Sampling Large Landscapes with Small-Scale 

Stratification—User’s Manual

Open-File Report 2011–1247

U.S. Department of the Interior

U.S. Geological Survey

Sampling Large Landscapes with Small-Scale 

Stratification—User’s Manual

By Jonathan Bart

Open-File Report 2011–1247

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

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Suggested citation:

Bart, Jonathan, 2011, Sampling large landscapes with small-scale stratification—User’s Manual:

U.S. Geological Survey Open-File Report 2011-1247, 14 p.
iii

Contents

Introduction.....................................................................................................................................................1

Steps in the Sampling Large Landscapes Process..................................................................................1

Step 1.—Define Populations...............................................................................................................1

Step 2.—Define Regions and Habitats..............................................................................................2

Step 3.—Make a Plots Shapefile ......................................................................................................3

Step 4.—Assign Plots to Strata..........................................................................................................6

Step 5.—Define Clusters or Clusters and Zones (optional)...........................................................7

Step 6.—Choose Sample Sizes within Strata ..................................................................................8

Step 7.—Select Plots to Survey .........................................................................................................9

Example: Snake River Birds of Prey Area................................................................................................10

Figures

Figure 1. Example of (A) initial superposition of square cells on a study area and (B) results 

after merging small polygons with surrounding larger ones ........................ 4

Figure 2. Example of plots configured to concentrate good habitat .............................. 5

Figure 3. Typical results from (A) simple random sampling and (B) cluster sampling. ......... 7

Figure 4. Snake River Birds of Prey NCA showing major and minor roads and the Orchard 

Training Area .............................................................................. 10

Figure 5. Regions defined for the Snake River Birds of Prey National Conservation Area ... 12

Tables

Table 1. Steps in the sampling large landscapes process ....................................... 1

Table 2. Three spatial populations .................................................................. 1

Table 3. Example of land cover categories and habitat types used in a study of 

shorebirds in Alaska ........................................................................ 6

Table 4. Example of assigning plots to habitat using the majority rule ........................ 6

Table 5. Land cover types in the Snake River Birds of Prey National Conservation Area...... 11

Table 6. Initial set of habitat types .................................................................. 13

Table 7. Initial and final sample sizes (SS) in each stratum ....................................... 13
iv

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Introduction

This manual explains procedures for partitioning a large 

landscape into plots, assigning the plots to strata, and selecting 

plots in each stratum to be surveyed. These steps are referred 

to as the “sampling large landscapes (SLL) process.” We 

assume that users of the manual have a moderate knowledge 

of ArcGIS and Microsoft® Excel. The manual is written for 

a single user but in many cases, some steps will be carried 

out by a biologist designing the survey and some steps will 

be carried out by a quantitative assistant. Thus, the manual 

essentially may be passed back and forth between these users. 

The SLL process primarily has been used to survey birds, 

and we refer to birds as subjects of the counts. The process, 

however, could be used to count any objects.

Steps in the Sampling Large 

Landscapes Process

The process is divided into seven steps, one of which 

(step 5) is optional (table 1). Each step is described in this 

manual followed by a detailed example.

Step 1.—Define Populations

“Populations” in this context refers to areas, not birds or 

other objects being counted. We distinguish three populations: 

the study area, the inferential population, and the sampled 

population (table 2). Each population is delineated in a 

shapefile. The study area is simply the outer boundary of the 

area being studied. Statistical inferences are not made outside 

of this area. The “inferential population” is the population that 

will be subdivided into plots and to which statistical inferences 

will be made. The inferential population often excludes areas 

that are completely unsuitable, such as open water when 

the objective is to record nests of landbirds. The sampled 

population is the plots that have positive probability of being 

included in the survey. 

Sampling Large Landscapes with Small-Scale 

Stratification—User’s Manual

By Jonathan Bart

Table 1. Steps in the sampling large landscapes process.

Step 1. Define populations

Step 2. Define regions and habitats

Step 3. Make a plots shapefile

Step 4. Assign plots to strata

Step 5. Define clusters or clusters and zones (optional)

Step 6. Choose sample sizes within strata

Step 7. Select plots to survey

Table 2. Three spatial populations.

Population Description

Study area Outer border; no surveys or statistical inferences 

made outside this area.

Inferential Area to which statistical inferences will be made; 

subdivided into plots.

Sampled Plots with positive probability of being surveyed.

Unsuitable areas could be subdivided into plots and we 

could then assert on the basis of biological reasoning (for 

example, landbirds do not nest in open water) that all plots 

in such areas have zero birds present. If this assertion is not 

made, then the unsuitable areas have to be subdivided into 

plots and assigned to strata, and the strata have to be included 

in tables, and so on, even though no surveys are actually made 

in these areas. 
2 Sampling Large Landscapes with Small-Scale Stratification—User’s Manual

 In many studies, some parts of the inferential population 

are inaccessible due to legal constraints or logistic issues 

but are similar enough to areas that can be surveyed, that 

investigators want to include inaccessible areas in the 

inferential population and extrapolate findings from surveyed 

areas to these inaccessible areas. Such areas are therefore 

included in the inferential population but are excluded from 

the sampled population. We discuss how statistical inferences 

are made to inaccessible areas in Step 4—Assign Plots to 

Strata, but, in brief, inaccessible areas are assigned to strata in 

which some parts are surveyed. Stratum means (for example, 

densities) are then calculated and the means are assumed to 

be the same in the part of the strata that was excluded from 

the sampled population. For example, in a study of the Lower 

Colorado River, some areas were considered unsafe to survey, 

yet our habitat maps included the entire area so we could 

assign unsafe areas to habitats and strata. We therefore placed 

the unsafe areas in similar strata that we could survey. In 

estimating densities and population totals, we assumed that the 

areas we could survey were similar, on average, to the unsafe 

areas. 

