes Any pertinent info specific to survey (e.g., inshore 

 obstructions to surveys) 

Main form

Subunit 1 letter, N or O, for near shore or offshore

Distance 4 digits (m) for parallel transect distance from shore 

Example 1250 m

Segment 1 letter A, B, C, or D for segment along shore

Seg length 2 digits for actual length traveled on parallel transect 

 (km to nearest 0.1 km). Example 5.2 km

Z Start A 3-digit code (m) for zigzag starting point along shore. 

 This is a distance beginning from left side of the PSU 

(looking out from shore). Example 120 m

Z Start O 4-digit code (m) for zigzag starting point offshore 

Example 1500 m

Z End A 3-digit code (m) for zigzag ending point along shore

Z End O 4-digit code (m) for zigzag ending point offshore

Z Length 3 digits for actual length traveled (km to nearest 0.1 km). 

Example 15.2 km

Time 4-digit code, military time. Taken at start of every segment 

and to show breaks 

Depth 4 digits bottom depth (ft). Read from depth sonar (fish 

finder) at beginning of every segment and at murrelets

Clouds Percentage cloud cover; ocular estimate

Precip 1 letter code for precipitation (N = none, D = drizzle, 

S = shower, L = light rain, R = steady rain, F = fog)

Visibility 4 digit or 1 letter horizontal distance of clear visibility (m); 

 >U = unlimited

Glare 3 digits for percentage of glare or reflection that is hindering 

 view of the water

Swell Dir 1- to 3-letter code for direction of swells (N = north, 

NNW = north northwest, etc.)
32

GENERAL TECHNICAL REPORT PNW-GTR-716

Swell Ht Height (m) of average swell from crest to trough 

(visually estimated to nearest 0.1 m)

Swell Time Average time (sec) between swells (crest to crest or 

 trough to trough)

Wave Dir 1- to 3-letter code for direction of wind waves or 

wavelets (N = north, NW = northwest, etc.)

Wave Ht Height (cm) of average wavelet (visual estimate)

Wind Speed 2 digits (mph) measured from anemometer

Beaufort Scale 1-digit code for Beaufort sea conditions

Wind Dir 1- to 3-letter code for wind direction

White Caps Average distance (m) between whitecaps on 

 different swells

P,S,B 1-letter code for side of boat of detection (Port, 

Starboard, Bow)

Species 4-letter species code for observation based on common 

name. First 2 letters of first word, first 2 letters of last 

word, or first letters of each word in common name. 

Example: White-winged Scoter = WWSC. For those 

identified only to genus, use first 4 letters of common 

generic name. Example: TERN or LOON

Number Group size of detection

Distance Perpendicular distance (m) of bird from transect line (use 

 center of a group of birds)

Behavior 1-letter code for behavior of murrelets (S = swimming, 

F = flying, T = taking flight, H = holding fish, D = 

 foraging dive, A = avoidance dive, V = vocalization)

Plumage Class Number of murrelets from total group in each of 7 

plumage classes recorded as definite or probable

1 = Brown bird, very little to no molt, entirely in 

 alternate plumage

2 = Obvious body and/or flight feather molt but 

>50 percent alternate (brown) 

3 = <50 percent brown but still distinguishable from 

juvenile by some brown on back, breast, and neck 

and/or presence of flight feather molt

4 = Black and white bird (basic plumage)—known adult 

5 = Black and white bird but confirmed HY (juvenile)

6 = Unknown black and white bird

7 = Unknown

Plumage Notes Additional information on plumage—as much detail as 

needed to support classification 

Note: Page numbers of the forms are not variables, but should be entered as 

follows: 1 of 2, 2 of 2, etc.
33

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Appendix 3: Field Training Protocol

Background

• The marbled murrelet (Brachyramphus marmoratus) is federally listed 

as threatened in Washington, Oregon, and California. Throughout the 

listed range of the species, the Northwest Forest Plan (the Plan) land base 

standards and guidelines are expected to make substantial contributions 

towards conservation and recovery. Specific monitoring requirements have 

been outlined to ensure the Plan is effective in maintaining and recovering 

this species long term.

• Marbled murrelet effectiveness monitoring under the Plan recommended 

assessing population trends at sea because of the cryptic nature of murrelets in their nesting habitat. There is also an inland component, whose goal 

is to establish a credible nesting habitat baseline. The ultimate goal is to 

track over time, both the at-sea population abundance and nesting habitat 

and show a strong correlation between population trends and nesting habitat so that nesting habitat can be monitored as a surrogate for the species 

population over the long term.

• A population team of state and federal representatives has developed the 

new sampling design and standardized survey methods to be implemented 

throughout the Plan area. These survey methods were employed beginning 

in 2000 and were developed to facilitate comparisons of data among studies 

in different geographic areas and to examine long-term population trends at 

sea.

Sampling Design

Target population

• Marbled murrelets from the Canadian border to San Francisco Bay 

(Northwest Forest Plan)—see map

• Inshore boundary: Closest navigable waters adjacent to the coast 

(between 100 and 400 m out to sea) 

• Offshore boundary: Varies based on available marbled murrelet 

distribution data in each zone, from 2 to 8 km from shore 

Sampling period

• Mid May to end of July 

• Time of year when breeding birds at sea are likely to be associated 

with land nesting habitat in the Plan area
34

GENERAL TECHNICAL REPORT PNW-GTR-716

Conservation zones

• Six conservation zones along the west coast and within Puget Sound 

(five of six occur within the Plan area):

• Zone 1—inland waters of Puget Sound

• Zone 2—outer coast of Washington—Cape Flattery to Columbia River

• Zone 3—northern to southern Oregon coast 

• Zone 4—southern Oregon coast to northern California coast

• Zone 5—northern to central California coast south to San Francisco

• Mean at-sea density and population trend estimates of marbled 

murrelets are calculated separately for each zone

Strata within zones

• Sampling effort based on marbled murrelet density→Strata 1 (northern 

Washington coast) more replicates than Strata 2 (southern Washington 

coast)

Primary sample unit (PSU)

• Rectangular “unit” along 20 km of coastline

• Each “unit” consists of one inshore and one offshore subunit; width differs 

by zone and stratum 

• Subunits have a density component

• Inshore subunit consists of four approximately 5-km segments parallel to 

shore at increments of 100 m from shore 

• Offshore subunit consists of a zigzag transect that traverses the entire 

width of the subunit and a portion (or all) of the PSU length

• PSU specifics for Zone 2 (outer Washington coast): Inshore boundary 350 

m, centerline boundary 1500 m, offshore boundary for Stratum 1 is 5000 

m and for Stratum 2 is 8000 m; offshore transect length is 20 to 30 km. 

Specifics for other zones are listed in table 1.

Overall sampling methodology (note: this example is from Zone 2; training 

methods are similar for crews in other zones, except that data are recorded 

into portable tape players in other zones.

• Each conservation zone has a target sample size of 30 PSU surveys. 

• High-density PSUs are sampled numerous times throughout the field 

season in random order (Zone 2 Stratum 1: 3 replicates of eight PSUs).

• Low-density PSUs are sampled only once (Zone 2 Stratum 2: 1 replicate 

of eight PSUs).
35

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

• Selection of PSUs is completed prior to the beginning of the field season. 

PSUs are generally selected randomly without replacement, and sampling 

should be spread evenly over the field season. 

• Port location and weather will constrain random PSU selection, but effort 

should be made to avoid “clustered” surveys (PSUs that are completed on 

the same or adjacent days for logistical reasons).

• All four inshore subunits and offshore zigzag of a PSU must be surveyed 

on the same day.

• If unable to survey 25 percent or more of the transect line owing to 

obstacles (e.g., reef or breakers), survey the next possible transect line 

moving away from shore in 100-m increments. Document why the line 

was moved.

• Partial surveys occur when less than 75 percent of the transect is complete, 

and these are not used for analysis.

• Ensure that actual transect length (meters) is recorded for each of the four 

inshore subunits and offshore zigzag transect by the global positioning 

system in the DLOG2 program.

• Record depth by using depth finder at the beginning and end of each 

transect and at each murrelet record.

• A “break” of 100 m should be maintained when offshore zigzag transect 

legs cross and when inshore and offshore transects abut at the centerline—

keep 100 m between adjacent lines or points.

• Stratum 3 (Grays Harbor, Willapa Bay and mouth of the Columbia River) 

has been surveyed in previous years. These data have not been used for 

population monitoring, and the monitoring team has decided that no 

surveys are to be completed in 2005 in these coastal estuaries.

Line Transect Distance Sampling

Used to estimate murrelet density (number of murrelets per unit area), which 

is then used to estimate population size.

Uses perpendicular distance to each murrelet observation (or group of 

murrelets) from the transect line and uses DISTANCE software (Buckland 

et al. 2001, program DISTANCE version 3.5, 4.1) to select a mathematical 

function that describes the effect of distance on numbers of groups of birds 

detected.
36

GENERAL TECHNICAL REPORT PNW-GTR-716

Important assumptions: 

1. Murrelets near the line are not missed or they have not moved away from 

the line (in response to the observer) prior to being detected. If murrelets 

are missed or move, density will be underestimated.

