AUTHOR'S PROOF
JrnlID 11252_ArtID 32_Proof# 1 - 17/07/2007
Urban Ecosyst
DOI 10.1007/s11252-007-0032-9
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Distance sampling as an effective method for monitoring
feral pigeon (Columba livia f. domestica)
urban populations
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Dimitri Giunchi & Valentina Gaggini &
N. Emilio Baldaccini
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# Springer Science + Business Media, LLC 2007
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Keywords Feral pigeons . Census technique . Distance sampling . Quadrate counts
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Introduction
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Feral pigeon (Columba livia f. domestica) populations have shown large numerical
increases both in Europe and in North America following World War II (see Johnston and
Janiga 1995 for a review). These large numbers have given rise to the development of a
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Abstract Current methods for estimating feral pigeon (Columba livia) population size and
for monitoring population trends are mainly based on indices, which according to the
current literature on wildlife census methods often produce biased results. Distance
Sampling techniques have never been used in this context, even though they could
theoretically produce absolute abundance estimates at relatively low costs. The aim of this
paper was to investigate the performance of Distance Sampling to census feral pigeons, and
to compare these results with those obtained by using Quadrate Counts, a widespread
method for monitoring these birds. Surveys were performed in Pisa (Italy) in two different
periods of the year 2004 (end of January–beginning of February, and November), which
correspond to a minimum (January–February) and a maximum (November) numbers for
pigeon populations. We conducted 40 line transects each about 250 m long for Distance
Sampling, and 40 250×250 m cells for Quadrate Counts. In both cases, sampling units were
randomized in a stratified design. In contrast to Quadrate Counts, Distance Sampling
detected the predicted increase of abundance from January–February to November with an
acceptable precision and no increase of costs per survey. Even though the possible biases
(due to the not rigorously random distribution of transects and to the spiked nature of
collected distances) should be further investigated, results suggest that Distance Sampling is
a viable and efficient alternative to the traditional methods used to estimate feral pigeons
population size and to monitor trends.
D. Giunchi (*) : V. Gaggini : N. E. Baldaccini
Dipartimento di Biologia, Università di Pisa, Via A. Volta 6, I-56126 Pisa, Italy
e-mail: dgiunchi@biologia.unipi.it
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considerable number of pest control techniques for this species (see Johnston and Janiga
1995 for a review), while, in comparison, research aimed to develop unbiased methods for
estimating pigeon population size has aroused far less interest. Unbiased estimates of pest
abundance are essential for: (1) the assessment of pest population size to justify control;
(2) the choice of appropriate control methods; (3) a plausible estimate of the costs for
control; and (4) an overall estimate the effectiveness of control. Pigeons counts are
intrinsically difficult and often costly because of the characteristics of urban environments
(e.g., complex structure and poor visibility), and of the pigeons themselves (e.g., clustered
distribution, high density, high vagility; see Johnston and Janiga 1995; Jokimäki and
Suhonen 1998; Buijs and Van Wijnen 2001; Rose et al. 2006; Soldatini et al. 2006, and
references therein). This often has led several authors to disregard methods whose
estimators adjust for imperfect detectability (e.g., capture–recapture) and to adopt a
number of ad hoc and uncalibrated indexes of population abundance, such as counts of
naturally occurring flocks (e.g., Buijs and Van Wijnen 2001), counts of birds attracted
with food (e.g., Sacchi et al. 2002), or uncorrected transect counts (e.g., Bursi et al. 2001).
Population indexes are widely used in wildlife monitoring programs because they are less
costly. There is, however, an increasing concern about their utilization (see Pollock et al.
2002; Rosenstock et al. 2002; Thompson 2002; Anderson 2003), because their critical
assumption—the proportionality between index and true population density–is usually
violated. A step in the direction to an unbiased estimate of feral pigeons abundance is
represented by Quadrate Counts (Uribe et al. 1984; Senar and Sol 1991; Senar 1996), i.e.