It is often tempting to exclude some areas from the 

sampled population because these areas are expected to have 

few birds. An alternative, however, is to define these areas as 

strata and then sample them with low intensity. This approach 

avoids the assumption that few birds are present yet little 

effort is consumed in surveying these areas. 

If non-surveyable areas may be quite different from 

the most similar areas that are surveyed, then it is best to 

exclude them completely. In the Lower Colorado River 

study, a portion of the Virgin River, which flows into Lake 

Meade from the north, was inside the study area. This area 

was difficult to survey and was eventually excluded from the 

sampled population. We considered including this area in the 

inferential population but the closest similar habitat was more 

than 100 mi away and we did not know if populations were 

similar in these two areas. Therefore, a decision was made 

to exclude the Virgin River from the inferential population 

and to acknowledge that we were not able to make statistical 

inferences to that part of the study area. 

Once decisions have been made on how to define the 

study area, inferential population, and sampled population, 

shapefiles are prepared for each population. Areas outside 

the inferential population must be completely outside the 

polygons depicting the inferential population. For example, 

if open water is to be excluded then there should not be any 

open water polygons in the shapefile. The reason for this is 

that a fishnet of plot-sized cells will be created and a union of 

it and the population will then be created as a way to begin 

subdividing the inferential population into plots. If excluded 

areas like open water occur in the shapefile of the inferential 

population, then the union may include polygons completely 

covered by excluded areas.

This step thus requires the following actions:

1. Prepare a shapefile that depicts the outer boundary of 

the study area. The shapefile normally has just one 

polygon but will have more than one polygon if the 

study area is disjunctive.

2. Prepare a shapefile that depicts the inferential 

population and thus excludes areas within the study 

area that are considered totally unsuitable for birds 

or are inaccessible and potentially quite different 

from surveyed areas.

3. Prepare a shapefile that depicts the sampled 

population, defined as all areas that have positive 

probability of being surveyed. The shapefile may 

be identical to, or smaller than, the inferential 

population but never extends outside the inferential 

population.

Step 2.—Define Regions and Habitats

The approach used here, and implemented in other 

software we have produced such as the analysis program DS, 

assumes that strata will be created and will be defined using 

one or two variables. In most studies, we have encountered, 

the variables are region and habitat so we use these two terms. 

Any two variables, however, may be used to define strata. For 

example, Region could be defined solely on the basis of access 

(for example, good, medium, poor) and Habitat could be based 

solely on importance from a management perspective (for 

example, high, medium, low). Defining only one region and/or 

one habitat also is permissible.

The first task in this step is thus to decide how the terms 

region and habitat will be defined. An advantage of forming 

many strata is that one can easily obtain stratum-specific 

estimates using DS or other analytic programs. Two plots 

must be surveyed in each stratum, however, so that stratumspecific variances can be calculated. The number of strata thus 

cannot exceed one-half the number of plots. In addition, when 

many strata are defined in poor habitat then too much time 

may be spent in these habitats. Furthermore, having dozens 

or hundreds of strata, even if the sample size is large enough 

to make this possible, is usually cumbersome especially if the 

sample sizes in most strata are so small that the within-stratum 

estimates are not very useful (due to poor precision). In our 

experience, Fewer than about 30 strata is usually best for 

programs that cover an area the size of a Western State.
Steps in the Sampling Large Landscapes Process 3

Defining regions and habitats is usually an iterative 

process and the first attempt often results in too many strata. 

Some of the possible combinations may not exist on the 

ground. For example, there might be 10 regions numbered 

1 to 10 and three habitats (good, medium, and poor) but 

region 7 might not have any good habitat. If this occurs, 

then the process described below will automatically exclude 

the stratum “7-good.” Nonetheless, it is quite common to 

define far too many strata. For example, in one study, regions 

were first defined by Bird Conservation Region, elevation 

category, and ownership and habitat was defined using several 

categories. We thus ended up with hundreds of permutations 

for a study with 180 plots. We used GIS methods to determine 

how much of the study area would be assigned to each stratum 

and then combined small strata. This process resulted in 20 

strata.

Once decisions have been made on the values for region 

and habitat, a shapefile with the habitats should be prepared. It 

is not necessary, at this stage, to make a shapefile for regions. 

This step thus requires the following actions:

a. Decide how regions will be defined. 

b. Decide how habitats will be defined. 

c. Assess whether the number of strata (region-habitat 

combinations) is too high or too low.

d. Repeat steps “a” through “c” as needed.

e. Make a habitats shapefile with the reduced number 

of habitats.

Step 3.—Make a Plots Shapefile 

Plots are made by subdividing the inferential population. 