2. Distance of murrelets from the transect line is accurately estimated.

Measurement Quality Objectives

For long-term murrelet population monitoring, quality assurance ultimately 

depends on the population estimate, which is composed of density and area. 

The density value is dependent on data collected both in the field and data 

used in or derived from analyses for density in the program DISTANCE.

Data collected during surveys that affect marbled murrelet density: 

• Number of groups observed: Need communication between observers 

to minimize missed detections (DISTANCE does not require that all 

groups will be detected)

• Group size: A “group” is a collection of birds separated by 2 m or 

less at first detection and moving together or, if greater than 2 m, 

the birds are exhibiting behavior reflective of birds together.

• Distance: Estimate and record a distance to every murrelet group 

observed during surveys, regardless of distance from the line. 

• Transect length: Actual distances traveled by the boat along the 

predescribed transect line, minus any deviations to get a better look 

at a bird or avoid large obstacles. 

Survey Protocol

• Two observers scan from 0° off the bow to 90° abeam of the vessel.

• More effort is expended watching for murrelets close to the transect line 

ahead of the boat (within 45° of line). The program used to analyze the 

survey data assumes that birds close to the transect line are not missed. 

• Observers should scan continuously, not staring in one direction, with a 

complete scan taking about 4 to 8 seconds. An observer focusing beyond 

100 m is likely to miss some birds that are closer, thus observers should 

vary their focus from close to far in scanning within the 90° arc on each 

side of the boat. 

• Scan far ahead of the boat for birds that may flush or dive in response to 

the boat. The intent is to record distance before the birds respond to the 

boat and move away. 
37

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

• Scan with the naked eye and use binoculars only to verify species or 

plumage. Binoculars should not be used to scan.

• To maintain effective transect width, birds detected with binoculars that 

would not otherwise have been detected with the naked eye, are recorded 

in the comments field as “off transect.”

• Record group size at first detection. Record the midpoint distance for a 

group of birds if greater than 2 m apart. 

• Estimate the perpendicular distance from the transect line of each group of 

murrelets as far as the eye can see in front of and to the side of the vessel. 

Generally, detections can be made to at least 200 m perpendicular distance 

(depending on sea conditions), but all distances, even those further than 

200 m should be recorded. The program used to analyze the survey data 

assumes that distance of murrelets from the transect line is accurately 

estimated.

• Observers should communicate on birds close to the transect line to avoid 

double counting.

• Avoid “lumping” distances at 0 m (e.g., use exact distance: 2 m, 7 m), and at 

>10 m. Record the exact distance at first detection as accurately as possible. 

• Distance to flying murrelets should equal the perpendicular distance from 

the transect line if the bird is roughly parallel to the boat, or the distance at 

first detection if its flight path is not parallel.

• Record behavior at first detection (on-water, flying, etc.). The intent is to 

record behavior before the birds respond to the boat.

• Record plumage class for each individual murrelet (see key below). The 

boat should be stopped to confirm identification if necessary and to confirm 

plumage class. The boat can leave the transect line to approach murrelets 

for a closer look if necessary and then resume the transect line at the point 

of departure.

• Data are recorded for all seabirds and marine mammals encountered; 

however, collecting marbled murrelet data is the primary focus of these 

surveys.

• If a large group of birds (>200) of any species is encountered, the boat may 

stop to allow the observers to scan and estimate numbers for each species. 

Estimating the percentage of the entire group for each species is an efficient 

way to do this.

• Survey speed is maintained at 8 to 12 knots, depending on sea conditions. 

The observers should set the survey speed within range according to their 

perceived ability to cover their survey area.
38

GENERAL TECHNICAL REPORT PNW-GTR-716

• Environmental data (Beaufort, glare, swell height, etc.) are recorded 

directly onto field forms at the beginning of each survey and updated 

as conditions change.

• Survey effort is ended if glare is code 2 or greater (glare 2 = missing 

2/3 of birds).

• Survey effort is ended if Beaufort scale is 3 or greater (see table 4).

• If fatigue begins, take a short break at the end of a subunit or zigzag. 

Do not compromise data collection.

Table 4—Beaufort Wind Scale developed in 1805 by Sir Francis Beaufort of England (0 = calm to 

12 = hurricane)

Wind Appearance of wind Appearance of wind Notes specific to on-water

Force (knots) Classification effects on the water effects on land seabird observationsa

0 < 1 Calm Sea surface smooth Calm, smoke rises Excellent conditions, no wind,

and mirror like vertically small or very smooth swell. You have the impression you could see anything.

1 1–3 Light air Scaly ripples, Smoke drift indicates Very good conditions, surface

no foam crests wind direction, still could be glassy (Beaufort 0), wind vanes but with some lumpy swell or

reflection from forests, glare, etc.

2 4–6 Light breeze Small wavelets, Wind felt on face, Good conditions, no whitecaps, 

crests glassy, no leaves rustle, vanes texture/lighting contrast of water

breaking begin to move make murrelets hard to see. Surface could also be glassy or have small ripples, but with a 

short, lumpy swell, thick fog, etc.

3 7–10 Gentle breeze Large wavelets, crests Leaves and small Fair conditions, scattered whitecaps

beginning to break, twigs constantly present, detection of murrelets

scattered whitecaps moving, light flags definitely compromised, a hit-or- extended miss chance of seeing them owing to water choppiness and high contrast. This could also occur at lesser wind with a very short 

 wavelength, choppy swell. 

4 11–16 Moderate Small waves 0.3 to Dust, leaves, and Poor conditions, end surveys,

breeze 1.1 m becoming loose paper lifted, whitecaps abundant, sea chop

 longer, numerous small tree branches bouncing the boat around, etc.

whitecaps move If you were nearly done with a 

 survey and running with the wind, 

 you could survey somewhat 

 effectively in these conditions (but shouldn’t).

5 17–21 Fresh breeze Moderate waves 1.1 Small trees begin

to 2.0 m taking longer to sway

 form, many whitecaps,

 some spray

a

Source: Strong 1998.
39

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Distance Quality Assurance/Quality Control 

Estimates of distance from the transect line are a critical part of the data collected; 

therefore, substantial time is spent practicing the technique prior to the survey 

season and followed by quality assurance tests during the survey season.

Presurvey distance tests

• Stationary targets are selected at a range of distances in front and to the 

side of the boat.

• Compare individual’s direct estimate of perpendicular distance to that 

recorded by a range finder.

• Provide immediate feedback and visual calibration between estimated 

distance and actual distance.

• Conduct 60 to 100 estimates per person. 

During survey distance tests

• Test every 3 survey days for distance calibration and record on test form 

(provided).

• Completed prior to or during the survey day (e.g., use targets encountered 

on water).

• Observers make five estimates of perpendicular distance to five different 

targets; if all five are within 15 percent of the actual distances, the trial is 

complete. If not, the observer continues in sets of five until all five distances 

are within 15 percent of the actual distances.

• Observers are given feedback on potential bias (consistently over, or under).

External audits

• Someone not part of the daily survey crew will make at least three visits to 

each crew during the survey period to verify the survey protocol is being 

implemented correctly and complete audit form (Huff 2003).
40

GENERAL TECHNICAL REPORT PNW-GTR-716

Key to Aging Marbled Murrelets At Sea

In the field, marbled murrelets (Brachyramphus marmoratus) are classified into 

seven age/plumage categories. Classes 1 through 4 are from Strong 1998; class 

5 was added to represent known juveniles, and two “unknown” categories were 

added to represent unknown age. Basic plumage is the black and white plumage 

seen in fall and winter. Alternate plumage is the brown mottled breeding plumage.

CLASS 1 Very little or no molt. Entirely in alternate plumage; bird 

appears brown.

CLASS 2 Obvious body molt but estimated at less than 50 percent of 

alternate plumage lost or replaced. Breast and neck obviously 

lighter than back.

CLASS 3 Over 50 percent of alternate plumage lost or replaced, but still 

clearly distinguishable from HY (juvenile) birds by brown 

alternate plumage feathers on back, breast, and belly. Molting 

birds placed in this class if throat and neck appeared whitish 

overall in color.

CLASS 4 Appears to be in basic plumage (black and white) from a 

distance. By definition, birds in this class require closer 

examination to distinguish between after hatch year 

(AHY, adult) and hatch year (HY, juvenile) murrelets. 

**For this protocol, birds recorded as class 4 (after close 

examination) are assumed to be adult birds in advanced molt. 

Otherwise, they would be recorded as class 5 or “unknown.”

CLASS 5 Entirely in basic plumage—confirmed HY bird.

UNKNOWN Unknown age, black and white bird (HY or AHY cannot 

be reliably determined).

UNKNOWN-B/W Plumage classification cannot be determined (inadequate 

viewing time, etc.)