pigeon counts carried out by walking along a random sample of square, non-overlapping
sampling units into which the study area is divided. Even though the choice of sampling
units could be based on a rigorous sampling protocol, Quadrate Counts always produce a
biased estimate of the population size, since they do not take into account the birds’
detectability. This bias could be adjusted by using an appropriate correction factor
estimated by means of a sort of double sampling procedure (Cochran 1977; Bart and
Earnst 2002), i.e. by surveying a subsample of units using an “intensive” survey method
such as a mark-resight procedure (Senar and Sol 1991; Senar 1996). Even though this
method can produce accurate results, it is costly and requires a noticeable number of
marked individuals (often>100). The few studies which estimated correction factor using
this procedure produced, however, quite consistent results (Senar and Sol 1991; Barbieri
and De Andreis 1991; Sacchi et al. 2002), leading Senar (1996) to propose to multiply the
results of Quadrate Counts by 3.5, i.e. a reasonable average figure of the correction
factors reported in the literature. The outcome of this “simplified” procedure should be
considered a very rough indication of the magnitude of actual population size, since it is
reasonable to hypothesize that the number of birds that will pass undetected in different
surveys is variable, depending on characteristics of the study area and on behavior of the
pigeons themselves [e.g., daily schedule of foraging activity (Lefebvre and Giraldeau
1984; Rose et al. 2006; Soldatini et al. 2006); breeding activity (Johnston and Janiga
1995); etc.]. Moreover, the precision of the estimate is biased, since variability of the
sampling estimate of correction factor is usually not considered in calculations.
As far as we know, Distance Sampling (Buckland et al. 2001) has never been used on
feral pigeons, even though it should theoretically produce accurate estimates of population
size at lower costs than other unbiased survey techniques, such as capture–recapture.
Despite the potential value of this method, problems concerning 1) the validity of statistical
assumptions underlying line transect methodology (see below), and 2) the statistical
background needed in order to analyze collected data have probably represented an obstacle
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Methods
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Study area and general sampling method
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The study was conducted in 2004 considering most of the built-up area of Pisa (43°43′ N,
10°24′ E, 30 m a.s.l., ∼90 000 inhabitants). Several studies document that the distribution of
feral pigeons is clumped. Indeed, even though production and survivorship tend to be
lowest in densest urban areas (see Haag 1990, 1991) as recorded for other synantropic bird
species (see e.g. Marzluff et al. 2001), pigeon density is usually higher in historical town
centres, which are characterized by higher number of suitable nesting sites, higher human
population density, and a relatively constant food availability (e.g. organic waste, public
feeding; see Johnston and Janiga 1995; Jokimäki and Suhonen 1998; Buijs and Van Wijnen
2001; Sacchi et al. 2002). In this situation, the use of a stratified random sampling is
recommended, because it can significantly increase the precision of the estimate (Senar and
Sol 1991; Senar 1996), even if it is based only on little prior information (Thompson et al.
1998; Buckland et al. 2001). The study area was thus subdivided into two strata (Fig. 1) on
the basis of environmental features of built-up areas, especially with regard to density and
architectural characteristics of buildings, and of previous information on the distribution of
feral pigeons in Pisa (Baldaccini et al., unpublished data). The first stratum (stratum 1=
2.6 km2) extended over the historic centre of the city and is characterized by a high density
of old buildings constructed before World War II (and a large part of them during the
Medieval Age). The second stratum included the less densely built peripheral area (stratum
2=7.7 km2) characterized by a large percentage of relatively more recent and architecturally
more variable constructions than stratum 1.
To test the power of these two census methods in detecting changes in size of an
unmanaged pigeon population, surveys were replicated during two different periods
(Thompson et al. 1998): end of January–beginning of February (hereafter “January”) and
November. Both periods were presumably characterized by low reproductive activity by
feral pigeons, as suggested by both personal observations and published data (Johnston and
Janiga 1995; Giunchi et al. 2007). This means that the number of birds virtually
undetectable when attending eggs or squabs should have been relatively low. Considering
the local climate and reported data on population dynamics of feral pigeons (Johnston and
Janiga 1995), January and November surveys sampled the population in two rather different
phases of its annual cycle. January counts were carried out in the coldest period of the year
just before the beginning of the breeding season, indicated by the large number of birds
observed in courtship behaviour. The November survey was performed after the breeding
season just before wintertime, when population size is expected to be at its annual peak.
Surveys were carried out by the same observer. Birds were counted within 2 h after sunup. During this time period most pigeons remain within the city, usually near nesting or
roosting sites, possibly searching for food nearby, while the number of birds leaving the city
for feeding grounds in agricultural areas is very low (pers. obs., Soldatini et al. 2006 and
references therein). This counting strategy should alleviate any eventual bias due to large
scale movements even though it has the drawback of a potential reduction of the visibility
of pigeons because of their relatively low mobility during the first daylight hours.
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to its application. This paper investigates the performance of Distance Sampling in this
context and compares results of this method with those obtained using Quadrate Counts.
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Urban Ecosyst
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Fig. 1 Map of the study area
and of the two strata used
during sampling procedures (a).