This can be done in two ways depending on how regions are 

defined. If regions are defined using strict borders, for example 

legal property lines, then it is usually best that plots do not 

cross these lines. In this case, the first step in making the plots 

shapefile is to subdivide the inferential population layer using 

a shapefile of the region boundaries. However, if the regions 

are broad ecological zones, then use the undivided inferential 

population layer, define the plots, and then assign each plot 

to a region based on the location of the plot’s centroid. With 

this approach, the regions shapefile thus becomes the set of 

plots assigned to each region. This results in a regions map 

with “stair-step” boundaries but the plots have north-south or 

east-west borders that are often much easier to follow in the 

field than borders that follow other bearings. The first task in 

this step is to decide whether to divide the inferential shapefile 

using the regions layer. We use “inferential layer” below to 

refer to the inferential population regardless of whether it has 

been subdivided using the regions shapefile. 

It is highly desirable that all plots be fully acceptable to 

surveyors. A sample will be selected and surveyed, and the 

density on surveyed plots in each stratum will be assumed 

to equal the density throughout the stratum apart from the 

effects of sampling error. Consequently, if a sample of plots 

is selected but the borders are changed for logistical reasons, 

then concern will arise that the surveyed plots may not 

actually be representative of the strata they are in.

Delineating the plots is often a complex and timeconsuming process. We have tried many different approaches 

and work in this area continues. Typically, the goals are 

(a) to assign good habitat to as few plots as possible so 

that surveys can be concentrated there, and (b) to produce 

plots that are feasible to survey. We illustrate goal (a) with 

a study of shorebirds in northern Alaska. The good habitat 

occurred around wetlands that covered a small portion of 

the landscape and were separated by habitat with very few 

birds. Many of these wetlands were small enough to survey 

completely. The birds would often flush when the surveyor 

was far away and would then circle overhead while the 

surveyor conducted the survey. If the plot border bisected the 

wetland, determining which birds were nesting inside the plot 

was difficult. Detecting that the bird was nesting somewhere 

within the wetland, however, was often quite easy. It was thus 

highly desirable that plot borders followed wetland borders 

and a substantial amount of time was expended developing 

GIS methods that would accomplish this. With respect to 

goal (b), the plots need to be of reasonable size (neither too 

small nor too large), the plots should not occur on both sides 

of uncrossable boundaries such as irrigation channels, and 

borders should be distinguishable and easy to follow in the 

field.

The first step in delineating plots is to impose a grid 

of cells of the average plot size and shape on the inferential 

population. This can be done easily using the fish net 

command in X Tools or using ArcGIS commands. The 

union of the plots and inferential population is then created 

producing a first “plots shapefile.” Columns should be added 

to the attribute table labeled Region, Habitat, Stratum, and 

Surveyed.

 The borders of the inferential population are nearly 

always irregular whereas the borders of the fishnet cells are 

straight lines oriented north-south and east-west. When the 

two layers are intersected, the result includes many polygons 

that are too small to survey (fig. 1). The first step in producing 

a final plots layer is thus to absorb these plots into surrounding 

larger plots subject to the restriction that if regional boundaries 

are included in the inferential population shapefile, then plots 

cannot be formed that cross region borders. 
4 Sampling Large Landscapes with Small-Scale Stratification—User’s Manual

Figure 1. Example of (A) initial superposition of square cells on a study area and (B) results after merging small polygons 

with surrounding larger ones. 

A.

B.
Steps in the Sampling Large Landscapes Process 5

In some studies, certain habitats (usually the best ones) 

need to be concentrated into as few plots as possible so that 

survey efforts can be concentrated in this habitat. One example 

of this, for wetlands in Alaska, was described above. Another 

example occurred in the Lower Colorado River study. The 

best habitat (“tall cottonwood-willow”) had the great majority 

of the birds the survey was designed to detect, yet over much 

of the study area these habitats occurred in small patches that 

covered a small fraction of the landscape (<1 percent). We 

therefore wanted the patches of good habitat to be within plots 

rather than having them bisected by plot borders (fig. 2). 

Many procedures can be imagined for consolidating 

good habitat into the smallest possible number of plots and 

we must rely, in large measure, on the GIS Specialist to 

devise solutions. The best method to use depends in part on 

whether the habitat map is raster or vector. In northern Alaska, 

the habitat layer was raster. We used the Majority Filter

command many times to convert isolated pixels to the values 

of the surrounding pixels. We then used the Region Group

and other Clean commands to convert the patches of identicalvalued cells to polygons and absorb small polygons into 

surrounding larger ones. We then used the original raster data 

to characterize upland and wetland polygons and subdivide the 

polygons into a few types.

Despite the most creative GIS work, final work on 

the plots layer will need to be done manually. Standard 

GIS methods can be used to identify plots that should be 

examined. For example, the smallest or largest plots may be 

worth looking at or all the plots with a rare but high-quality 

habitat might be examined. We have found that final border 

adjustments can be made quite quickly by subdividing a plot 

and then merging small parts with surrounding plots. We 

recommend that a few weeks (at least) of GIS Specialist time 

be budgeted for making final corrections to the plot borders. 

Doing this well will be helpful in all future stages of the 

project.