These classes are intended for observations made throughout the summer 

and early fall, before adults have completed prebasic molt. Juveniles can begin to 

appear in mid to late June, but they can be distinguished from adults at this time. It 

becomes more difficult to distinguish juveniles and adults once class 4 birds begin 

to appear. For Puget Sound, this generally occurs by late July, and class 4 birds 

become increasingly more numerous through August. 
41

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Appendix 4: Estimation of the Detection Function1

An important aspect of the line transect method is the estimation of the detection 

function. The detection function describes the probability of detecting an object in 

relation to its distance from a random line or point. In analyzing the data from 2000 

through 2005, the DISTANCE program (Version 4, Release 1, Buckland et al. 2001) 

was used to estimate the detection function. The individual perpendicular distances 

to an observed group of birds were used to fit the half-normal, hazard-rate, and 

uniform key functions with up to a five-parameter cosine series multiplier. This 

provided additional flexibility but only allowed parameters that result in a strictly 

nonincreasing detection probability with distance. The curve form was selected 

that had the smallest Akaike’s Information Criterion (AIC) value that was corrected 

for a finite sample size bias (AICc). AIC is a method for assessing the fitness of a 

model (i.e., a small deviation from observed data or large likelihood), taking into 

account the number and order of model parameters. This process is automated in 

DISTANCE.

Estimated Detection Functions for the 2002 Zones 4 

and 5 Surveys

Following the 2002 field season, we reevaluated our analysis of the detectability. 

Using the 2002 data as an example, we found evidence that the hazard-rate model 

might give spurious results, depending on the shape of the detection function. 

Therefore, we did a more thorough evaluation of the various options for model 

selection, and results are described in this appendix. Figure 6 shows the best AICc 

half-normal, hazard-rate, and uniform detection function estimates for the 2002 

data from Zones 4 and 5. There are 730 observations (i.e., 730 individual perpendicular distances to groups of birds), with a large relative frequency of counts near 

zero perpendicular distance. Histograms (using 25 equally spaced nonoverlapping 

intervals) are superimposed over each detection function such that the area under 

the histogram equals the area under the detection function out to the maximum 

distance. For this example, the maximum distance is 175 m. The histogram plot in 

figure 6 shows the number of observations for each histogram bar. The detection 

functions all have similar curve forms estimated for effective strip half-widths 

1

Appendix 4 was developed by Jim Baldwin, U.S. Department of Agriculture, Forest 

Service, Pacific Southwest Research Station, P.O. Box 245, Berkeley, CA 94701.

The detection 

function describes 

the probability of 

detecting an object 

in relation to its 

distance from a 

random line or point.
42

GENERAL TECHNICAL REPORT PNW-GTR-716

Figure 6—Estimates of detection functions along with the display of the histogram of the counts in each of 25 categories for the 

observed data in the 2002 Zones 4 and 5 surveys.

Perpendicular distance (m)

Pro

b

a

bility

of d

ete

ctio

n

Half normal key

μ = 94.5 m

ƒ(0) = 0.010578

AICc = 7,269.8

0 20 60 100 140 180

0

1

2

3

Perpendicular distance (m)

Perpendicular distance (m) Perpendicular distance (m)

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Hazard-rate key

μ = 96.3 m

ƒ(0) = 0.010386

AICc = 7,270.7

0 20 60 100 140 180

0

1

2

3

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Uniform key

= 96.0 m

ƒ(0) = 0.010421

AICc = 7,268.7

0 20 60 100 140 180

0

1

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3

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Histogram of

observed distances

n = 730

0 20 60 100 140 180

0

50

100

150

200

μ

(μ = 94.5, 96.3, and 96.0 m for the half-normal, hazard-rate, and uniform detection 

functions, respectively) and similar estimates of the detection function probability, 

ƒ(0). The uniform key is chosen because of having the lowest AICc value. Effective 

strip half-width can be thought of as the width of a strip on one side of the transect 

over which essentially all of the objects (murrelets) are detected and is equal to the 

inverse of ƒ(0).
43

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Some Problems Estimating Detection Functions

Under the above settings for the estimation of a detection function, different 

estimates for the curve occur occasionally for some particular bootstrap samples. 

The estimated effective strip half-widths (μ = 92.5, 14.4, and 9.1 m for the halfnormal, hazard-rate, and uniform detection functions, respectively) differ considerably for the bootstrap sample shown in figure 7. (The bootstrap is a method for 

estimating the distribution of an estimator by simulated resampling of data with 

replacement). The estimate for the hazard-rate key has an extremely small estimate 

Figure 7—Estimates of detection functions along with the display of the histogram of the counts in each of 25 categories for a particular 

bootstrap sample from 2002 Zones 4 and 5 surveys.

μ = 92.5 m

ƒ(0) = 0.010810

AICc = 7,762.4

μ = 14.4 m

ƒ(0) = 0.069694

AICc = 7,473.4

Uniform key

μ = 90.1 m

ƒ(0) = 0.011099

AICc = 7,759.0

n = 792

Perpendicular distance (m)

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Half normal key

0 20 60 100 140 180

0

1

2

3

Perpendicular distance (m)

Perpendicular distance (m) Perpendicular distance (m)

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Hazard-rate key

0 20 60 100 140 180

0

1

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3

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0 20 60 100 140 180

0

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Histogram of

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0 20 60 100 140 180

0

50

100

150

200
44

GENERAL TECHNICAL REPORT PNW-GTR-716

of the effective strip half-width, which corresponds to a very large estimate of ƒ(0). 

The problem arises when certain predictors produce unreasonable outcomes for 

individual bootstrap samples. The effects of this are seen, for example, at 20 m for 

the hazard-rate estimate, which predicted a probability of less than .20 to observe a 

group of murrelets for this distance. This type of lack of fit for the hazard-rate function occurred in about 10 to 20 of the 1,000 bootstrap samples of the 2002 Zones 

4 and 5 surveys, resulting in very large estimates of ƒ(0) and density estimates 

with large standard errors. Although data with large standard errors are plausible, 

the ones observed with the standard hazard-rate key are spurious because of the 

unjustifiable estimates of ƒ(0). Although removal of the hazard-rate key function is 

defensible, unfortunately none of the key functions fit the histograms very well as 

shown by the large number of observations near zero meters.

The estimates of the detection functions for the 2002 at-sea surveys and the 

scaled histogram of the observations for each zone are shown in figure 8. Scaling 

has the effect of making area under the histogram equivalent and the area under the 

detection function <1. Zone 1 shows a “spike” of observations near zero meters, as 

do Zones 4 and 5. This is characteristic of the condition called “guarding the centerline.” One approach to reduce this effect after the fact is to group data into intervals 

and then use the grouped data to estimate the detection functions. Using the 2002 

Zones 4 and 5 survey data as an example, the estimated detection functions for all 

three key functions in figure 9 appear to fit better than that of the ungrouped data 

shown in figure 7; and, the estimates of ƒ(0) differ little between the grouped and 

ungrouped data. Refitting of the extreme bootstrap of ungrouped data shown in 

figure 7 with the distances grouped at every 20 m shown in figure 10 gives a much 

more reasonable estimate of the effective half-strip width for the hazard-rate key 

function. However, even after grouping the data, up to 10 bootstrap samples from 

the 2002 Zone 4 and 5 surveys result in extreme estimates of ƒ(0) and associated 

detection function that are unsuitable. 

Adjustments to Analysis Methods

To eliminate the inappropriate estimates of ƒ(0) and the associated detection 

functions, data were grouped into seven intervals after truncating 5 percent of the 

most extreme distances from all observations in a zone. An alternative method 

where the grouping is selected from a data-driven process, as recommended by 

Barabesi et al. (2002) will be investigated as this is not yet a feature of DISTANCE. 

Based on the current data, an interval of 20 m seems appropriate. As more data 

are gathered with the future monitoring, additional investigation will be done on 

selecting the appropriate intervals.
45

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

Figure 8—Estimated detection functions for at-sea surveys taken 2002 for each zone along with the scaled histograms. Note 

that, until 2002 in Zone 2, observers were instructed to record observations out to only 100 m (this instruction was eliminated in 

subsequent years).

Zone 1

0 25 50 75 125 175

0.4 0.8 1.2 1.6 2.00.4 0.8 1.2 1.6 2.0

Zone 2

0 25 50 75 125 175

00

0.4 0.8 1.2 1.6 2.00.4 0.8 1.2 1.6 2.0

00

Zone 3

0 25 50 75 125 175

Zones 4 and 5

0 25 50 75 125 175

Perpendicular distance (m)

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Perpendicular distance (m)

Perpendicular distance (m) Perpendicular distance (m)

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The hazard-rate key function has been dropped from the marbled murrelet 

population analyses because of the unrealistic ƒ(0) estimates encountered from 

Zones 4 and 5. Similar problems have occurred with this function in other studies 

with somewhat spiked data. Buckland et al. (2001) reported that the hazard-rate 

function can give density estimates with large positive bias, especially when the 

data spikes are an artifact of data rounding. 
46

GENERAL TECHNICAL REPORT PNW-GTR-716

Figure 9—Detection functions for the observed data in 2002, Zones 4 and 5, fit with distances grouped at every 20 m.