Selected sampling units used in
Distance Sampling (black segments) and Quadrate Counts
(hatched squares) (b)
Distance sampling
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40 line transects were allocated proportionally to each stratum (stratum 1 had 10 transects,
stratum 2 had 30 transects; Fig. 1). Position and orientation of these transects were
randomly determined by means of the extension “DNR random sampling tools 1.1” of GIS
ARCVIEW 3.2, considering 300 m as transect length and 150 m as minimum transect
spacing in order to reduce the likelihood of double counts. Transects created by the
software were then adapted to the urban road network using a 1:2000 map of the study area
(Regione Toscana, Carta Tecnica Regionale, available at http://www.rete.toscana.it/sett/
territorio/carto/cartopage/index.htm) by considering the best overlapping linear path. In
order to avoid very short trails, we also took into account transects with moderate curvature,
as Distance Sampling should apply also in these cases (Buckland et al. 2001). Due to the
convoluted road network of the city, length of transects was less than 300 m (mean±SD;
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1. Transects should be randomly distributed with respect to the species’ distribution.
2. All birds located on the transect should be detected.
3. Birds located near or on the transect should be detected before they are disturbed by the
observer.
4. Distances should be measured accurately.
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261±31 m), but total sampling effort still remained roughly proportional to the stratum area
(total transects length: stratum 1=2739 m, stratum 2=7697 m).
We walked transects at a slow pace, paying attention to all birds seen or heard. To
increase the probability of detection of pigeons resting on buildings roofs or façades in the
vicinity of the line, the observer followed a zigzag path by alternating very short paths on
left and right pavements and occasionally looked behind in search of birds passed
undetected. The position of detected birds was accurately determined (±2 m) on the map of
the study area. As for surveys of birds in forest (see Buckland et al. 2001), the location of
pigeons perching on buildings was mapped on a point on the ground vertically below the
birds themselves. Due to the flocking behaviour of feral pigeons, birds were often detected
as groups. These groups were treated as single locations placed on the gravity centre of the
groups themselves, since this technique improves robustness of the estimate (Buckland et
al. 2001). All locations recorded on the printed maps were successively digitalized and the
perpendicular distances from the transect calculated using the ARCVIEW extension
“Distance Matrix 1.2”.
In order to correctly apply Distance Sampling methods, four main assumptions should
be satisfied (Buckland et al. 2001):
Taking into consideration this specific study, we observed that:
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Distance data were transformed into 2-m intervals and analyzed using the software
DISTANCE 5.0 (Thomas et al. 2005). We modelled the detection-probability function
considering the clusters of individuals. Birds density estimation was then obtained by
multiplying clusters density by mean cluster size, as preliminary inspections of the data did
not indicate any size bias problem (Buckland et al. 2001).
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1. Transects were clearly not randomly distributed. Contrary to the recommendations of
Buckland et al. (2001), transects followed the urban road network, and thus did not
represent a random sample of various habitats of the city. Moreover, each linear path
was located on centres of roadways where pigeon density is obviously low, since the
birds could be disturbed by road traffic. These conditions could lead to a significant
underestimate of population density. It is important to note, however, that this are
intrinsic, structural biases related to urban habitats, and thus it should affect all surveys
similarly in the same season but in different years. To reduce the possible effects of this
sampling problem, we left-truncated the data in order to exclude the low-density area
near each transect (see below; Buckland et al. 2001).
2. The assumption that all birds on the transect are detected seems reasonable considering the
open habitat (road centres) within which transects were laid.
3. The assumption that birds are not initially disturbed by the observer seems to be easily
satisfied, since feral pigeons are habituated to humans and could be approached quite
easily with practically no escape reactions.
4. Given the detailed maps at hand, the familiarity with the city of the observer and the
relatively short distances of detections of feral pigeons (more than 50% of detections were
within 15 m from transects), the assumption for accurate measurements seems to be met.
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Urban Ecosyst
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1. Half-normal plus up to three cosine adjustment terms.
2. Hazard-rate plus up to three simple polynomials terms.
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Given the current limitations of DISTANCE regarding analysis of nested design, we
analyzed the data collected in the two periods separately. We hypothesized that in each
period the shape of the detection function in the two strata was essentially the same, only
differing in scale due the different density of buildings. We thus considered two different
multiple covariates Distance Sampling models for the two periods, fitting a global model
for the detection-probability function, and using stratum as a factor covariate. In each
model, mean cluster size was estimated globally, since we have no reason to assume any
difference between strata in the flocking behaviour of feral pigeons, while encounter rate
(number of clusters per unit length of transect) was estimated by stratum.