Figure 2. Example of plots configured to concentrate good habitat.
6 Sampling Large Landscapes with Small-Scale Stratification—User’s Manual

This step thus requires the following actions:

a. Make the initial plots file using a fishnet or other 

similar command. Add columns to the attribute 

table labeled Region, Habitat, Strata, and 

Surveyed. 

b. Intersect it with the inferential population layer.

c. Merge small polygons with adjacent ones. 

d. Re-define plot borders as needed using one of the

approaches described above.

Step 4.—Assign Plots to Strata

Plots are assigned to strata by assigning them to regions 

and habitats using the definitions adopted in Step 2. Final 

adjustments to the strata then sometimes have to be made due 

to small sample sizes in some strata or too many strata.

As mentioned in Step 2, the shapefile depicting the 

sampled area may or may not include region boundaries. If 

the shapefile does include region boundaries then the plot 

definition procedure automatically keeps plot borders from 

crossing region borders so it is easy to assign plots to regions. 

If the inferential population shapefile does not include region 

borders then the easiest way to assign plots to regions is by 

establishing a centroid for each plot and then determining 

which region the centroid is in. This information is then 

entered in the Region column of the attribute table of the plots 

shapefile.

Assigning plots to habitat is complicated and warrants 

careful thought. As a first step, we carefully define the 

schemes used to describe habitat. The SLL process usually 

makes use of three schemes. The first is a land cover, rather 

than habitat, map produced by a program such as GAP or 

Land Fire or produced specially for the project area. These 

schemes nearly always have too many categories to be used 

directly. This scheme is thus condensed, in Step 2 above, to 

a few (usually 4–7) categories, some of which are unsuitable 

habitat, for use in the SLL process. We will refer in the future 

to the original categories as “land cover” categories and the 

reduced set of them as “habitat types” (table 3). A raster or 

assignment process much easier and we see no gain in having 

different schemes. We assume below that they are the same. 

The first task in assigning plots to habitats is to calculate 

the proportion of each plot covered by each habitat type and 

to enter this information in the attribute table of the plots 

shapefile. The procedures for doing this differ depending on 

whether the habitat layer is raster or vector. We assume the 

GIS Specialist can accomplish this task. 

Defining the rule set to assign plots to habitats often 

warrants careful consideration. A very simple rule set, often 

appropriate is “use the most common habitat type,” perhaps 

excluding unsuitable areas (table 4). For example if the habitat 

types were Good, Fair, and Poor, and they covered 50, 40, 

and 10 percent of the plot, respectively, then the plot would be 

assigned to habitat Good. This does not mean we ever assume 

all of the habitat type in the plot is good. We are just using the 

label Good to describe the plot. 

Table 4. Example of assigning plots to habitat using the majority rule. 

[In this example, P(unsuitable) was ignored in making the habitat assignments]

Plot Area P(unsuitable) P(wet) P(moist) P(dry) Habitat

1 0.10 0.15 0.53 0.21 0.11 Wet

2 0.11 0.00 0.25 0.43 0.32 Moist

3 0.13 0.00 0.03 0.37 0.60 Dry

4 0.09 0.43 0.21 0.17 0.19 Wet

5 0.13 0.35 0.21 0.44 0.00 Moist

6 0.12 0.00 0.05 0.34 0.61 Dry

vector “habitat shapefile ” should be made with 

the habitat types entered as values (rasters) or 

used to create new polygons (vector layers). 

Once the habitat shapefile has been made, 

each plot must be assigned to a single habitat, 

even though many plots will include more than 

one habitat type. We use the terms “habitat 

type” for the condensed list of categories based 

on the land cover map (table 3) and “habitats” 

as the categories to which plots are assigned. 

We recommend using the same category 

names for habitat types and habitats. This is 

not strictly necessary but it makes the habitat 

Table 3. Example of land cover categories and habitat types 

used in a study of shorebirds in Alaska.

Land cover categories Habitat type

Water, clear Unsuitable

Water, turbid Unsuitable

Ice Unsuitable

Aquatic, Carex aquatilus (50–80 percent water) Wet

Aquatic, Arctophila (50–80 percent water) Wet

Flooded, low-center polygons (25–50 percent water) Wet

Flooded, non-patterned (25–50 percent water) Wet

Wet, Carex aquatilus (10–20 percent water) Moist

Moist, sedge-grass meadow (10–20 percent water) Moist

Moist, tussock tundra Moist

Moist, moss and lichens Moist

Shrub, dwarf Upland

Shrub, medium Upland

Shrub, tall Upland

Barren, dry dunes Unsuitable

Barren, sparse vegetation Unsuitable

Barren, other Unsuitable
Steps in the Sampling Large Landscapes Process 7

In many studies, the best habitat types only rarely cover 

a majority of the plot. In such cases, the “majority rule” above 

does not work very well. A series of questions may then work 

best. In the Lower Colorado River study area, the rule set was: 

1. If tall woody polygons cover more than 5 percent 

of the plot, then classify the plot as tall woody; 

otherwise 

2. If tall woody and low woody polygons cover more 

than 50 percent of the plot, then classify the plot as 

low woody; otherwise 

3. If herbaceous polygons cover more than 30percent 

of the plot, then classify the plot as herbaceous; 

otherwise 

4. If unvegetated polygons cover more than 30 percent 

of the plot, then classify the plot as unvegetated; 

otherwise assign the plot to the type that covers the 

largest proportion of the plot.

