Northern Prairie Wildlife Research Center

- Figure 1 - Example of a breeding range of a bird and study area and point counts.
- Figure 2 - Location and hypothetical paths of birds in the study area.
- Figure 3 - Detection zones for a bird by an observer.
- Figure 4 - Cumulative detection zones of a bird by a highly skilled observer and a less-skilled observer.
- Figure 5 - Using playbacks of calls to increase the detection zone of a bird.
- Figure 6 - A bird may be double counted when stations are too close together.
- Figure 7 - Roads may increase the count of a bird in a detection zone.

Point counts are used to sample bird populations for estimating densities in local areas, determining trends in populations over regional areas, assessing habitat preferences and other scientific and population monitoring purposes. Difficulty in analyzing point counts of birds arises from confusion about—or lack of—definitions. Rarely is a clear statement made about what is being estimated and often the objectives of conducting a point count are unclear or conflicting. Burnham (1981) harshly criticized the use of measures such as point counts because they lacked a clear connection to biological parameters such as population densities. This paper is intended to provoke thinking about what parameter of interest is estimated by point counts. It also provides an elementary precursor to the important and more mathematical contribution by Barker and Sauer, in this volume. It gives in straightforward terms one perspective of what point counts are attempting to accomplish. Mathematical models of point counts are introduced, not to complicate the life of the ornithologist, but to provide a concrete and explicit formulation of the assumptions involved and to guide further work.

A point count, or circular-plot survey, involves a series of points or stations
at which birds are counted. Observers spend a prescribed time (usually 3 to
20 minutes, with longer times occasionally suggested for areas with more complex
vegetation structure or where travel times between stations is a serious limitation)
at each station, looking and listening for birds. Stations are to be separated
by sufficient distance to preclude sighting the same bird at more than one
station. Observers may restrict attention to birds within a prescribed distance
of the station (fixed-distance circular plots) or record birds regardless
of the distance (unlimited-distance circular plots). Although sighting distance
might be recorded and used to develop estimates of density, typical point
counts do not use information on sighting distance (Reynolds and others 1980).
See International Bird Census Committee (IBCC) (1977) and Blondel and others
(1981) for further details of the method, which is akin to the *Indice Ponctuel
d'Abondance* (IPA) method. The North American Breeding Bird Survey (BBS)
represents a cluster of 50 point counts (Droege 1990).

Consider a population of a species of bird, distributed over its breeding
range during its breeding season. We assume for simplicity that birds are
territorial and sexually dimorphic and that the population can be enumerated
by counting territorial males; say there are *N* of them during the breeding
season of a particular year. The real world is more complicated than that,
but we make these simplifying assumptions to avoid clouding the main issues.
Interest might be in estimating *N*, but more typically we want to compare
population size for 2 or more years and especially to determine if there is
a consistent trend, either upward or downward. Another goal might be to identify
habitat associations of the birds (Ralph and others); this objective requires
a fundamentally different approach (Pendleton).

The distribution of territories can be considered as the outcome of a stochastic
point process operating over the breeding range. That is, the locations of
territories are viewed as random events in space. The intensity of the process
(i.e., the density of territories) varies spatially and reflects the number
of birds in the population, the size of the breeding range, and the quality
and attractiveness of habitats at various locations within the breeding range.
*Figure 1* illustrates a greatly simplified situation, with only *N*
= 50 territories. Notice that territories are more dense in the upper (northern)
part of the breeding range, presumably reflecting higher-quality habitat there.
The lower part of the breeding range has unoccupied areas.

Assume now that the distribution of territories is fixed—the birds have
established their territories for the season—and that the area is far
too large for complete enumeration by, for example, territory mapping. We
select one or more sample study areas from within the breeding range. One
such study area is shown schematically in *figure 1* (top right). A study
area probably contains some territories in their entirety, parts of other
territories, and voids where no territories cover. One measure of bird abundance
for a study area is the total number of birds whose territories are at least
partly included in the study area; this is four for the example in *figure
1*. A more useful measure is the total number of fractions of territories
in the area; for the example in *figure 1*, that value is about 2.75
(one each from complete territories, 0.5 from the fraction of the territory
at the upper left, and 0.25 from the part of the territory at the upper right).
The usefulness of such numbers stems from the fact that they can give estimates
of density of territories, and a random sample of study areas produces values
with expectation *N/A* Therefore, the total population size *N*
can be estimated if *A*, the size of the study area, is known. Territory
mapping is the principal method used to obtain such estimates of density,
but I am not aware of its application to study areas randomly selected from
a large breeding range. For example, North American Breeding Bird Censuses
(Engstrom 1988) and the British Common Birds Census (Marchant and others 1990)
involve sites that were not randomly chosen. For waterfowl, counts based on
observations of "indicated pairs" are used to that end (Martin and others
1979).