= 92.2 m

ƒ(0) = 0.010846

AICc = 2,908.3

= 92.3 m

ƒ(0) = 0.010839

AICc = 2,910.1

= 96.6 m

ƒ(0) = 0.010350

AICc = 2,909.5

n = 795

μ μ

Uniform key

μ

Perpendicular distance (m)

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Half normal key

0 20 60 100 140 180

0

1

2

3

Perpendicular distance (m)

Perpendicular distance (m) Perpendicular distance (m)

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Hazard-rate key

0 20 60 100 140 180

0

1

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3

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0 20 60 100 140 180

0

1

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Histogram of

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0 20 60 100 140 180

0

50

100

150

200
47

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

= 87.3 m

ƒ(0) = 0.011456

AICc = 3,025.6

= 73.4 m

ƒ(0) = 0.013624

AICc = 3,020.8

= 88.3 m

ƒ(0) = 0.011323

AICc = 3,024.1

n = 795

μ μ

Uniform key

μ

Perpendicular distance (m)

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0

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3

Perpendicular distance (m)

Perpendicular distance (m) Perpendicular distance (m)

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Half normal key Hazard-rate key

0 20 60 100 140 180

0

1

2

3

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0 20 60 100 140 180

0

50

100

150

200

Figure 10—Detection functions for an “extreme” bootstrap sample from the 2002 Zones 4 and 5 data fit with distances grouped at 

every 20 m.
48

GENERAL TECHNICAL REPORT PNW-GTR-716

Appendix 5: An Example of SAS Code for Performing Bootstrap Analysis1

* Get density estimates for all Zones;

* Include SAS macros;

 option spool nomprint;

 %include “c:\Docume~1\jbaldwin\mydocu~1\mamu\atseamacros.sas”;

* Set season dates: starting month, day, year and ending month, day, year;

 %SetSeason(5,15,2005,7,31,2005)

 * Zone 1;

 %FileLocations(c:\Docume~1\jbaldwin\mydocu~1\mamu\2005\z1\,

 c:\progra~1\distan~1\)

 %analysis(zone1_2005,1000,3,0);

* Zone 2;

 %FileLocations(c:\Docume~1\jbaldwin\mydocu~1\mamu\2005\z2\,

 c:\progra~1\distan~1\)

 %analysis(zone2_2005,500,3,0);

 * Zone 3;

 %FileLocations(c:\Docume~1\jbaldwin\mydocu~1\mamu\2005\z3\,

 c:\progra~1\distan~1\)

 %analysis(zone3_2005,500,3,0);

* Zones 4 and 5;

 options mprint;

 %FileLocations(c:\Docume~1\jbaldwin\mydocu~1\mamu\2005\z45\,

 c:\progra~1\distan~1\)

 %analysis(zone45_2005,250,3,0);

 run;

* AtSeaMacros.sas;

* Contains macros used in the bootstrap process;

* Version 1.0, February 2, 2001;

* Jim Baldwin, Pacific Southwest Research Station;

%macro analysis(filename,nbootstraps,noModelAssist,FixedWidth);

 * Main analysis routine for obtaining estimates;

 /*

 Parameters Description

 filename Name of Excel data file (mamu3, mamu45, etc.) (Don’t put in 

 .xls extension)

 nbootstraps Number of bootstrap runs (1,000 takes about 3 hours)

 noModelAssist 3 for no model assisted estimation

 FixedWidth 0 => line transect estimation. Any positive number is 

 interpreted as the transect halfwidth for fixed-width transect estimation

 */

 * First, set some of the constants that will rarely be changed;

 %global maxC maxPSU maxStrata TruncateP maxf0;

1

Appendix 5 was developed by Jim Baldwin, U.S. Department of Agriculture, Forest 

Service, Pacific Southwest Research Station, P.O. Box 245, Berkeley, CA 94701.
49

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 %let maxC = 100; * Maximum number of clusters in a stratum;

 %let maxPSU = 100; * Maximum number of PSUs within a cluster;

 %let maxStrata = 4; * Maximum number of strata per zone;

 %let TruncateP = .05; * Truncation proportion;

 %let maxf0 = 1; * Maximum value of f0 allowed;

 %if &FixedWidth > 0 %then %let TruncateP = .00;

 

 * Estimate density (without the bootstrap);

 data summary; run;

 %settings(nobootstraps=1,nbootstraps=1,nomodelassist=&noModelAssist,

 notempfiledelete=0,FixedW=&FixedWidth)

 %boot(&filename..xls)

 data raw; set summary;

 * Bootstrap runs (if any);

 %if &nbootstraps > 0 %then %do;

 * Discard all log output to get ready for bootstrap runs;

 filename logout dummy;

 proc printto log=logout;

 data summary; run; * Initialize summary file;

 %settings(nobootstraps=0,nbootstraps=&nbootstraps,nomodelassist=&noModelAssist,

 notempfiledelete=0,FixedW=&FixedWidth)

 %boot(&filename..xls)

 data bootstraps; set summary;

 %summarize(bootstraps)

 %end;

 * Restart log output;

 proc printto;

 * Output all of the results to a text file that can be directly imported into Excel;

 %summarize(raw)

 data;

 set raw %if &nbootstraps > 0 %then bootstraps;;

 file “&datadir.summary_&filename..csv”;

 if _n_ = 1 then put 

 “Type,f0,Es,TruncateDistance,zone,density1,density2,density3,density4,”

 “stratumarea1,stratumarea2,stratumarea3,stratumarea4,”

 “birds1,birds2,birds3,birds4,”

 “zonedensity,zonebirds,zonearea”;

 

 put type “,” f0 “,” Es “,” TruncateDistance “,” zone “,”

 density1 “,” density2 “,” density3 “,” density4 “,”

 stratumarea1 “,” stratumarea2 “,” stratumarea3 “,” stratumarea4 “,” 

 birds1 “,” birds2 “,” birds3 “,” birds4 “,”

 zonedensity “,” zonebirds “,” zonearea;

 run;

%mend analysis;

%macro SetSeason(ssmonth,ssday,ssyear,eemonth,eeday,eeyear);

 * Sets the beginning and ending dates for the season. Observations outside of these

 dates are not used in the analysis;

 %global smonth sday syear emonth eday eyear;

 * Starting date of season;

 %let smonth = &ssmonth;
50

GENERAL TECHNICAL REPORT PNW-GTR-716

 %let sday = &ssday;

 %let syear = &ssyear;

 * Ending date of season;

 %let emonth = &eemonth;

 %let eday = &eeday;

 %let eyear = &eeyear;

%mend SetSeason;

%macro summarize(summary);

 * Summarizes results;

 * Remove the first record as it just contains missing values and add in

 estimates of the number of birds;

 data xsummary;

 set &summary;

 data &summary;

 set &summary;

 drop z5area1 z5area2 z5density1 z5density2;

 if “&summary” = “raw” then type = “Raw “; else type = “Boot”;

 * Skip lines that contain missing values for Zone;

 if zone = . then delete;

 * Separate Zones 4 and 5;

 if zone = 45 then do;

 zone = 4;

 z5area1 = stratumarea3;

 z5area2 = stratumarea4;

 z5density1 = density3;

 z5density2 = density4;

 stratumarea3 = .;

 stratumarea4 = .;

 density3 = .;

 density4 = .;

 zonedensity = (stratumarea1*density1+stratumarea2*density2)/

(stratumarea1+stratumarea2);

 zonearea = stratumarea1 + stratumarea2;

 output;

 zone = 5;

 stratumarea1 = z5area1;

 stratumarea2 = z5area2;

 density1 = z5density1;

 density2 = z5density2;

 zonedensity = (stratumarea1*density1+stratumarea2*density2)/

(stratumarea1+stratumarea2);

 zonearea = stratumarea1 + stratumarea2; output; end;

 else output;

 data &summary;

 set &summary;

 if stratumarea1 ne . then birds1 = density1*stratumarea1; else birds1 = .;

 if stratumarea2 ne . then birds2 = density2*stratumarea2; else birds2 = .;

 if stratumarea3 ne . then birds3 = density3*stratumarea3; else birds3 = .;

 if stratumarea4 ne . then birds4 = density4*stratumarea4; else birds4 = .;

 zonebirds = zonedensity*zonearea;

 proc sort data=&summary out=&summary;

 by zone;
51

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 proc means data=&summary mean stddev n;

 by zone;

 run;

%mend summarize;

%macro FileLocations(data,prog);

 * Sets the data file and program file directories;

 

 %global datadir distdir;

 %let datadir = &data;

 %let distdir = &prog;

%mend FileLocations;

%macro settings(nobootstraps,nbootstraps,nomodelassist,notempfiledelete,fixedW);

 * Sets common settings;

 %global noboot nboot noassist nodelete FixedWidthOnly TransectHalfWidth;

 %let noboot = &nobootstraps;

 %let nboot = &nbootstraps;

 %let noassist = &nomodelassist;

 %let nodelete = ¬empfiledelete;

 %let TransectHalfWidth = &fixedW;

 %if &fixedW = 0 %then %let FixedWidthOnly = 0; %else %let FixedWidthOnly = 1;

 %put “FixedWidthOnly = &FixedWidthOnly”;