If pilot study data are available, then it may be useful 

to design an Microsoft® Excel workbook to assign plots to 

habitats and thus to strata and to calculate densities for each 

stratum and the fraction of the population covered by each 

stratum. We did this in the Lower Colorado River study after 

collecting data during a 3-year pilot study. A first worksheet 

contained one row for every plot in the study area and columns 

for each of the original land cover categories. The entries were 

the proportion of the plot covered by the land cover category. 

A second worksheet also contained one row for every 

plot. The columns were the habitat types. Embedded rules 

calculated the proportion of the plot covered by the habitat 

type. A third worksheet with rows for every plot had Region 

and Habitat columns and contained rules for assigning plots 

to habitats. This worksheet also identified which plots were 

surveyed and recorded the number recorded of each species 

of interest. A final worksheet calculated stratum sizes and the 

densities and their variances for each of species of interest. 

We were then able to explore the implications of different 

rules for (a) consolidating land cover types into habitat types 

and (b) rules for assigning plots to habitats on stratum size and 

densities. This led us to recommend substantial changes in 

how strata were defined for the long-term survey.

This step thus requires the following actions:

a. Assign plots to regions.

b. Develop a rule set for assigning plots to habitats.

c. Assign plots to strata using their region and habitat.

d. Revise the procedures used in “a” to “c” as needed to 

achieve good stratum sizes and variation in density 

between strata.

Step 5.—Define Clusters or Clusters and Zones 

(optional)

Clusters and zones are groups of plots that are selected 

together (fig. 3). If the design includes selecting locations and 

then visiting several plots or points in close proximity, then 

we have cluster sampling. If, in contrast, a “simple random 

sample” of plots is selected—meaning that each location is 

selected without reference to any other locations—then we 

have (stratified) random sampling and neither clusters nor 

zones need be created. 

Figure 3. Typical results from (A) simple random sampling and (B) cluster sampling.

A. B.
8 Sampling Large Landscapes with Small-Scale Stratification—User’s Manual

In standard survey sampling methods, plots in a cluster 

are assigned to the same stratum. Cluster sampling is usually 

used for logistical reasons. For example surveyors might be 

able to survey five plots or points in a morning if the locations 

are close together but if the points are selected independently 

then travel time between them may be too great to do five 

locations. This is a common occurrence familiar to nearly 

anyone who designs bird surveys. If cluster sampling (without 

zones) is used, then a cluster shapefile should be prepared 

that defines the plots in each cluster. Cluster numbers must 

be unique within regions but they can be repeated between 

regions. Statistical methods are well defined for cluster 

sampling and are implemented by program DS.

Zones are groups of plots selected together whose 

members are assigned to more than one stratum. Consider 

an analysis of BBS data in which habitats are defined and 

each location for a 3-minute count is assigned to a habitat. 

A given route, with 50 locations, will nearly always include 

counts in different habitats. This causes a problem in error 

estimation because in stratified sampling, we normally assume 

independent selection between strata. This is more than 

an academic problem as shown by the following example. 

Suppose 6 groups of plots were defined and we selected 

10 plots in each. The habitats are Good, Fair, and Poor. 

Furthermore, suppose that each group had some plots of each 

habitat type. If we ignored the lack of independence, then the 

equations used to calculate variances would assume that we 

surveyed 18 different clusters, 6 with Good plots, 6 with Fair

plots, and 6 with Poor plots. If we had actually done that, 

coverage probably would have been quite a bit better than we 

achieved with only 6 groups. The lack of independence thus 

needs to be acknowledged. In this example, our 6 groups of 

plots are zones because they each contain good, fair, and poor 

plots. Program DS contains routines to analyze designs that 

include zones. 

In summary, if plots are going to be selected in groups, 

usually for logistical reasons, then delineate the group 

boundaries in a shapefile and assign each plot to exactly one 

group. Next assign cluster numbers to each plot being careful 

not to duplicate cluster numbers within regions and keeping 

in mind the definition of clusters—groups of plots in the same 

stratum. If groups contain plots from different strata, then also 

assign numbers to the groups (that is, zones). For example, 

the zones might be numbered 1, 2, 3... and the clusters within 

zones might be numbered according to their habitat, 1=good, 

2=fair, and 3=poor for example. The full cluster numbers 

might then be constructed as “zone number, decimal, habitat 

number.” Thus, 23.2 would mean fair plots in zone 23. The 

output of this step is thus that the attribute table for the plots 

Shapefile is given a new column for cluster number and a 

column for zone number if zones were defined.

If clusters, or clusters and zones, were defined, then Program DS needs a table reporting how many plots are in each 

cluster and the total area they cover. These tables have the 

following columns:

Clusters only: region, habitat, cluster, number of plots, 

area covered

Clusters and zones: region, habitat, zone, cluster, number 

of plots, area covered

See the DS User’s Manual for more details. The needed 

information is easily tabulated using ArcGIS and Microsoft® 

Excel commands.

This optional step (needed only if clusters were defined) 

thus requires the following actions:

a. Define and number the groups of plots.

b. If plots within groups are in more than one stratum 

then number the clusters within each group.

c. Add the cluster number, and zone number if zones 

were defined, to the attribute table for the plots 

shapefile.

d. Make a table of clusters (and zones if relevant) with 

sizes and areas.