Suppose a series of point counts, instead of territorial mappings, are made
in the study area (*fig. 1*, bottom right). In the example, three stations
are included. At each station, the number of males seen is tallied. Depending
on the distance between stations, the size and configuration of territories,
the behavior of the birds, and the skills of the observer, the same bird may
be counted on more than one station. Such double counting is to be avoided,
if possible. Probably more birds are missed than counted twice.

Denote the true count of territories in a study area by *X* and the
observed count by *Y*. What relation does *Y* have with *X*?
We consider three reasonable possibilities, among many.

The most straightforward approach is to suppose that *Y* and *X*
are linearly related by

*Y* = (1-*b*)*X* + ε,

where, on average, the observed count is a fraction (1-b) of the true count,
*b* is the bias rate, and ε represents
the sampling error. That means that, if the survey were repeated numerous
times in the same area under identical conditions (which is possible only
conceptually, because conditions never stay the same), the averages would
be related by

= (1-*b*)*X*

and the ε values would be the departures
from count to count in that relation. If *b* = 0, the count is unbiased
and we have the equivalent of a complete census, except for the sampling error.
Most often some birds are missed, so that *b* > 0, often substantially
so. Also, the sampling error depends on *X*; if no birds are in the area
(*X* = 0), repeated counts will turn up similar numbers (usually *Y*
= 0) so that the variation from count to count will be small; if the population
is very large, variability from count to count will be greater.

Under this additive model, the true error, the difference between observed and actual population sizes, is

True error = *Y* - *X* = (1-*b*)*X* +
ε - *X*

= -*bX* + ε,

essentially the bias plus sampling error for that specific count.

Because a true population of zero generally leads to an observed value of zero, it may be more reasonable to assume a relation of the form:

*Y* = (1-*a*)*X*ε,

in which* a* represents the bias and the error term affects the observed
count multiplicatively. Here *X* = 0 implies *Y* = 0, but not the
converse. That is, if no birds are present, the observer probably will count
none, but a count of zero does not necessarily mean that the species is absent.
The true error under this model is

True error = *Y* - *X* = (1-*a*)*X*ε
- *X*

= [(1-*a*)ε - 1]*X*,

which now involves the product of the bias term (1-*a*) and the sampling
error (ε). This formulation is mathematically
more difficult to handle than the additive model. It can be reduced to a linear
additive form by taking logarithms of both sides, but zero counts render that
remedy ineffective.

Often it is hoped only that point counts correlate strongly with the actual population. Then bias does not matter, as long as it is relatively constant. An appropriate model for this situation is

*Y* = *CX*,

where now *C* is not a fixed parameter, as were *b* and *a*
in the models described earlier, but a random variable. More will be said
about its variability shortly. We call *C* the detection probability,
as used by Barker and Sauer in their counterpart to this model. It is the
probability that a specific bird will be detected on a particular point count.
Other index models are plausible (Caughley 1977:15).

The key point, brought out also by Barker and Sauer, is that the variation
in *Y* incorporates variation in both *C* and *X*. Specifically,

Var(*Y*) = *C*^{2}Var(*X*) + *X*^{2}Var(*C*)
+ Var(*X*)Var(*C*),

approximately, if *C* and *X* are independent. (If they are not
independent—a very real possibility—the situation is complicated
even further [Goodman 1950]).

When using point counts to compare areas or years, the comparison involves
the *C* values as well as the populations. Let the two areas or years
be indexed by subscripts 1 and 2. Then

*Y*_{1} - *Y*_{2} = *C*_{1}*X*_{1}
- *C*_{2}*X*_{2}.

If detection probabilities are the same for both areas or both years, C_{1}
= C_{2} = C, say, then Y_{1} - Y_{2} = C(X_{1}
- X_{2}) and the observed difference faithfully reflects the actual
difference. If detection probabilities are not the same, then

*Y*_{1} - *Y*_{2} = *C*_{1}(*X*_{1}
- *X*_{2}) + (*C*_{1} - *C*_{2})*X*_{2},

or equivalently

*Y*_{1} - *Y*_{2} = *C*_{2}(*X*_{1}
- *X*_{2}) + (*C*_{1} - *C*_{2})*X*_{1}.

