Snail Kites (Rostrhamus sociabilis) in Florida were monitored between 1969 and 1994 using a quasi-systematic annual survey. We analyzed data from the annual Snail Kite survey using a generalized linear model where counts were regarded as overdispersed Poisson random variables. This approach allowed us to investigate covariates that might have obscured temporal patterns of population change or induced spurious patterns in count data by influencing detection rates. We selected a model that distinguished effects related to these covariates from other temporal effects, allowing us to identify patterns of population change in count data. Snail Kite counts were influenced by observer differences, site effects, effort, and water levels. Because there was no temporal overlap of the primary observers who collected count data, patterns of change could be estimated within time intervals covered by an observer, but not for the intervals among observers. Modeled population change was quite different from the change in counts, suggesting that analyses based on unadjusted counts do not accurately model Snail Kite population change. Results from this analysis were consistent with previous reports of an association between water levels and counts, although further work is needed to determine whether water levels affect actual population size as well as detection rates of Snail Kites. Although the effects of variation in detection rates can sometimes be mitigated by including controls for factors related to detection rates, it is often difficult to distinguish factors wholly related to detection rates from factors related to population size. For factors related to both, count survey data cannot be adequately analyzed without explicit estimation of detection rates, using procedures such as capture-recapture. Received 29 April 1997, accepted 24 July 1998.
Department of Wildlife Ecology and Conservation, University of Florida, Gainesville, Florida 32611, USA;
2USGS Patuxent Wildlife Research Center, 11510 American Holly Drive, Laurel, Maryland 20708, USA; and
USGS Patuxent Wildlife Research Center, Southeast Research Group, University of Georgia,
Athens, Georgia 30602, USA
COUNT DATA have been widely used to mon-
itor changes in bird populations (Barker and
Sauer 1992, Johnson 1995). Counts are obser-
vation-based surveys in which an observer re-
cords some unknown portion of the birds ac-
tually present at a site. A complete census of a
bird population is seldom feasible (Lancia et al.
1994), and alternative approaches (e.g. capture-
recapture) often are too expensive or are logis-
tically impractical (Link and Sauer 1997, 1998).
However, count-based inferences about chang-
es in population size can be severely biased if
the detection rate (i.e. the fraction of animals
counted) varies among counts, particularly if
that variation has a temporal component (Burn-
ham 1981, Nichols 1992, Johnson 1995, Link
and Sauer 1997).
Unfortunately, many factors may influence
4 Present address: Station Biologique de la Tour
du Valat, Le Sambuc, 13200 Arles, France. E-mail:
bennetts@tour-du-valat.com
the detection of birds during counts. Examples
include: (1) temporal and behavioral differenc-
es among individuals, sometimes related to
population density or habitat at sample sites
(e.g. Gates 1966); (2) inconsistencies in count-
ing methods among sample sites (Robbins et al.
1989, Geissler and Sauer 1990); (3) inherent dif-
ferences in ability among observers when more
than one observer conducts a survey (Faanes
and Bystrak 1981, Sauer et al. 1994); (4) changes
in observer ability associated with experience
(e.g. first-time observer effects; Kendall et al.
1996); and (5) variation in effort (in terms of
time or number of observers) expended for a
given survey (Butcher and McCulloch 1990).
Although some investigators feel that these
sources of variability in detection rates can
completely invalidate count-based surveys
(Burnham 1981), most analyses of such surveys
generally attempt to adjust for sources of vari-
ation in detection rate through use of covariates
in the analysis, and then assume that changes
in the covariate-adjusted counts reflect changes
in the actual population. However, simple an-
alyses of count data that do not adjust for
sources of variation in detection rate may result
in biased estimates of population change (e.g.
Sauer et al. 1994).