Step 6.—Choose Sample Sizes within Strata

Choosing the number of plots to survey in each stratum 

usually requires decisions that seem arbitrary. Here, we 

present a process designed to remove some of the arbitrary 

nature of the process and, most of all, to enable users to move 

rapidly through this step. 

The first action is to make a table with the number of 

plots in each stratum. Second, select the total sample to be 

surveyed. Usually this decision is based on the available 

resources. Sometimes, managers will ask the biologists 

or analysts how large a sample they “need.” Responding 

rigorously to this question is difficult because estimates are 

required of quantities that usually are poorly known. 

Once the total sample size has been set, we recommend 

calculating the proportion of the plots that are in each stratum 

and then assigning the same proportion of the plots to be 

surveyed. To take a simple example, if there were just three 

strata and the proportion of plots in them were 20, 50, and 

30 percent, and if 100 plots were to be surveyed, then the 

initial allocation of plots to strata would be 20, 50, and 30 

for the three strata, respectively. Once the initial allocation 

is made, the results can be inspected and adjustments made, 

while maintaining the total sample size. Adjustments usually 
Steps in the Sampling Large Landscapes Process 9

increase sample size in strata with high-quality habitat or 

regions of high interest or in strata with very few plots in the 

initial allocation. Addressing these issues—using common 

sense and experience with the study area—is important, 

especially when some strata receive very few plots in the 

initial allocation yet may contain abundant birds. If sample 

sizes are not increased in these strata (and decreased in 

others), results may be very unstable.

This step thus requires the following actions:

a. Display the number of plots in each stratum in a 

table.

b. Decide the total number of surveys.

c. Allocate them proportional to the number of plots in 

each stratum.

d. Adjust the results to increase sample size in highinterest strata and strata with very few surveys under 

the initial allocation.

Step 7.—Select Plots to Survey

The procedure for plot selection depends on which 

sampling plan is followed within strata: simple random 

sampling, cluster sampling, or cluster sampling with zones 

(Step 5). Regardless of the sampling plan, however, we prefer 

to distribute the surveyed plots throughout the strata rather 

than using a procedure that might result in surveyed plots 

being concentrated largely or entirely in one small part of 

the stratum. This is usually easy to accomplish by taking a 

systematic sample of the FID numbers of the plots, clusters, or 

zones. To do this, transfer the FID numbers to a spreadsheet, 

sort them, and proceed as follows within each stratum. Divide 

the FID numbers into as many groups as the number of plots 

to be selected, keeping the group sizes as similar as possible. 

For example, if a stratum has 93 plots and the desired sample 

size is 5, then the group sizes would be 19, 19, 19, 18, and 

18. The groups would be plots 1-19, 20-38, 39-57, 58-75, and 

76-93. A number between 1 and 19 inclusive would be chosen 

randomly and that plot would be selected. Then 19, 19, 18, 

and 18 would be added to that number to select the remaining 

plots. This procedure ensures that non-existent plots do not get 

identified for inclusion in the sample.

 In cluster sampling, the procedure is similar except that 

it is carried out on the clusters and in each selected cluster, a 

fixed number of plots are randomly selected. Ideally, the plots 

are selected within clusters completely at random but if this 

results in excessive travel time between plots, then groups of 

plots—all fairly close together—may be defined and one of 

the groups can be selected at random. This procedure does 

introduce some selection bias due to the plots being close 

together, but this may be a reasonable trade off with the costs 

of plots being too far apart.

Sample selection with zones and clusters is complicated 

and advice from a statistician may be needed. The most 

rigorous approach is to select the desired number of plots 

in each zone completely at random. The problem with this 

approach, however, is that it does not control the sample size 

within strata and rare habitats—which may be especially 

important to survey well—may hardly ever be included. It 

may be possible to overcome this problem by defining regions 

in such a way that they largely contain plots assigned to just 

one habitat, or at least that the habitats of greatest concern are 

concentrated into one or a few regions. If this can be done, 

then random selection of plots within regions—and selecting 

more plots in the regions of greatest interest—may still result 

in the desired number of plots in each habitat (although it 

will not be exactly the desired number because the habitat is 

determined by random selection). More experience is needed 

with how to use zone and cluster sampling to obtain desired 

numbers of plots in each stratum.

If plots will be covered during several years, or other 

periods, then it is important that in each period the surveyed 

plots cover the entire study area as evenly as possible. 

Otherwise strong year effects can easily produce apparent 

variation across the study area that is due to transitory effects, 

such as poor weather in 1 year.

This step thus requires the following actions:

a. Number the plots, clusters, or zones sequentially 

within regions.

b. Arrange them in sequential order using the FID 

numbers.

c. Select the desired number systematically as 

described above.

d. If clusters are defined, selected the desired number 

in each cluster randomly or by defining groups and 

selecting one of the clusters.

e. If zones are defined, either select plots completely 

at random or devise a method—with help from a 

statistician—that will yield essentially unbiased 

estimates of density in each stratum. 
10 Sampling Large Landscapes with Small-Scale Stratification—User’s Manual

Example: Snake River Birds of Prey 

Area

A detailed example of the SLL process is presented in 

this section. We use this example in workshops—presenting 

the background for each step and then asking participants to 

divide into groups and discuss how they would carry out each 

task. Each group then presents the approach they have devised 

and, afterwards, we discuss the approach we followed. We 

then proceed to the next step, using the materials that we have 

previously prepared based on the approach we adopted. We 

encourage you to participate in this process and have presented 

the material below so that you can study the information at the 

beginning of each step and then decide how you would carry 

out the task before reading the rest of the section to see how 

we proceeded. The introductory material and the description 

of the choices we made are separated by a line of asterisks.