%mend settings;

%macro MakeDen;

* Create Distance batch file for densities (first analysis from Laake and Raphael);

data;

 file “&datadir.mamu1.txt”;

 put “out1.txt”;

 put “log1.txt”;

 put “densitystats.txt”;

 put “boot1.txt”;

 put “plot1.txt”;

 put “Options;”;

 put “ Type=Line;”;

 put “ Length /Measure=’Kilometers’ /Units=’Kilometers’;”;

 put “ Distance=Perp /Measure=’Meters’ /Units=’Meters’;”;

 put “ Area /Units=’Sq. kilometers’;”;

 put “ Object=Cluster;”;

 put “ SF=1;”;

 put “ Selection=Sequential;”;

 put “ PValue=.150;”;

 put “ Lookahead=1;”;

 put “ Maxterms=5;”;

 put “ Bootstraps=999;”;

 put “ Seed=0;”;

 put “ Confidence=95;”;

 put “ Print=Selection;”;

 put “End;”;

 put “Data /Structure=Flat;”;

 put “ Fields=STR_LABEL, STR_AREA, SMP_LABEL, SMP_EFFORT, DISTANCE, SIZE;”;

 put “ Infile=’&datadir.mamu.dat’;”;
52

GENERAL TECHNICAL REPORT PNW-GTR-716

 put “End;”;

 put “Estimate;”;

 put “ Distance /Nclass=7 /Width=&TruncateDistance /Left=0;”; 

 /* put “ Distance /Intervals=0,20,40,60,80,100,120,140,160,180,200,210,220,240,260 /

Width=&TruncateDistance /Left=0;”; */

 /* put “ Distance /Nclass=9 /Width=180 /Left=0;”; */

 put “ Density=All;”;

 put “ Density=Stratum /Design=Strata /Weight=Area;”;

 put “ Encounter=Stratum;”;

 put “ Detection=All;”;

 put “ Size=All;”;

 put “ Estimator /Key=HN /Adjust=CO /Criterion=AIC;”;

 /* put “ Estimator /Key=HA /Adjust=CO /Criterion=AIC;”; */

 put “ Estimator /Key=UN /Adjust=CO /Criterion=AIC;”;

 put “ Monotone=Strict;”;

 put “ Pick=AIC;”;

 put “ GOF;”;

 put “ Cluster /Bias=GXLOG /Test=.15;”;

 put “ VarN=Empirical;”;

 put “End;”;

 run;

%mend MakeDen;

%macro MakeER;

* Create Distance batch file for encounter rates

 (second analysis from Laake and Raphael);

data;

 file “&datadir.mamu2.txt”;

 put “out2.txt”;

 put “log2.txt”;

 put “erstats.txt”;

 put “boot2.txt”;

 put “plot2.txt”;

 put “Options;”;

 put “ Type=Line;”;

 put “ Length /Measure=’Kilometers’ /Units=’Kilometers’;”;

 put “ Distance=Perp /Measure=’Meters’ /Units=’Meters’;”;

 put “ Area /Units=’Sq. kilometers’;”;

 put “ Object=Cluster;”;

 put “ SF=1;”;

 put “ Selection=Sequential;”;

 put “ PValue=.150;”;

 put “ Lookahead=1;”;

 put “ Maxterms=5;”;

 put “ Bootstraps=999;”;

 put “ Seed=0;”;

 put “ Confidence=95;”;

 put “ Print=Selection;”;

 put “End;”;

 put “Data /Structure=Flat;”;

 put “ Fields=STR_LABEL, STR_AREA, SMP_LABEL, SMP_EFFORT, DISTANCE, SIZE;”;

 put “ Infile=’&datadir.mamu.dat’;”;

 put “End;”;

 put “Estimate;”;

 put “ Distance /Width=&TruncateDistance;”;

 /* put “ Distance /Intervals=0,20,40,60,80,100,120,140,160,180,200,220,240,260 /

Width=&TruncateDistance /Left=0;”; */

 put “ Encounter by Sample;”;

 put “ Estimator /Key=HN /Adjust=CO /Criterion=AIC;”;

 /* put “ Estimator /Key=HA /Adjust=CO /Criterion=AIC;”; */
53

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 put “ Estimator /Key=UN /Adjust=CO /Criterion=AIC;”;

 put “ Monotone=Strict;”;

 put “ Pick=AIC;”;

 put “ GOF;”;

 put “ Cluster /Mean;”;

 put “ VarN=Empirical;”;

 put “End;”;

 run;

%mend MakeER;

%macro MakeBat;

* Create the MS-DOS batch file to run Distance;

data;

 file “&datadir.mamu.bat”;

 put ‘echo off’;

 put ‘rem Batch file for estimating density with Distance’;

 put ‘ ‘;

 put ‘rem Run the first analysis that creates densitystats.txt’;

 put “cd &datadir”;

 put “&distdir.d4 0 mamu1.txt”;

 put ‘ ‘;

 put ‘rem Run the second analysis that creates erstats.txt’;

 put “&distdir.d4 0 mamu2.txt”;

 put ‘ ‘;

 put ‘rem Add to complete results file’;

 put ‘type results.txt >> bootstrap.txt’;

 put ‘ ‘;

 put ‘rem Keep track of log files and outputfiles for testing purposes’;

 put ‘rem type log1.txt >> logs.txt’;

 put ‘rem type out1.txt >> logs.txt’;

 put ‘ ‘;

 *if &noDelete = 0 then do;

 * put ‘rem Clean-up’;

 * *put ‘del log1.txt’;

 * put ‘del log2.txt’;

 * put ‘del boot1.txt’;

 * put ‘del boot2.txt’;

 * put ‘del plot1.txt’;

 * put ‘del plot2.txt’;

 * put ‘del out1.txt’;

 * put ‘del out2.txt’;

 * put ‘del results.txt’;

 * put ‘del densitystats.txt’;

 * put ‘del erstats.txt’;

 * put ’del PSUBoot.txt’;

 * put ’del Strtm.txt’;

 * put ’del mamu.dat’;

 * put ’del bootstrap.txt’;

 * put ’ ’;

 *end;

 put ’rem Return to SAS’;

 put ’exit’;

 run;

%mend MakeBat;

%macro GetPSU;

 proc sort data=PSUFile out=PSUFile;

 by zone stratum psu;

 run;

 * Now turn areas into an array by strata;
54

GENERAL TECHNICAL REPORT PNW-GTR-716

 data PSUInfo;

 set PSUFile;

 by zone stratum psu;

 array area(200) a1-a200;

 array psuID(200) psuID1-psuID200;

 retain a1-a200 psuID1-psuID200 nn;

 keep zone stratum a1-a200 psuID1-psuID200 nn;

 if first.stratum then do;

 nn=0;

 do i=1 to 200; area(i)=.; psuID(i)=.; end;

 end;

 if first.psu then do;

 nn = nn + 1;

 area(nn) = psuarea;

 psuID(nn) = psu;

 end;

 if last.stratum then output;

 run;

 proc sort data=PSUInfo out=PSUInfo;

 by zone stratum;

 run;

%mend GetPSU;

%macro GetDetect;

 * Get a listing of the clusters within a strata;

 proc sort data=Project out=Project;

 by zone stratum cluster psu days;

 data bootraw1;

 set Project;

 by zone stratum cluster;

 keep zone stratum cluster;

 if first.zone or first.stratum or first.cluster then output;

 proc sort data=bootraw1;

 by zone stratum cluster;

 run;

 * Get a listing of the PSU-date combinations for each cluster 

 within each stratum;

 data bootraw2;

 set Project;

 by zone stratum cluster psu days;

 keep zone stratum cluster psu days;

 if first.zone or first.stratum or first.cluster or first.psu or first.days then output;

 proc sort data=bootraw2;

 by zone stratum cluster psu days;

 run;

%mend GetDetect;

%macro TruncateBoot;

 * Removes the observations with the largest 100p percent of the distances;
55

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 * Get a dataset just with detections;

 data detections;

 set boot;

 if n > 0;

 run;

 * Sort by perpendicular distance;

 proc sort data=detections out=detections;

 by perp_dist;

 run;

 * Determine truncation distance;

 data;

 set detections nobs=nobs;

 retain k;

 * Determine nearest integer to nobs*(1-&TruncateP);

 if _n_ = 1 then k = int(nobs*(1-&TruncateP) + .5);

 if _n_ = k then call symput(’TruncateDistance’,perp_dist);

 run;

%mend TruncateBoot;

%macro GetBoot;

 * Get a random sample of clusters;

 data boot1;

 set bootraw1;

 by zone stratum cluster;

 array cl(&maxc) cl1-cl&maxc; * Array of cluser IDs;

 array clf(&maxc) clf1-clf&maxc; * Arrary of frequencies for clusters;

 retain seed nclusters cl1-cl&maxc;

 keep zone stratum cluster f;

 if _n_ = 1 then seed = -1;

 if first.stratum then nclusters=0;

 if first.cluster then do; nclusters=nclusters + 1; cl(nclusters) = cluster; end;

 if last.stratum then do;

 do i=1 to nclusters; clf(i) = 0; end; * initialize counts of clusters;