Detection-probability function was a-priori modelled considering the following key
functions:
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40 sampling units (250×250 m; about 24% of the total study area, see Senar 1996) were
allocated proportionally to each stratum (stratum 1 had 10 units, stratum 2 had 30 units;
Fig. 1), and randomly placed using a grid superimposed over a map of the study area. Unit
size was determined as a trade-off between the need of taking into account a reasonable
number of units for reliable abundance estimations and large enough in place of not too
small with respect to pigeon movements and distribution in order to avoid “border effects”
or low precision due to a high number of zero counts (Thompson et al. 1998). In this case, a
“border effect” could be ruled out because of the small perimeter/area ratio, while the unit
size satisfied the criterion suggested by Williams et al. (2002) in that the proportion of units
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The best model was chosen using Akaike Information Criterion (AIC; Buckland et al. 2001;
Burnham and Anderson 2002). We started with a model with no adjustments, and gradually
added one term at a time in order to improve the fit of the model. These models were then
used to calculate density only if χ2 goodness-of-fit test was not significant. We discarded all
the observations beyond 38 m (January; 18% of distance data) and 42 m (November; 13% of
distance data) in order to improve the fit of the curve and to avoid the smallest estimated
probabilities of detection of clusters being below 0.2 (Thomas et al. 2005). Mean cluster size
was calculated using the same truncation distances specified above.
Data were also left-truncated by excluding the first 4 m near the line. The width of this
left truncation was chosen to represent width of the roads upon which transects were laid.
Using ARCVIEW, we classified the half-width of each road segment to the nearest meter
(excluding both pavements), and then calculated the median of distributions of these halfwidths, which was 4.5 m considering all the pooled transects (stratum 1=4 m, stratum 2=
4.5 m). The truncation band was then set to 4 m, i.e., rounding down the median half-width
in order to reduce the chance of overestimating pigeon density.
Given the aim of this paper and available sample size, we determined global density
estimates and calculated bootstrap variances by means of 1000 replications. Comparisons
among parameters involved in these estimates were performed by considering the 95%
confidence interval (CI95%), as suggested by Johnson (1999). Detectability in the two
periods was compared by means of the effective strip half-width (μ), i.e., the distance for
which the number of birds detected beyond μ and the number of birds missed within μ of
the line are equal (Buckland et al. 2001).
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with reasonable probability of being empty is well below 50%. In addition, sampling times,
during which feral pigeons are moving less (see above), should have contributed to alleviate
problems related to unit size.
As mentioned in the Introduction, we counted pigeons while walking along roads in the
sampled units. Population mean and variance were then calculated using the package
“Survey 3.6-2” (Lumley 2004) of the statistical software R 2.4.1 (R Development Core
Team 2006), considering 1000 bootstrap replications. As stated by Williams et al. (2002),
estimates based on less than 30 sampling units are generally biased (variance is
underestimated) especially if they are based on clustered distributed populations. For this
reason we estimated abundance only at global level. Following Johnson (1999), the results
of the surveys were compared using CI95%. According to Senar (1996), we corrected
Quadrate Counts by 3.5 in order to obtain a rough figure of pigeons abundance (see
Introduction),.
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Power analysis
α=0.05
β=0.8
Linear or exponential type of change
Negative rate of change
1-tail tests for significance
constant CV (variance linearly related to the squared mean of abundance)
Number of sampling occasions: 6 (1 per year)
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The power of Distance Sampling and Quadrate Counts in detecting a negative trend of
pigeons population was evaluated by estimating the Minimum Detectable Rate of Change
(MDRC) given the precision of these two methods [Coefficient of Variation (CV)] using the
software TREND 3.0 (Gerrodette 1987, 1991, 1993). Since we were lacking suitable pilot
data from a multiyear study, our power calculations were based solely on within-year
variations of abundance. According to Hatch (2003) this kind of procedure leads to
overestimates of power. It should be noted, however that the relatively limited home range
of pigeons (Johnston and Janiga 1995; Sol and Senar 1995; Rose et al. 2006 and references
therein) and the stability of urban habitat should substantially reduce the inter-annual
variation of counts and thus the likelihood of power overestimation. This low inter-annual
variability is also confirmed by periodic censuses performed in a small number of European
cities (e.g. Barcelona, Bratislava, Venice; see Johnston and Janiga 1995; Giunchi et al. 2007
and references therein). Given the high costs of pest control plans on feral pigeons (see e.g.