The Snake River Birds of Prey National Conservation 

Area (NCA) in southern Idaho was created in part as a refuge 

for birds of prey during the summer and winter (fig. 4). The 

canyon along the Snake River is especially valuable for birds 

of prey, in part as nesting sites, but the other areas also are 

used extensively. The NCA is owned by the Department of 

Defense and is used by them for training, especially in the 

Orchard Training Area (OTA). For this example, we assume 

that a long-term survey of breeding birds is being designed for 

the NCA. 

The goals of the survey are to:

1. Estimate trends in abundance for species of concern 

including raptors, threatened or endangered species 

and other species on “of concern” lists. 

2. Help assess impact of training and other activities on 

migratory birds.

3. Provide data useful in studying habitat and other 

relations.

We will assume that the survey will be conducted during 

the day by two, 2-person teams, each with a vehicle for 3 

months excluding training. In addition, one person-month by 

a supervisory biologist will be available for hiring, training, 

analysis, and reporting.

Figure 4. Snake River Birds of Prey NCA showing major and minor roads and the Orchard Training Area. 
Example: Snake River Birds of Prey Area 11

Step 1.—Define Populations 

Introduction: Recall that this step requires you to define 

the study area, the inferential population, and the sampled 

population. Give some thought to how you would define 

populations before continuing.

**************************************************

Our decisions: The study area was defined for us as the 

NCA. The borders shown in figure 4 thus delineate the study 

area. We considered removing the Snake River from the inferential population but did not do so because aquatic birds frequently use the Snake River and would be counted on surveys. 

We also decided that the area was small enough that all parts 

of the area could be surveyed, although areas far from roads 

might be lightly sampled, and that no areas warranted exclusion because no birds would be present. We therefore defined 

both the inferential and sampled populations as including all 

parts of the study area.

Step 2.—Define Regions and Habitats

Introduction: A detailed land cover map, with 26 types in 

the NCA, was available (table 5). 

Table 5. Land cover types in the Snake River Birds of Prey National 

Conservation Area.

Land cover types Hectares

Inter-Mountain Basins Playa 6

Inter-Mountain Basins Active and Stabilized Dune 739

Quarries, Mines. and Gravel Pits 18

Inter-Mountain Basins Cliff and Canyon 291

Columbia Plateau Steppe and Grassland 15,956

Columbia Basin Foothill and Canyon Dry Grassland 1,895

Inter-Mountain Basins Semi-Desert Grassland 4,769

Introduced Upland Vegetation - Annual Grassland 91,332

Recently burned grassland 743

Introduced Upland Vegetation - Forbland 115

Pasture/Hay 2,800

Cultivated Cropland 13,315

Columbia Plateau Ash and Tuff Badland 2,217

Inter-Mountain Basins Greasewood Flat 5,529

Inter-Mountain Basins Mixed Salt Desert Scrub 15,767

Inter-Mountain Basins Semi-Desert Shrub-Steppe 10,075

Rocky Mountain Lower Montane-Foothill Shrubland 3

Inter-Mountain Basins Big Sagebrush Steppe 2,427

Inter-Mountain Basins Big Sagebrush Shrubland 65,800

Columbia Plateau Western Juniper Woodland and Savanna 38

Rocky Mountain Aspen Forest and Woodland 1

Developed, Open Space 3,314

Developed, Low Intensity 463

Developed, Medium Intensity 222

Developed, High Intensity 18

Open Water 4,255

In this step, you define habitat types based on the land 

cover types or any other information you wish to use, and 

regions again defined using any variables you wish to use. 

Consider the information above and then construct your list 

of habitats and regions. Remember that each region-habitat 

combination becomes a stratum (unless it has no plots) and 

that two plots must be selected in each stratum. Recall that at 

this stage you also decide whether regions will be defined now 

and intersected with the shapefile of the inferential population 

or whether plots will first be defined and assigned to regions 

that implicitly defines the regions. This example provides an 

illustration of why this can be an important decision to make 

correctly.

**************************************************

Our decisions: We felt that three regions were fairly 

obvious: the canyon, because it is of great importance as a 

nesting site; the OTA because it is used for training and one 

of the goals was assessing impacts of training on the birds; 

and the rest of the area that must be included because the 

inferential population includes the entire study area. We also 

were concerned about travel time to reach plots far from roads 

and about the fact that small roads were concentrated in only 

one part of the study area. We therefore decided to define a 

second set of regions based on distance from a major road. 

We initially defined three buffers using 3 km and 6 km as the 

divisions (fig. 5), but we were concerned about having too 

many strata and the more than 6 km buffer covered only a 

small area so we decided to use just two buffers, 0–3 km 

and more than 3 km. 

Regarding the issue of how and when to delineate 

regions on the inferential population shapefile, the OTA 

was a political subdivision so it seemed important that plots 

not cross its boundaries. More importantly, however, the 

canyon walls were essentially uncrossable during a survey 

so it was important that plots not cross them. We therefore 

defined the rim of the canyon as the border of the canyon 

region and then intersected the inferential population 

shapefile with the regions shapefile.