(Note that either of these reduces to *C*(*X*_{1} - *X*_{2})
when *C*_{1} = *C*_{2} = *C*.) This simply
states that an observed difference in point counts reflects not only the true
difference in the bird counts (*X*_{1} - *X*_{2})
but also the difference in detection probabilities (*C*_{1} -
*C*_{2}). Barker and Sauer (1992) elaborate on how unequal detection
probabilities can lead one to conclude that bird populations differ even when
they do not. Because detection probabilities are presumed to vary so much
from one habitat to another, point count data are rarely used to compare bird
densities by habitat. If detection probabilities vary markedly from one occasion
to another, the comparison of point counts overtime can be equally hazardous.

For an effective index, we need *C* to be independent of *X* and
Var(*C*) to be small. We assume the first condition, although it too
can fail in practice; detectability has been reported both to increase and
to decrease with increases in population density (Verner 1985). What can be
done about Var(*C*)? One approach is not to worry about it and to assume
its effects can be neglected, especially in large samples. Barker and Sauer
showed the follies of this Pollyanna approach (*sensu* Johnson 1981);
estimators of population change (trend) remain biased even for very large
samples if detection probabilities are not identical.

The customary approach is to specify acceptable conditions for conducting
point counts (Ralph and others 1993). Suppose *p* variables *z*_{1},
*z*_{2}, .... *z*_{p} are thought to influence
detection probabilities. These include variables such as date, time of day,
weather conditions, etc. With this approach we specify suitability ranges
within which surveys can be conducted:

*z*_{i}^{L} ≤ *z*_{i}
≤ *z*_{i}^{U}, for *i* = 1, 2, ..., *p*.

The survey is to be conducted only if each *z* value is between a lower
limit *z*^{L} and an upper limit *z*^{U}. For example,
in the North American Breeding Bird Survey, the time must be between one-half
hour before sunrise and about 1030.

By taking this approach, it is hoped to minimize Var(*C*). Two drawbacks
are (1) even within acceptable ranges, the variation of *z*_{i}
probably will induce variation in *C*; and (2) increasing the width of
acceptable ranges exacerbates the difficulty, but decreasing the width may
result in conditions too stringent in practice, so that the survey does not
get performed. A further drawback arises if observers actually conduct the
survey when one or more conditions are not met.

On a side note, often conditions are prescribed to maximize the counts of
birds recorded. This is equivalent to maximizing the detection probability
*C*. There is no assurance that conditions that maximize *C* also
minimize Var(*C*), so that criterion should be evaluated. Specifically,
the "dawn chorus" provides a high value of *C* but is of such short duration
that its results can be used only in comparison with other counts also made
at dawn (Ralph and others 1993). A more complex but promising method is to
derive "adjusted" detection probabilities. If we knew and could estimate how
detection probabilities were affected by the variables *z*_{1},
*z*_{2}, .., *z*_{p}, and if we could measure
those variables, we could adjust the observed counts accordingly (Dawson 1981).
This practice is widely done in other fields. For example, unemployment rates
are adjusted to accommodate seasonal patterns and to give a picture of long-term
trends not confused by normal month-to-month fluctuations. In our application,
numerous variables that may influence detection probabilities of birds have
been identified; see Diehl (1981) and other papers in Ralph and Scott (1981)
for a review. Little work has been done to quantify the relations, and that
will be a challenging—or hopeless (Burnham 1981)—task.

Recall that the detection probability (*C*) is the probability that
a specific bird, indexed by *j*, will be detected on a particular point
count. (This formulation does not allow the observer to double-count a bird.
More generally, the detectability could be prescribed as the expected number
of times a bird is detected and counted as separate individuals.) Detection
probabilities vary in response to numerous variables, such as the observer's
visual acuity, hearing ability, and experience; length of time spent at a
station; season of year; time of day; wind, temperature, and other weather
conditions; habitat features; and the bird's reproductive status and behavior.

Consider graphically the detection probability as a function of certain variables.
At any instant the birds in a study area are located at specific points (*fig.
2*, top). When viewed over a period of time, the birds follow certain paths
through their territories and possibly outside them (*fig. 2*, bottom).
The term utilization distribution has appropriately been used to characterize
the probability of using specified areas of a territory (Jennrich and Turner
1969).

Now let us invoke an observer, with a certain set of abilities to see, hear,
and identify the bird. At any instant, she will detect the bird if she is
within the *detection zone* for that bird (*fig. 3*, left). Treating
detection zones as circles would be convenient, but overly simplistic; for
example, the view of the bird might be blocked from one direction. Suppose
our observer stays at a station for several minutes. She will detect the bird
if at any time during her stay she falls within any detection zone generated
by the bird during that time (*fig. 3*, right). The bird would be double
counted if its movements were such that the observer thought two sightings
or hearings represented different birds. The count of birds at a station is
the number of birds present on the study area whose detection zones contain
the station during the time the observer is recording.