 * Generate a random cluster number;

 do i=1 to nclusters;

 k = 1 + int(nclusters*uniform(seed)); if k > nclusters then k = nclusters;

 clf(k) = clf(k) + 1;

 end;

 * Make output data set with cluster and frequency of selection;

 do i=1 to nclusters;

 if &noboot=1 then do; * Undo bootstrap selection if &noboot=1;

 f = 1;

 cluster = cl(i);

 end;

 else do;

 f = clf(i);

 cluster = cl(i);

 end;

 output;

 end;

 end;

 run;
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GENERAL TECHNICAL REPORT PNW-GTR-716

 proc sort data=boot1;

 by zone stratum cluster;

 data boot;

 merge boot1 bootraw2;

 by zone stratum cluster;

 if f ne 0;

 run;

 * Dataset boot has the random sample of clusters with the associated frequency;

 * Now select PSUs with replacement;

 data boot;

 set boot;

 by zone stratum cluster;

 keep zone stratum cluster psu days f;

 array fp(&maxPSU) fp1-fp&maxPSU;

 array p(&maxPSU) p1-p&maxPSU;

 array d(&maxPSU) d1-d&maxPSU;

 retain seed n p1-p&maxPSU d1-d&maxPSU;

 if _n_ = 1 then seed = -1;

 if first.cluster then n=0; 

 n = n + 1;

 p(n) = psu;

 d(n) = days;

 if last.cluster then do;

 do j = 1 to n; fp(j) = 0; end; * initialize PSU frequencies;

 * Select random sample of clusters;

 do i = 1 to f;

 do j = 1 to n;

 k = 1 + int(n*uniform(seed)); if k>n then k=n;

 fp(k) = fp(k) + 1;

 end;

 end;

 * Output dataset of randomly selected PSUs with frequencies;

 if &noboot=1 then do;

 do j = 1 to n;

 psu = p(j);

 days = d(j);

 f = 1;

 output;

 end;

 end;

 else do;

 do j = 1 to n;

 if fp(j) > 0 then do;

 psu = p(j);

 days = d(j);

 f = fp(j);

 output;

 end;

 end;

 end;

 end;

 * Now merge with raw data;

 data boot;
57

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 merge Project boot;

 by zone stratum cluster psu days;

 if f ne .;

 run;

 * Now determine truncation distance;

 %put ”TruncateBoot”;

 %TruncateBoot

%mend GetBoot;

%macro GetFixedWidthDensity;

 * Estimates density based on a fixed width transect of size &TransectHalfWidth;

 %put ”GetFixedWidthDensity”;

 %let Es = .;

 %let f0 = .;

 data bootxx;

 set boot;

 by zone stratum cluster psu days rep subpsu;

 retain count;

 

 if first.subpsu then count = 0;

 * Change counts to zero if perpendicular distance > &TransectHalfWidth;

 if perp_dist ne . then do;

 if perp_dist > &TransectHalfWidth then do;

 perp_dist = .;

 n = 0;

 end;

 end;

 count = count + n;

 if last.subpsu then output;

 * Now get density per PSU-day-rep combination;

 proc sort data=bootxx out=bootxx;

 by zone stratum cluster psu days rep;

 data bootxxx;

 set bootxx;

 by zone stratum cluster psu days rep;

 retain density totalarea;

 if first.rep then do;

 density = 0;

 totalarea = 0;

 end;

 density = density + subpsuarea * 1000 * count / (&TransectHalfWidth * 2 * survey_effort);

 totalarea = totalarea + subpsuarea;

 if last.rep then do;

 density = density / totalarea;

 output;

 end;
58

GENERAL TECHNICAL REPORT PNW-GTR-716

 %put ”Exiting GetFixedWidthDensity”;

 run;

%mend GetFixedWidthDensity;

%macro CleanUp;

* Clean up left-over files;

data;

 file ”&datadir.cleanup.bat”;

 put ”echo off”;

 if &noDelete = 0 then do;

 put ”del &datadir.mamu.bat”;

 put “del &datadir.mamu1.txt”;

 put “del &datadir.mamu2.txt”;

 put “del &datadir.log1.txt”;

 put “del &datadir.log2.txt”;

 put “del &datadir.boot1.txt”;

 put “del &datadir.boot2.txt”;

 put “del &datadir.plot1.txt”;

 put “del &datadir.plot2.txt”;

 put “del &datadir.out1.txt”;

 put “del &datadir.out2.txt”;

 put “del &datadir.results.txt”;

 put “del &datadir.densitystats.txt”;

 put “del &datadir.erstats.txt”;

 put “del &datadir.PSUBoot.txt”;

 put “del &datadir.Strtm.txt”;

 put “del &datadir.mamu.dat”;

 put “del &datadir.bootstrap.txt”;

 end;

 put ”exit”;

 run;

x ”&datadir.cleanup.bat”;

%mend CleanUp;

%macro MakeBoot;

* Expand based on the frequencies of selection;

 data boot;

 set boot;

 do rep = 1 to f; output; end;

 run;

 proc sort data=boot out=boot;

 by zone stratum cluster psu days rep subpsu;

 run;

 data bootxx;

 set boot;

 by zone stratum cluster psu days rep subpsu;

 keep zone stratum psu subpsu rep survey_effort days 

 psuarea subPSUarea stratumarea PSUNum;

 retain PSUNum;

 if _n_ = 1 then PSUNum = 0;

 if last.subpsu then do;

 PSUNum = PSUNum + 1;

 output;

 end;

 proc sort data=bootxx out=bootxx;

 by PSUNum;
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Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

* Makes file readable by Distance and obtains info for creating PSUBoot.txt;

 data psuareas;

 set boot;

 by zone stratum cluster psu days rep subpsu;

 file ”&datadir.mamu.dat”;

 keep psuarea1 psuarea2 psu zone stratum;

 retain nstrata PSUNum psuarea1 prevPSUNum;

 * Initialize counters for unique strata and unique psu-subunits;

 * (This is because I think Distance requires this. The problem

 occurs when two consecutive entries have the same psu id and

 have zero counts. Either having unique ids or separating the

 observations seems to work.);

 if _n_ = 1 then do;

 nstrata = 0;

 PSUNum = 0;

 prevPSUNum = -1;

 end;

 if first.stratum then do; nstrata = nstrata + 1; end;

 if first.subpsu then do; PSUNum = PSUNum + 1; end;

 %put stratum cluster psu days rep subpsu n;

 if n = 0 then do;

 *put nstrata stratum ’09’x stratumarea ’09’x PSUNum psu 3.0 subpsu

 ’09’x survey_effort ’09’x ’09’x;

 * Do not put out a zero if the previous observation has a non-zero count as

 Distance 3.5 complains;

 if prevPSUNum ne PSUNum then

 put stratum ’09’x stratumarea ’09’x PSUNum psu 3.0 subpsu

 ’09’x survey_effort ’09’x;

 end;

 else do;

 *put nstrata stratum ’09’x stratumarea ’09’x PSUNum psu 3.0 subpsu

 ’09’x survey_effort ’09’x perp_dist ’09’x n;

 put stratum ’09’x stratumarea ’09’x PSUNum psu 3.0 subpsu

 ’09’x survey_effort ’09’x perp_dist ’09’x n;

 end;

 if subpsu = ”N” then psuarea1 = subpsuarea;

 if subpsu = ”x” then do;

 psuarea1 = subpsuarea; psuarea2 = 0;

 end;

 if last.subpsu and subpsu = “O” then do; 

 psuarea2 = subpsuarea; output; 

 end;

 if last.subpsu and subpsu = “x” then do;

 psuarea1 = subpsuarea; psuarea2 = 0; output;

 end;

 prevPSUnum = PSUnum;

 run;

%mend MakeBoot;

%macro TooFew;

 * Checks for warning from Distance that there are too few observations;

 * Macro variable “status” is set to “1” if sufficent observations,

 “0” if too few observations;
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GENERAL TECHNICAL REPORT PNW-GTR-716

 %put “TooFew”;

 %let status=1;

 run;

 data log1;

 length logrecord $ 50;

 infile “&datadir.log1.txt” missover;

 input logrecord $ 1-50;

 * Initialize status;

 * Check for a line in log1.txt that contains “number of observations is small”;

 if index(logrecord,”number of observations is small”) > 0 then do;

 call symput(“status”,”0”); 

 end;

 run;

 %put “Status = &status”;

 run;

%mend TooFew;

%macro GetERStats;

 * Now get encounter rates for each PSUNum from erstats.txt;

 data erstats;

 infile “&datadir.erstats.txt”;

 keep PSUNum numobs;

 if _n_ = 1 then input;

 input istrat isample iest imod istat value;

 if imod = 1 and istat = 1 then do;

 PSUNum = isample;

 numobs = value;

 output;

 end;

 

 proc sort data=erstats out=erstats;

 by PSUNum;

 run;

 data bootxx;

 merge bootxx erstats;

 by PSUNum;

 erate = numobs / survey_effort;

 run;

%mend GetERStats;

%macro GetDensity;

 * Reads DensityStats.txt and retrieves the estimates of f(0) and E(s).