Johnston and Janiga 1995; Zucconi et al. 2003), power estimation took into account a
relatively short study period ( 6 yr). The parameters used in the calculations were:
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Results
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Distance sampling
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Figure 2 reports the frequency distribution of perpendicular distances of clusters detected in
the two strata. It is evident that the number of detections on or close to the transect line was
rather low. Considering the general tameness of feral pigeons, it seems unlikely that this
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Fig. 2 Frequency distribution of perpendicular distances (bar width = 4 m) of clusters detected in the two
strata and in the two considered periods (January–February and November). Open bars indicate the lefttruncated interval
result was due to undetected evasive movements in response to the observer. While few
detections near the transect line were expected, considering the non-random distribution of
transects, these results support our choice to left truncate distance data (see Methods).
Table 1 reports the ranking of candidate models. In both surveys the hazard key with one
simple polynomial adjustment term was selected for the detection function (Fig. 3). These
models were characterized by μ=15.2 m±1.0 SE in January and by μ=10.3 m±0.7 in
November with an acceptable fit in both surveys. It should be noted, however, that
detection probability of November survey decreased quite rapidly near the line, producing a
remarkably narrow shoulder of the detection function.
Summary statistics of parameters of the two models selected by minimum AIC are
reported in Table 2. Encounter rate turned out to be substantially higher in stratum 1, which
included the historic centre of the city, than in stratum 2 and it tended to increase from
January to November. Mean cluster size was substantially comparable between the two
periods, although there was a slight reduction in November. Given the remarkably spiked
distribution of distance data, November estimates were less precise than January.
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Table 1 Ranking of candidate models used in Distance Sampling based on the difference in Akaike’s
information criterion (AIC)
t1.1
Modela
Kb
AIC
ΔAICc
wei
χ2 (P)e
t1.2
January–February
Right truncation=38 m
Left truncation=4 m
HR+1 polynomial terms
HN+1 cosine terms
HR
HN+2 cosine terms
HR+2 polynomial terms
HN+3 cosine terms
HR+3 polynomial terms
HN
HR+1polynomial terms
HN+1 cosine terms
HR+2 polynomial terms
HN+3 cosine terms
HN+2 cosine terms
HR+3 polynomial terms
HR
HN
4
3
3
4
5
5
6
2
4
3
5
5
4
6
3
2
840.48
841.64
841.66
842.33
842.67
844.33
844.89
847.26
1,192.85
1,194.63
1,194.65
1,195.97
1,196.61
1,196.83
1,203.79
1,205.55
0.00
1.17
1.18
1.85
2.20
3.85
4.41
6.78
0.00
1.79
1.81
3.12
3.77
3.99
10.95
12.70
0.32
0.18
0.18
0.13
0.11
0.05
0.04
0.01
0.32
0.13
0.13
0.07
0.05
0.04
0.00
0.00
0.10
0.06
0.05
0.06
0.06
0.04
0.04
0.01
0.42
0.38
0.30
0.40
0.30
0.35
0.03
0.01
t1.3
t1.4
t1.5
t1.6
t1.7
t1.8
t1.9
t1.10
t1.11
t1.12
t1.13
t1.14
t1.15
t1.16
t1.17
t1.18
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November
Right truncation=42 m
Left truncation=4 m
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Period
t1.19
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All the parameters were computed by Distance
a
The models tested were Half-Normal (HN) plus up to three cosine adjustment terms and Hazard-Rate (HR)
plus up to three simple polynomials terms
Number of parameters
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Difference in AIC from the best model
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Model weights (see Burnham and Anderson 2002)
e
P-value of the χ2 goodness of fit test
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Nevertheless, pigeon density was considerably higher in November than in January, as
expected.
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As summarized in Table 3, population estimates obtained in the two surveys were quite
different and both much lower than results from Distance Sampling (Fig. 4). Contrary to
expectations, January abundance turned out to be substantially higher than November (663
birds/km2 vs. 429 birds/km2). The precision (CV) of these estimates decreased accordingly
from January to November, but in both periods it was noticeably higher than that obtained
using Distance Sampling (January: 0.14 vs. 0.17; November: 0.10 vs. 0.20). Using a
correction factor=3.5 (see Methods), our results correspond to a population estimate of ca.
24 000 in January, about double the Distance Sampling estimate of the same period, and ca.
15 500 in November, perceptibly lower than Distance Sampling estimate.