Mathematically, the observed count at a station is

Y = |
Pr{detect bird j | bird j present} |
× | Pr{bird j present}, |

where the summation is over all birds in the population and a bird is defined to be present if it is on the study area. If all birds on the study area could be detected, then

Pr { detect bird
*j* | bird *j* present} = 1

and

Y = |
Pr{ bird j present}. |

If we define the proportion of the territory of bird *j* that lies
within the study area to be *r*_{j} (similar to what we
did in association with *figure 1*) and
assume that the bird spends time in the study area proportional to *r*_{j},
then Pr{bird *j* present} = *r*_{j} at any instant.
But as the count period is extended, the number of birds present sometime
during the count period increases, because of territories that partially overlap
the study area (Granholm 1983, Scott and Ramsey 1981). Thus, lengthy counting
periods tend to inflate the component of *Y* involving the presence of
a bird. Another danger in using the total number of birds seen as a criterion
to optimize is that that value may reflect not only an increase in detectability
but also an increase in the count of birds not associated with the study area.

I illustrate a few of the numerous variables that influence the detection
probability. A highly skilled observer, with better eyesight, hearing, and
experience, has a much larger detection zone (*fig. 4*, left) than a
less-skilled observer (*fig. 4*, center); Ramsey and Scott (1981) found
that differences in hearing abilities could affect the area sampled by an
order of magnitude. Increasing the counting period enhances the detection
zone (*fig. 4*) but, as was mentioned, also increases the chance of counting
nonstudy-area birds (Scott and Ramsey 1981). Granholm (1983) found that density
estimates for three common and conspicuous bird species were 22 percent to
56 percent higher for 10-minute point counts than for 5-minute counts. As
a logistical issue, longer counting periods also reduce the number of point
counts that can be made in a fixed time period.

Similarly, the use of calls can increase the detectability of birds in an
area and is especially useful for certain nocturnal or secretive species (Johnson
and others 1981; *fig. 5*). Playbacks and the like can also induce birds
to move into the study area, however. The tradeoffs with respect to objectives
have to be assessed carefully because such devices may not only markedly increase
the detection probability, *C*, but may also increase the variability
in detection probabilities, Var(*C*), and thereby reduce the value of
the count as an index.

If stations are too close together, the same birds can be counted at both
(*fig. 6*). Unfortunately, what is too close depends on several things,
including the openness of the habitat, the size of the bird's home range and
its behavior, and the duration of the count.

The influence of roads on surveys in forested habitat is of considerable
interest, with ease of access a potential trade-off with bias in the counts
(Hutto, and Keller and Fuller). The issue is whether roads increase the detectability
of birds in the habitat (Ralph and others; *fig. 7*, center) or increase
the actual number of birds using the habitat (Keller and Fuller; *fig. 7*,
right).

To conclude, a point-count survey should be designed under a clear statement of objectives, whether they be estimating population size, assessing trends in populations, determining habitat preferences, or providing recreation. A survey designed for one objective (or not designed at all) is of limited suitability for another. Unlike many quantitative applications in ecology, point counts of birds are not directly estimating a clearly defined population parameter. Of the three models proposed for point counts, the additive and multiplicative models include unknown biases. The index model, the most reasonable of the lot, involves the product of bird density (the parameter of interest) and detectability. We need to better understand the role of the detection probabilities if we are to draw inferences from the counts about bird populations.

In some ways the problems inherent in point counts of birds are mitigated by large sample sizes, but not always. Theoretical and simulation studies are needed to determine which shortcomings are most critical, and field studies are needed to evaluate the extent of those departures from the ideal.

I am grateful to Rolf R. Koford, John R. Sauer, and Terry L. Shaffer for comments on the manuscript, and to Diane L. Larson, Michael D. Schwartz, and John M. Steiner for preparing figures.

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Johnson, Douglas H. 1995. Point counts of
birds: what are we estimating? Pages 117-123 *in* C. J. Ralph, J. R.
Sauer, and S. Droege, technical editors. Monitoring bird populations
by point counts. U.S. Department of Agriculture, Forest Service,
Pacific Southwest Research Station, Berkeley, California. General
Technical Report PSW-GTR-149.

**This resource should be cited as:**

Johnson, Douglas H. 1995. Point counts
of birds: what are we estimating? Pages 117-123 *in* C. J. Ralph, J.
R. Sauer, and S. Droege, technical editors. Monitoring bird populations
by point counts. U.S. Department of Agriculture, Forest Service, Pacific
Southwest Research Station, Berkeley, California. General Technical
Report PSW-GTR-149. Jamestown, ND: Northern Prairie Wildlife Research
Center Online. http://www.npwrc.usgs.gov/resource/birds/ptcounts/index.htm
(Version 05OCT2000).

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