 The values are put into macro variables called &f0 and &es.

 ;

 %put ”GetDensity”;

 data density;

 infile ”&datadir.densitystats.txt”;

 if _n_ = 1 then input;

 input istrat isample iest imod istat value;

 if istrat = 0 and isample = 0 and imod = 2 and istat = 4 then do;

 call symput(’f0’,value);

 end;
61

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 if istrat = 0 and isample = 0 and imod = 3 and istat = 4 then do;

 call symput(’es’,value);

 end;

 run;

 %GetERStats

 data bootxx;

 set bootxx;

 density = 1000 * erate * &f0 * &es / 2;

 * Now get individual PSU-day-rep estimates of density;

 proc sort data=bootxx out=bootxx;

 by zone stratum psu days rep subpsu;

 data bootxxx;

 set bootxx;

 by zone stratum psu days rep subpsu;

 keep zone stratum psu PSUNum density psuarea days psudays stratumarea;

 retain PSUDensity TotalArea;

 if first.rep then do;

 PSUDensity = 0;

 TotalArea = 0;

 end;

 PSUDensity = PSUDensity + density*subpsuarea;

 TotalArea = TotalArea + subpsuarea;

 if last.rep then do;

 density = PSUDensity / TotalArea;

 psudays = psu*days;

 output;

 end;

 run;

 * Make data file with subPSU densities;

 data bootsubpsu;

 set bootxx;

 by zone stratum psu days rep subpsu;

 keep zone stratum psu days neardensity neararea nearbirds fardensity fararea farbirds;

 retain neardensity neararea nearbirds;

 if subpsu = ”N” then do;

 neardensity = density;

 neararea = subpsuarea;

 nearbirds = density*subpsuarea;

 end;

 if subpsu = ”O” then do;

 fardensity = density;

 fararea = subpsuarea;

 farbirds = density*subpsuarea;

 output;

 end;

 if subpsu = ”x” then do;

 neardensity = density;

 neararea = subpsuarea;

 nearbirds = density*subpsuarea;

 fardensity = .;

 fararea = 0;

 farbirds = .;

 output;

 end;

 run;
62

GENERAL TECHNICAL REPORT PNW-GTR-716

 proc means data=bootsubpsu mean noprint;

 by zone stratum psu;

 var fardensity neardensity farbirds nearbirds fararea neararea;

 output out=bootsubpsusum mean=fardensity neardensity farbirds nearbirds

 fararea neararea;

 run;

 %put ”Exiting GetDensity”;

%mend GetDensity;

%macro ModelAssist;

 * Calculate the model assisted estimate for each strata;

 

 * Perform model-assisted regression (just one regression for zone);

 proc reg data=bootxxx outest=bootr noprint;

 model density = psu days psudays;

 run;

 data;

 set bootr;

 call symput(’Intercept’,Intercept);

 call symput(’b_psu’,psu);

 call symput(’b_days’,days);

 call symput(’b_psudays’,psudays);

 data boots;

 merge PSUInfo StratumFile;

 by zone stratum;

 keep a1-a100 psuID1-psuID100 stratum Intercept 

 b_psu b_days b_psudays nn stratumarea f0 Es;

 f0 = &f0;

 Es = &Es;

 Intercept = &Intercept;

 b_psu = &b_psu;

 b_days = &b_days;

 b_psudays = &b_psudays;

 run;

 data bootg;

 set boots;

 array area(100) a1-a100;

 array psuID(100) psuID1-psuID100;

 keep zone stratum density stratumarea f0 Es;

 

 * Determine number of days in time period of interest;

 ndays = juldate(mdy(&emonth,&eday,&eyear)) - juldate(mdy(&smonth,&sday,&syear)) + 1;

 stratum_mean = 0;

 totalarea = 0;

 *put ’nn = ’ nn;

 *put stratum 3.0 @;

 *do j = 1 to nn;

 *put psuID(j) 5.0 @;

 *end;

 *put ;

 do i = 1 to ndays;

 *put i 3.0 @;

 do j = 1 to nn;

 den = Intercept + b_psu*psuID(j) + b_days*i + b_psudays*i*psuID(j);
63

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 *put den 5.1 @;

 if den < 0 then den = 0;

 stratum_mean = stratum_mean + area(j)*den;

 totalarea = totalarea + area(j);

 end;

 *put ;

 end;

 density = stratum_mean / totalarea;

 *put ;

 *put density;

 *put ;

 * Calculate weighted mean (weighted by stratum area);

 proc sort data=bootg out=bootgg;

 by zone stratum;

 * Now combine stratum estimates to a single zone estimate;

 

 * Attach stratum areas to stratum means;

 data bootv;

 merge bootgg StratumFile;

 by zone stratum;

 data bootv;

 set bootv end=LastOne;

 by zone stratum;

 keep Zone ZoneArea ZoneDensity nstrata Density1-Density&maxStrata 

 StratumArea1-StratumArea&maxStrata f0 Es;

 array den(&maxStrata) density1-density&maxStrata;

 array sarea(&maxStrata) StratumArea1-StratumArea&maxStrata;

 retain ZoneDensity nstrata ZoneArea Density1-Density&maxStrata 

 StratumArea1-StratumArea&maxStrata;

 if _n_ = 1 then do; ZoneDensity = 0; ZoneArea = 0; nstrata = 0; end;

 nstrata = nstrata + 1;

 ZoneDensity = ZoneDensity + density * stratumarea;

 if ZoneDensity = . then do;

 put stratum density stratumarea;

 end;

 ZoneArea = ZoneArea + stratumarea;

 *den(nstrata) = density;

 den(stratum) = density;

 *sarea(nstrata) = Stratumarea;

 sarea(nstratum) = Stratumarea;

 if LastOne = 1 then do;

 ZoneDensity = ZoneDensity / ZoneArea;

 output;

 end;

 run;

%mend ModelAssist;

%macro NoAssist;

 * Estimates mean density without the model-assisted approach;

 

 proc sort data=bootxxx out=bootxxx;

 by zone stratum;
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GENERAL TECHNICAL REPORT PNW-GTR-716

 proc means data=bootxxx mean noprint;

 by zone stratum;

 var density stratumarea;

 weight psuarea;

 output out=bootzzz mean=den sarea;

 proc sort data=bootzzz out=bootzzz;

 by zone stratum;

 * Now put results for each stratum into a single record;

 data bootv;

 set bootzzz nobs = NumObs;

 by zone stratum;

 array density(&maxstrata) density1-density&maxStrata;

 array stratumarea(&maxstrata) stratumarea1-stratumarea&maxStrata;

 retain density1-density&maxStrata stratumarea1-stratumarea&maxStrata

 nstrata ZoneArea ZoneDensity;

 keep zone stratum density1-density&maxStrata stratumarea1-stratumarea&maxStrata 

 Es f0 nstrata ZoneArea ZoneDensity;

 if _n_ = 1 then do;

 nstrata = 0;

 ZoneArea = 0;

 ZoneDensity = 0;

 end;

 nstrata = nstrata + 1;

 ZoneArea = ZoneArea + sarea;

 density(nstrata) = den;

 ZoneDensity = ZoneDensity + den*sarea;

 stratumarea(nstrata) = sarea;

 if _n_ = NumObs then do;

 ZoneDensity = ZoneDensity / ZoneArea;

 f0 = &f0;

 Es = &Es;

 output;

 end;

%mend NoAssist;

%macro WeightedPSU;

 * Estimates weighted mean density of PSU means;

 

 %put ”WeightedPSU”;

 * Get PSU means;

 proc sort data=bootxxx out=bootxxx;

 by zone stratum psu;

 

 proc means data=bootxxx mean noprint;

 by zone stratum psu;

 var density psuarea stratumarea;

 output out=bootzzz mean=density psuarea stratumarea;

 

 * Get weighted means of PSU means;

 proc sort data=bootzzz out=bootzzz;

 by zone stratum;

 proc means data=bootzzz mean noprint;

 by zone stratum;
65

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 var density stratumarea;

 weight psuarea;

 output out=bootvv mean=den sarea;

 

 proc sort data=bootvv out=bootvv;

 by zone stratum;

 * Now put results for each stratum into a single record;

 data bootv;

 set bootvv nobs = NumObs;

 by zone stratum;

 array density(&maxStrata) density1-density&maxStrata;

 array stratumarea(&maxStrata) stratumarea1-stratumarea&maxStrata;

 retain density1-density&maxStrata stratumarea1-stratumarea&maxStrata

 nstrata ZoneArea ZoneDensity;

 keep zone stratum density1-density&maxStrata stratumarea1-stratumarea&maxStrata 

 Es f0 f00 nstrata ZoneArea ZoneDensity TruncateDistance;

 if _n_ = 1 then do;

 nstrata = 0;

 ZoneArea = 0;

 ZoneDensity = 0;

 end;

 nstrata = nstrata + 1;

 ZoneArea = ZoneArea + sarea;