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Table 4 reports MDRC estimated using the software TRENDS. As expected, Quadrate
Counts outperformed Distance Sampling in all cases due to its lower value of CV. It is
interesting to note that difference in MDRC between the two methods was quite low in
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µ
Fig. 3 Detection probability (continuous line) plot, histogram of perpendicular distances, and effective strip
width (μ) for January–February and November surveys
January, while it substantially increased in November, when Quadrate Counts estimate was
unexpectedly low. Overall, these results suggested that both methods were able to detect a
noticeable negative trend in population size which corresponded roughly to a decrease of at
least 10% yr−1.
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Table 2 Encounter rate, cluster size, and density estimates obtained by Distance Sampling and computed
from Distancea
t2.1
Survey
Stratum
No. of
clusters
Encounter rate
(clusters/km)
Mean
cluster size
Cluster/km2
Animals/km2
CVb
t2.2
January–
February
1
85
2.8
(2.3–3.3)
497.2
(391.4–704.9)
1388.3
(1137.0 –1812.8)
0.15
t2.3
2
1
74
126
2.3
(2.1–2.8)
1081.0
(691.5–1592.5)
2471.5
(1857.1–3364.3)
0.21
t2.5
2
108
31.0
(21.5–44.8)
9.6 (7.0–13.2)
46.0
(36.8–57.4)
14.0
(8.7–22.5)
t2.4
F
t2.6
O
November
a
CV refers to animal density
PR
b
t2.7
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CI 95% [2.5% and 97.5% quantiles of the bootstrap estimates (R = 1,000 resamples)] are reported in
parentheses
Discussion
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Table 3 Summary statistics (± bootstrap SE) of results of the Quadrate Counts analysis
t3.1
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Results obtained in this study suggest that Distance Sampling is a viable and efficient
alternative to traditional methods used to estimate feral pigeon population size and to
monitor population trends. Even though we did not perform a proper test of accuracy,
Distance Sampling performed fairly well under our sampling conditions and it clearly
outperformed Quadrate Counts. For instance, the trend of the two Distance Sampling
estimates evidenced a clear increase of abundance from January to November, as predicted
by considering demographic characteristics of feral pigeons populations (Johnston and
Janiga 1995) and, in particular, the annual trend of breeding activity recorded in the nearby
city of Lucca (Giunchi et al. 2007). On the other hand, it is hard to give a reasonable
biological explanation of the consistent decrease of abundance indicated by Quadrate
Counts in the second survey, which followed the main part of the breeding season of the
population. On the contrary, it seems reasonable to hypothesize that pigeon detectability
varied consistently across both census periods. As mentioned in the Introduction, the first
survey was indeed carried out at the beginning of the breeding season with few active nests.
In fact, most detections were of pigeons courting or searching for mates. These behaviours
probably favoured detecting pigeons during the first hours after dawn and increased the
fraction of population actually detected during the survey. On the other hand, in November
the few breeding and courting pigeons were detected. In this period, most birds were
relatively inactive since they began feeding later in the morning (see also Lefebvre and
Survey
Stratum
January–February 1
2
November
1
2
a
Total
sampling
units
Selected
sampling
units
Birds recorded Birds/units
Abundance
CV a
t3.2
42
123
42
123
10
30
10
30
973
672
679
384
41.5±5.6
6841.8±932.0
0.14
t3.3
26.8±2.7
4426.2±438.2
0.10
t3.5
CV refers to animal abundance
t3.4
t3.6
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Fig. 4 Estimated abundances [± 95% confidence intervals (CI 95%)] obtained in Distance Sampling and
Quadrate Counts analysis during the two surveys
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Table 4 Minimum detectable rate of change (MDRC) of feral pigeon populations estimated using Trends
3.0 (Gerrodette, 1987, 1991, 1993) and precision (CV) obtained by Distance Sampling and Quadrate Counts
methods
t4.1
Survey
Method
CV
Type of trend
Annual MDRC
t4.2
January–February
Distance Sampling
0.15
Quadrate Counts
0.14
Distance Sampling
0.21
Quadrate Counts
0.10
Linear
Exponential
Linear
Exponential
Linear
Exponential
Linear
Exponential
−0.09
−0.10
−0.08
−0.10
−0.11
−0.14
−0.06
−0.07
t4.3
t4.4
t4.5
t4.6
t4.7
t4.8
t4.9
t4.10
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Giraldeau 1984; Johnston and Janiga 1995; Soldatini et al. 2006). This change in behavior
of pigeons likely decreased the fraction of birds detected in November. Interestingly, the
hypothesis of a decreased detectability in November is also supported by the reduction of μ
recorded in this survey. Given these considerations, it is evident that the use of “fixed”
correction factor is of no help in correcting the intrinsic biases of Quadrate Counts
estimates. Indeed, as stated by several authors (see e.g. Sutherland 1996), the use of
correction factors derived under specific conditions in completely different contexts is best
avoided, since it could lead to misleading results. Considering our specific case, it is clear
that the fractions of birds detected in January and November are not the same, and, given
the data at hand, there is no way to assess in which case the chosen correction factor is
more appropriate, if it is. This further leads us to stress the need to estimate an appropriate
correction factor each time Quadrate Counts method is used.