The number of land cover codes obviously had to 

be reduced to just a few. We initially defined seven types 

(table 6). Birds in agriculture, grassland, and shrubsteppe 

would be different and that estimates would be wanted 

for them. We would have liked to keep the rest of the 

habitats but that would have given us too many strata. We 

decided that the “canyon” habitat would be captured by the 

“canyon” region and that it was surrounded by shrubsteppe 

so we combined it with shrubsteppe. We decided that the 

“developed” category was particularly interesting and it 

was surrounded with agriculture so we combined it with 

that category. We combined playa, dunes and woodland 

with shrubsteppe because they covered such tiny areas and 

were surrounded by shrubsteppe. We thus defined three 

habitat types: agriculture, grassland, and shrubsteppe. 
12 Sampling Large Landscapes with Small-Scale Stratification—User’s Manual

Figure 5. Regions defined for the Snake River Birds of Prey National Conservation Area. A. Snake River 

corridor, Orchard Training Area, rest of area; B. buffers defined by distance to roads). In the final design, only 

two buffers, 0–3 and more than 3 km were used.

B.
Example: Snake River Birds of Prey Area 13

Step 3.—Make a Plots Shapefile

In this step we imposed a grid of square cells on the 

inferential population. We used 16-ha squares because the 

squares can easily be surveyed in a morning in open country 

with fairly sparse birds. This approach results in fewer plots 

than doing several plots per morning, but such groups of 

plots have to be defined as clusters or zones so the effective 

sample size is well below the number of plots. Furthermore, 

by doing one plot per morning we do not lose time during the 

survey period to travel between plots, less time is spent trying 

to decide whether birds on the edge are in or out of the plot 

(because the edge-to-area ratio is more favorable), and we do 

not have to worry about the complexities of sampling with 

clusters or zones and clusters.

Step 6.—Choose Sample Sizes within Strata

Introduction: Review the description of this step above 

to be sure you understand the tasks. Only the second one can 

be done without access to the detailed data. In this study, as in 

most, the resources were fixed so sample size can be estimated 

from the resources available and the field methods described 

immediately above. 

**************************************************

Our decisions: The project description said two, 2-person 

teams would each work for 3 months. This works out to about 

240 person-days assuming a 5-day work week and that a few 

days are lost to weather or other problems. We said, under 

step 3 above, that each person would survey one plot/day so 

we assume that a maximum of 240 plots can be surveyed. The 

reality might be closer to 200 plots if logistical problems arise, 

but it is safest to select the maximum number of plots and then 

be sure —as the field work proceeds—that effort is evenly 

distributed across strata so that at least two plots are surveyed 

in every stratum even if the number of plots surveyed turns out 

to be fewer than the optimistic initial estimate.

We initially distributed sample sizes across the strata 

proportional to stratum size (table 7). We then increased 

sample sizes where necessary to insure that each stratum had 

at least 10 plots. If agriculture had covered a larger area, we 

would have decreased sampling there, because it was less 

interesting habitat for this survey, but it actually covered 

so little area that we had to increase the number of plots in 

agriculture in each region to meet the “minimum of ten” rule.

Table 6. Initial set of habitat types.

Habitat type Hectares Percent

Agriculture 16,115 7

Canyon 2,508 1

Developed 4,017 2

Grassland 114,811 48

Playa dunes 745 <1

Shrubsteppe 99,601 42

Woodland 38 <1

Table 7. Initial and final sample sizes (SS) in each stratum.

[Region: OTA, Orchard Training Area]

Region Habitat type Area 

(ha) Prop. Sample sizes (SS)

Initial Final

Canyon Agriculture 2,056 0.009 2 10

Canyon Grassland 12,334 0.052 12 12

Canyon Shrubsteppe 3,548 0.015 3 10

OTA Agriculture 8,234 0.035 8 10

OTA Grassland 43,566 0.183 43 40

OTA Shrubsteppe 32,884 0.138 33 31

Other Agriculture 9,842 0.041 9 10

Other Grassland 58,911 0.248 59 57

Other Shrubsteppe 66,460 0.279 67 60

Totals 237,835 1 236 240

Step 7.—Select Plots to Survey

Plots would be selected using simple random sampling.

Step 4.—Assign Plots to Strata

Introduction: In this step, we assigned 

plots to regions and habitats and checked that 

the resulting strata had appropriate numbers of 

plots. The issues to consider are how to assign 

plots to regions and how to define habitats.

*************************************

Our decisions: Because the inferential 

population had region borders embedded 

within it, the plot delineation process 

automatically prevented plots from crossing 

region borders. It was therefore easy to 

determine which region each plot was within. 

We considered assigning habitats using a series 

of questions as described earlier in this report 

but decided that a simple majority rule was 

sufficient.

Step 5.—Define Clusters or Clusters and Zones 

(optional)

We did not carry out this step because we 

used simple random sampling within strata.
14 Sampling Large Landscapes with Small-Scale Stratification—User’s Manual

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 777 NW 9th Street, Suite 400

 Corvallis, Oregon, 97330

 http://fresc.usgs.gov/
Bart—Sampling Large Landscapes with Small-Scale Stratification—User’s Manual—Open-File Report 2011–1247