 *density(nstrata) = den;

 density(stratum) = den;

 ZoneDensity = ZoneDensity + den*sarea;

 *stratumarea(nstrata) = sarea;

 stratumarea(stratum) = sarea;

 if _n_ = NumObs then do;

 ZoneDensity = ZoneDensity / ZoneArea;

 f00 = &f0;

 f0 = &f0;

 if f0 > &maxf0 then do;

 abort return;

 f0 = &maxf0;

 ZoneDensity = &maxf0 * ZoneDensity / f00;

 do i=1 to &maxStrata;

 if density(i) ne . then density(i) = &maxf0 * density(i) / f00;

 end;

 end;

 Es = &Es;

 TruncateDistance = &TruncateDistance;

 output;

 end;

 

 %put ”Exiting WeightedPSU”;

%mend WeightedPSU;

%macro TimeAssist;

 * Estimates mean density with the model-assisted approach only on time;

 

 data bootg;

 density = 1.2;

 run;
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GENERAL TECHNICAL REPORT PNW-GTR-716

%mend TimeAssist;

%macro GetData;

* Import MAMU data from Excel into SAS;

 %put ”&datadir.&datafile”;

 %put ”-----------------------”;

* Get Stratum File;

 PROC IMPORT OUT=StratumFile

 DATAFILE=”&datadir.&datafile” 

 DBMS=EXCEL2000 REPLACE;

 GETNAMES=YES;

 RANGE = ”Strata$”;

 proc sort data=StratumFile out=StratumFile;

 by zone stratum;

 run;

* Get PSU Info;

 PROC IMPORT OUT=PSUFile

 DATAFILE=”&datadir.&datafile” 

 DBMS=EXCEL2000 REPLACE;

 GETNAMES=YES;

 RANGE = ”PSUs$”;

 data PSUFile;

 set PSUFile;

 drop near_area off_area;

 psuarea = near_area + off_area;

 if zone = 1 and stratum = 3 then do;

 subpsu = ”x”; subPSUarea = near_area; output;

 end;

 else do;

 subpsu = ”N”; subPSUarea = near_area; output;

 subpsu = ”O”; subPSUarea = off_area; output;

 end;

 run;

 proc sort data=PSUFile out=PSUFile;

 by zone stratum PSU subpsu;

 * Make a dataset with just the PSU totals;

 data PSUInfo;

 set PSUFile;

 by zone stratum PSU;

 drop subpsu subPSUarea;

 if first.PSU;

* Get Cluster info;

 proc import out=clusters0

 datafile=”&datadir.&datafile”

 dbms=excel2000 replace;

 getnames=yes;

 range=”Clusters$”;

 data clusters;

 set clusters0;

 mo = month(date);

 dy = day(date);

 yr = year(date);
67

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 proc sort data=clusters out=clusters;

 by zone stratum psu yr mo dy;

* Get detection data;

 PROC IMPORT OUT=project

 DATAFILE=”&datadir.&datafile”

 DBMS=EXCEL2000 REPLACE;

 GETNAMES=YES;

 RANGE = ”Project$”;

 run;

 %put ’Project 1’;

 data project0;

 set project;

 data project1;

 set project;

 drop PSUID;

 if zone = . then delete; * Remove any data lines with a missing zone;

 subpsu = substr(PSUID,length(PSUID));

 psu = input(substr(PSUID,1,length(PSUID)-1),1.);

 *mo = month(datepart(date));

 *dy = day(datepart(date));

 *yr = year(datepart(date));

 mo = month(date);

 dy = day(date);

 yr = year(date);

 %if &FixedWidthOnly = 0 %then %do;

 if perp_dist = -1 then do;

 delete; * Get rid of records with missing values;

 put ”Deleted because perp_dist = -1”;

 end;

 %end;

 if n = 0 then perp_dist = .;

 

 * Number of days since starting date;

 days = juldate(mdy(mo,dy,yr)) - juldate(mdy(&smonth,&sday,&syear)) + 1;

 proc sort data=project1 out=project1;

 by zone stratum psu yr mo dy;

 %put ’Project after some manipulation’;

 run;

 * Merge project and cluster information;

 data project2;

 merge project1 clusters;

 by zone stratum psu yr mo dy;

 proc sort data=project2 out=project2;

 by zone stratum psu subpsu;

 %put ’Merged with project and cluster information’;

 run;

 * Merge with stratum and PSUFile;

 %put ”Merge with stratum and PSUFile”;

 data project3;

 merge project2 PSUFile;

 by zone stratum psu subpsu;

 if cluster ne .; * Get rid of unsampled PSUs;

 proc sort data=project3 out=project3;

 by zone stratum psu subpsu;
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GENERAL TECHNICAL REPORT PNW-GTR-716

 

 %put ”Merged with PSUFile”;

 run;

 %put ”Merge project and StratumFile”;

 data project4;

 merge project3 StratumFile;

 by zone stratum;

 if survey_effort ne .;

 proc sort data=project4 out=project;

 by zone stratum cluster days psu subpsu;

 run;

%mend GetData;

%macro boot(data);

 * Make bootstrap runs;

 %global status f0 Es datafile;

 * Initialize bootstrap results file;

 data;

 file ”&datadir.bootstrap.txt”;

 run;

 * Initialize some macrovariables;

 %let status = .;

 %let f0 = .;

 %let Es = .;

 %let maxStrata = 4;

 %let datafile = &data;

 %put ”&datafile”;

 %put ”****************”;

 %put ”&data”;

 %put ”****************”;

 run;

 * Initialize some datasets;

 data boot;

 data bootxx;

 data bootxxx;

 data bootz;

 data bootzzz;

 run;

 * Make MS-DOS batch file to run Distance batch files;

 %MakeBat

 * Get input data (stratum, PSU, and observations);

 %GetData

 %GetDetect

 %GetPSU

 %if ”&noboot” = ”1” %then %let nboot = 1;

 * Perform bootstrap iterations;

 %do ii = 1 %to &nboot;
69

Regional Population Monitoring of the Marbled Murrelet: Field and Analytical Methods

 * Get a random sample of clusters within each stratum 

 and then a random sample of PSUs within clusters;

 %put ”GetBoot”;

 %GetBoot

 * Write to mamu.dat in a format that Distance can read;

 %put ”MakeBoot”;

 %MakeBoot

 * Make distance batch file for estimates of density and encounter rates;

 %put ”MakeDen”;

 %MakeDen

 %put ”MakeER”;

 %MakeER

 * Create PSUBoot.txt;

 data;

 set psuareas;

 file ”&datadir.PSUBoot.txt”;

 put psuArea1 psuArea2;

 run;

 * Create Strtm.txt;

 data sfile;

 merge psuareas StratumFile end=LastStrata;

 by zone stratum;

 retain npsu nstrata;

 

 if _n_ = 1 then nstrata = 0;

 if first.stratum then do; nstrata = nstrata + 1; npsu = 0; end;

 npsu = npsu + 1;

 if last.stratum then output;

 if LastStrata=1 then call symput(’nstrata’,nstrata);

 run;

 data;

 set sfile;

 file ”&datadir.Strtm.txt”;

 if _n_ = 1 then put ”&nstrata”;

 put stratumarea npsu npsu;

 run;

 %put ”Fixed width only: &FixedWidthOnly”;

 %if &FixedWidthOnly = 0 %then %do;

 * Run analyses with Distance;

 * (Output will be in bootstrap.txt);

 x ”&datadir.mamu.bat”;

 run;

 * Check for too few observations;

 %TooFew

 * If there are too few observations, then estimate density based on a 

 fixed width transect of size &TransectHalfWidth;

 %if &status = 0 %then %do;

 %put ”Fixed width density being estimated”;

 %GetFixedWidthDensity;

 %end;

 * Otherwise get estimates of f(0) and E(s) and PSU densities;

 %if &status = 1 %then %GetDensity;
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GENERAL TECHNICAL REPORT PNW-GTR-716

 %end;

 %else %do;

 %let status = 0;

 %GetFixedWidthDensity;

 %end;

 * Model-assisted adjusted mean or not?;

 %if &noassist = 0 %then %ModelAssist;

 %if &noassist = 1 %then %NoAssist;

 %if &noassist = 2 %then %TimeAssist;

 %if &noassist = 3 %then %WeightedPSU;

 * Accumulate results;

 data summary;

 set summary bootv;

 run;

 * Clean up SAS ODS results files;

 dm ’odsresults’ clear;

 run;

 %end;

 * Delete some temporary files;

 *%CleanUp;

%mend boot;
Pacific Northwest Research Station

Web site http://www.fs.fed.us/pnw/

Telephone (503) 808-2592

Publication requests (503) 808-2138

FAX (503) 808-2130

E-mail pnw_pnwpubs@fs.fed.us

Mailing address Publications Distribution

Pacific Northwest Research Station

P.O. Box 3890

Portland, OR 97208-3890
U.S. Department of Agriculture

Pacific Northwest Research Station

333 SW First Avenue

P.O. Box 3890

Portland, OR 97208-3890

Official Business

Penalty for Private Use, $300