Given these considerations, it seems clear that the relatively high precision recorded for
Quadrate Counts is substantially useless when trying to assess population trends of pigeons,
given the biases of this method, and the problems of repeatability for any index of abundance
(Sutherland 1996; Thompson et al. 1998; Schwarz and Seber 1999; Pollock et al. 2002;
Rosenstock et al. 2002). It should be noted, moreover, that the use of case-specific correction
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factors, while likely improving the accuracy, should reduce the precision of Quadrate Counts,
because variability of the estimate of correction factor has to be included in calculation of
global variance. For instance, if we use the “Delta Method” (Burnham et al. 1987) to estimate
the variance of corrected Quadrate Counts and if we assume a rather precise estimate of
correction factor (CV=0.10), comparable to that reported in Senar and Sol (1991), we obtain
two values of CV (January=0.16, November=0.13), which are not far from those recorded
for Distance Sampling, at least in the first period (see Table 2). In terms of this last method,
the precision of the two estimates is comparable with those recorded in other wildlife surveys
(examples in Sutherland 1996; Thompson et al. 1998; Bibby et al. 2000; Buckland et al.
2001; Williams et al. 2002). Even though the above mentioned problems of overestimation
should be born in mind (see Methods), the results of power analysis suggests that at least the
precision recorded in January is probably enough for evaluating expected results of a pest
control action, since published rates of decrease recorded in field studies or obtained in
simulated analyses are usually higher than 10% yr−1 (e.g. Haag 1995; see also Giunchi et al.
2007), at least during the first years of pest control. This power could be further increased by
improving the precision of estimates by (1) accounting for variability among strata when
allocating sampling units (Neyman allocation; see Thompson et al. 1998); (2) increasing the
number of strata and/or by considering habitat covariates; and (3) increasing coverage.
Regarding point (1), it should be noted that at least in the present case this technique should
have significantly improved precision only in November, given the noticeably variability of
encounter rate recorded only in this survey (encounter rate CV, January: Stratum 1=
Stratum 2=0.16; November: Stratum 1=0.09, Stratum 2=0.23). For what concern point
(2), the presented data confirmed that the stratified design is particularly recommendable
for feral pigeons survey, given the strong heterogeneity recorded among the two strata. It
is likely that the incorporation of habitat variables (e.g. road density, buildings
characteristics) into the survey design could further increase the precision by reducing
habitat heterogeneity within strata, even though care should be taken in order to avoid
over-stratifying the study area. While the two above mentioned improvements of the
survey design are feasible both for Distance Sampling and Quadrate Counts since they do
not significantly rise the survey costs, the increase of coverage seems particularly
recommendable for Distance Sampling. Indeed, even though we did not perform a precise
evaluation of their actual costs, it seems evident that the two methods did not imply any
substantial difference both in observer effort of collecting data and in transfer time
between sampling units, given the comparable number of units and their random
distribution. We could assume, then, that the costs of Quadrate Counts and Distance
Sampling should have been proportional to the total length of the roads walked during
each survey. For Distance Sampling this length was equal to the total length of the
transects, i.e., about 10 km. Since Quadrate Counts is based on an intensive search of
pigeons in each sampling unit, a minimum figure of the effort could be derived by
considering the total length of all road segments within each cell, i.e. about 34 km. This
means that Distance Sampling estimates of population abundance were obtained with less
than one-third of the effort employed for Quadrate Counts. Since the considered coverage
of Quadrate Counts (about 24% of the study area) should not be probably further reduced,
in order to obtain reliable results (see Senar 1996), it seems evident that any unbiased
Quadrate Counts estimate of feral pigeon population size, which provides for a contextual
determination of a suitable correction factor, would need far more effort than those
needed for a reasonably precise Distance Sampling estimate.