Snail Kites (Rostrhamus sociabilis) in Florida
were monitored from 1969 to 1994 using a qua-
si-systematic annual survey (Sykes 1979, 1982;
Rodgers et al. 1988, Bennetts et al. 1994). The
survey has been reported as: (1) a census
(Sykes 1979, 1983; Snyder et al. 1989, Beissinger
1995); (2) an index of the relative number of
birds in a given wetland over time (Rodgers et
al. 1988); (3) a response variable for explana-
tory environmental variables (Beissinger 1995);
(4) a basis for estimates of annual survival
(Beissinger 1986, 1995); and (5) a basis for es-
timates of population trend (Sykes 1979, 1983;
Bennetts et al. 1994).
Here, we analyze population change in the
annual survey of Snail Kites using a general-
ized linear model. We then use the model to
document several previously overlooked sourc-
es of variation that might influence detection
rates of Snail Kites.
Site Legend
ELT = Et Lake Totl<,ea
LT = Lake Tohol3ekaga
LK = Lake K]alnqmee
USJM = UlOer St. Johr Marah
LO = Lake Okeechobee
LPR = Lake Park Rearvoit
LNWR = Loxahat=hee Namal
WCA2A = Water Ceraon
Area 2A
WCA2B = Water Conser,'aon
A,-ea 2B
WCA3A = Water Corervaon
A,-ea 3A
WCAaB = Water Con#aon
Area 3B
ENP = Ev$ Namal Pek
BCNp = Big G' Naxlal
NESR8 = North Eeat Shark
Rk, er eugh
LTi ELT
Gulf of
Mexico
0 100km
Atlantic
Ocean
METHODS
The annual Snail Kite survey.--Annual surveys were
conducted in November and December, 1969
through 1994 (Sykes 1979, 1982; Rodgers et al. 1988,
Bennetts et al. 1994). Counts were initially conducted
via airboat using parallel transects about 0.5 km
apart; however, we maintained the established pro-
tocol of using sites, rather than transects, as the sam-
pling unit (Sykes 1982). As technology advanced, the
position and alignment of transects were determined
with a LORAN C navigational unit, and eventually a
global positioning system. In large areas, where
dense vegetation precluded placement of transects,
or the number of birds (>10) indicated the presence
of an evening roost, transect counts were corrobo-
rated or replaced with counts at communal roosts
(Rodgers et al. 1988). Counts at roosts were con-
ducted by positioning observers near the roost at
least 1.5 h before sunset so that birds could be easily
counted as they entered the roost.
Since 1969, three principal observers have con-
ducted the annual survey: P. W. Sykes, Jr. (1969 to
1980), J. A. Rodgers, Jr. (1981 to 1990), and R. E. Ben-
netts (1991 to 1994), although each of these observers
may have had from one to several observers assisting
them (Sykes 1979, Rodgers et al. 1988, Bennetts et al.
1994, Sykes et al. 1995). No independent surveys
were conducted during the transition from one prin-
cipal observer to another, although Rodgers accom-
FIG. 1. Central and southern Florida showing
wetland sites surveyed for Snail Kites and included
in our analysis.
panied Sykes for much of the 1980 survey as an ob-
server.
Sites at which the annual survey was conducted
have been escribed by Sykes (1984), Rodgers et al.
(1988), and Bennetts and Kitchens (1997a). The sur-
veyed area of these sites ranged in size from ap-
proximately 5,000 ha at Lake Park Reservoir to
178,000 ha at Water Conservation Area 3A. A total of
15 sites was included in our analysis, 10 of which
were surveyed in all 26 years (Fig. 1). As the distri-
bution of kites became better known, and/or
changed over time, the wetlands included in the sur-
vey changed accordingly. Thus, sites tended to be
added over time, which generally corresponded with
changes in observers. However, there was also con-
siderable turnover in the surveying of smaller or
more sporadically used wetlands. Such wetlands
that were haphazardly surveyed with no consistency
among observers or years were excluded from our
analysis, although these wetlands generally account-
ed for a small percentage (f = 1.7%) of the total num-
ber of birds counted.