Obviously, Distance Sampling is not immune from drawbacks. Given the relatively short
right truncation distance, we are confident that the use of mean cluster size instead of other
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techniques (e.g. size-biased regression; see Buckland et al. 2001) did not introduce any
significant bias in our abundance estimation, even though we have to acknowledge the
relevant variability of recorded flock size, especially evident in November, which
significantly decreased the precision of the estimates. This result further stresses the
opportunity of surveying feral pigeons abundance when their flocking behaviour is less
extreme, i.e. before the beginning of the breeding season, and before pigeons form large
aggregations near relevant food sources, i.e. early in the morning (see also Lefebvre and
Giraldau 1984; Lefebvre 1985; Johnston and Janiga 1995). The main problem of Distance
Sampling is however related to the non-random distribution of transects. Indeed, the
strongly inhomogeneous accessibility of urban habitat prevented the use of any automatic
procedure for designing the survey, such as the survey design component of DISTANCE.
Instead, we were forced to adapt the randomly chosen transect to the urban road network,
thus rendering the distribution of sampling units not truly random. As stated in the
Methods, however, this sampling problem should be regarded as intrinsic of any urban
ground-based birds count, and thus it could not be easily solved, except by using markrecapture/resight techniques, which are rather more costly and generally not well suited for
counting birds in the urban habitat (Senar 1996). The solution here adopted to alleviate this
problem—i.e. left truncation of distance data—was not devoid of defects. Indeed, since
detectability at 0 distance was inferred on the basis of the frequency distribution of contacts
recorded at distances not subjected to truncation, it is possible that it could have been
overestimated, leading to an overestimated abundance (Buckland et al. 2001). Moreover,
the use of the median road half-width could be considered not completely satisfying, given
the substantial heterogeneity of the roads where the transects laid. Overall, the likelihood of
this theoretical overestimation seems rather low, especially considering the figures obtained
using the corrected version of Quadrate Counts, but clearly this topic deserve further
investigation. It should be noted, however, that this eventual bias could be at least partially
reduced under a long-term pest control protocol, by estimating pigeons’ detectability at
transect level and using different left-truncation distances depending on the actual width of
the roads where each transect lays. This procedure needs at least≥40 contacts per transects
in order to obtain reliable estimates (see Buckland et al. 2001), but, given the recorded
encounter rate of feral pigeons, it seems likely that this threshold could be easily reached by
pooling data collected during the same season over a relatively small number of years. A
second problem, which clearly emerged from this study, was the spiked nature of distance
data, which was mainly due to the high number of visual hindrances (caused mainly by
high buildings), which determined an abrupt reduction of pigeon detectability even
relatively close to the transects. November distance data, in particular, were particularly
problematic, given the very narrow shoulder of the detection function. This type of
frequency distribution of distances posed several problems when modelling distance data
(Buckland et al. 2001), and, indeed, the fit of even the best models was not particularly
high. It should be noted, however, that abundance estimates of the highest ranking
candidate models (differing by AICs of 2 or fewer from the best model) were rather
comparable (data not presented), thus indicating that model selection do not have a crucial
effect on the presented results. Again, it seems likely that this problem could be at least
partially solved under a long-term pest control program by pooling data collected in
different years (see above), even though it seems reasonable to recommend to avoid
counting pigeons at their annual population peak.
In the end, it is important to remark that the above-mentioned theoretical problems of
accuracy of Distance Sampling should not have any relevant effect on its repeatability,
given their dependence on the structural characteristics of the urban environment, which
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should be roughly the same in different years. This means that, contrary to Quadrate
Counts, even a systematically biased Distance Sampling should be an unbiased tool for
detecting population trends.
To conclude, our data suggest that Distance Sampling is an effective survey method for
feral pigeons, and therefore it could be profitably used in population studies on these birds
in urban environment. Moreover, this technique should be extremely useful as part of
effective management programs, because it helps to rigorously assess both the costs for
control, by providing a reasonable estimate of population size, and the effectiveness of
eventual control actions, by objectively quantifying their actual effects on pigeons
abundance.
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Acknowledgments Thanks are due to Cecilia Soldatini and to Enrica Pollonara for their valuable comments
on an earlier draft of this manuscript. We appreciate the improvements in English usage made by Peter
Lowther through the Association of Field Ornithologists’ program of editorial assistance.
D
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Q3
AUTHOR QUERIES
AUTHOR PLEASE ANSWER ALL QUERIES.
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Q1. Sol and Senar 1995 is cited in the body but is not found in the
reference list. Please provide references or else delete it from
the body.
Q2. Please provide update on the publication status of Giunchi et
al., 2007 if already available.
Q3. Is the reference by Zucconi et al. 2003 a journal? Please check.