Modeling population change.--A common and fre-
quently reasonable assumption for analyses of count
data is that counts have Poisson distributions. The
family of overdispersed Poisson distributions was
introduced to generalize and improve such analyses
by relaxing the restrictive assumption that the vari-
ance and mean are equal. Generalized linear models
(GLMs) based on assumptions of overdispersed
Poisson distributions are widely acknowledged as
appropriate for analyses of count data (McCullagh
and Nelder 1989, Diggle et al. 1994). They are easily
fitted using software such as GLIM (Francis et al.
1994). We modeled population change in Snail Kites
using an overdispersed GLM described by Link and
Sauer (1997).
Patterns in counts of wildlife are a composite of
patterns of population change and patterns induced
by variation in detection rates; thus, the models we
used included parameters describing site and ob-
server effects, population change, and the effect of
covariates on detection rates (Link and Sauer 1998).
We used a loglinear model that included main effects
for year, site, observer, water level, and effort and all
two-way interactions of site, observer, water level,
and effort.
We treated year as a factor with distinct values for
each year of the survey. This "year-effects" model
stands in contrast to models in which it is assumed
that the pattern of population change can be repre-
sented by a polynomial or other smooth function.
The latter have the advantage of parsimony, because
they include a reduced set of parameters relative to
year-effects models. Our choice of a year-effects
model to describe the Snail Kite data was motivated
by an important limitation of the data set: the time
periods covered by distinct observers did not over-
lap. Thus, in years of observer change, population
change was confounded with change in observer
ability. Fitting a smooth pattern of population
change across years involves interpolation across
years of observer change on the basis of the patterns
within each consecutive observer's periods. Doing so
relies heavily on the assumption that the pattern of
population change is smooth, and in particular that
anomalous population changes have not coincided
with changes in observers.
Because it was likely that observers differed in
their methods of counting kites, we used primary ob-
server as a factor in the analysis. Because time peri-
ods covered by distinct observers did not overlap, in-
clusion of this factor limits comparisons of popula-
tion sizes to within periods of primary observers.
Consequently, changes in counts coincident with ob-
server change cannot be attributed to change in pop-
ulation; population change is confounded with any
changes associated with observers.
We defined effort, o, as the number of observer
days associated with a count. An observer day was
considered to be one observer for one full day, or two
observers for 0.5 days each, etc. We estimated ob-
server days to the nearest 0.25 days (assuming a 12-
h day) that we could reasonably determine from the
original records of each observer. Each principal ob-
server had from one to eight observers assisting, par-
ticularly during simultaneous counts at multiple
roosts. We modeled the effect of effort as propor-
tional to exp(-c/o) for some c > 0; thus, 1/o was
treated as an additive variable in the loglinear mod-
el. In this model, the proportion of animals counted
is a concave upward function of effort for low levels
of effort, then becomes a concave downward func-
tion of effort for high levels of effort, leading to a fi-
nite asymptote (i.e. more effort leads to proportion-
ately less increase in counts as effort increases). The
possibility that the effect of effort could vary among
sites or observers, or in association with water levels,
was examined by consideration of the relevant inter-
action terms.
Because water level can have an important effect
on Snail Kite counts and population size (Sykes 1983,
Beissinger 1995), the models we considered also in-
cluded site-specific water levels, measured in
"stage." Stage is defined as the elevation at the water
surface relative to mean sea level. Stage is also the
standard unit of measure for site-specific gauges at
each location maintained by the South Florida Water
Management District, St. Johns River Water Manage-
ment District, U.S. Army Corps of Engineers, U.S.
Geological Survey, and the city of West Palm Beach.
The specific gauges used are reported in Bennetts
and Kitchens (1997a). Yearly mean water levels were
imputed for sites that could not be associated with
gauges. Because water depth can be highly variable
within sites, and reliable elevation data to estimate
site-specific depth are lacking, we used variation in
stage as the basis for our assessment of water levels.
We estimated an average of the minimum annual
stage over the 26-year period covered by the kite sur-
veys. We then used the number of standard devia-
tions above or below that average, for any given year,
as a measure of relative water levels. This measure
provides an objective assessment of water levels that
can be applied to all areas and that corresponds well
with the subjective designation of drought years re-
ported in previous studies (e.g. Bennetts and Kitch-
ens 1997a).
The final component of our GLM is the overdis-
persion structure. Following Link and Sauer (1997),
we allowed a distinct overdispersion parameter for
each of the 15 sites. This overdispersion accounts for
unmodeled variation in counts, such as variation in
patterns of population change among sites. Tests be-
tween nested models were carried out treating
changes in scaled deviance as having a chi-squared
distribution.
RESULTS
The data consist of 323 records obtained at 15
sites during 26 years. Eleven of the 15 sites
were initiated by the first observer (team); data
8O0
19691971 19731975197719791981 19831985198719891991 1993
Year
FIe. 2. Total number of Snail Kites counted dur-
ing each annual survey by each observer from 1969
through 1994, plotted with amount of effort expend-
ed in each survey year. Line denotes effort as mea-
sured by the total number of observer days for a giv-
en year.
were collected in all 26 years at 10 of the sites.
The total number of birds observed over all
sites ranged from 65 birds in 1972 to 964 birds
in 1994; counts clearly were associated with to-
tal effort (Fig. 2). Survey periods did not over-
lap among primary observers, so it was not
possible to test for differences among observ-
ers. It was possible to test for observer-specific
differences among sites (i.e. site by observer in-
teractions), however, which were highly signif-
icant (X 2 = 101.7, df = 24, P < 0.001).
The effect of effort did not vary among sites
(X 2 = 15.18, df = 14, P = 0.37) nor in association
with water levels (X 2 = 1.63, df = 1, P = 0.20).
However, a significant interaction occurred be-
tween effort and observers (X 2 = 16.04, df = 2,
P < 0.001), which indicated that distinct values
of the parameter c describing the effect of effort
should be assigned for each observer Exami-
nation of the data by observer revealed that ef-
fort had no significant effect on counts for the
second (X 2 = 1.56, df = 1, P = 0.21) or third (X 2
= 0.90, df = 1, P = 0.34) observers, but that the
effect of effort was significant for the first ob-
server (X 2 = 16.43, df = 1, P < 0.001).
Next, we considered the effects of water level.
These did not vary in association with observer
(X 2 = 0.21, df = 2, P = 0.90) but did vary among
sites (X 2 = 36.09, df = 14, P = 0.001). The model
with 15 site-specific effects of water level could
be reduced to a model with only two distinct
effects of water level (X 2 = 20.10, df = 13, P =
0.093). The first of these effects is that water lev-
el at all sites was significant and was positively
associated with counts. The second identified
1968 1970 1972 lg74 lg76 1978 1980
Year
FG. 3. Estimates (_+ SE) of Snail Kite population
change controlling for effort, observer, site, and wa-
ter level (open circles connected by lines). Population
changes are scaled for comparability with the total
counts within each observer. Solid squares denote
unadjusted counts.
two sites as being even more sensitive to dif-
ferences in water level.
Our final model thus included site effects
and their interactions with observers, some ef-
fort effects, and some effects of water level; the
hypothesis tests we have described reduced the
number of estimable parameters by 31 without
affecting the overall fit of the model (X 2 = 37.92,
df = 31, P = 0.18). Estimates based on this
model suggested a quite different pattern of
population change than that suggested by un-
adjusted counts. Although relative changes in
population were not consistently higher or low-
er using adjusted counts, they indicated that
population increases were more pronounced
during the mid 1980s compared with the late
1970s as indicated by unadjusted counts (Fig.
3).
DISCUSSION
Our results show several previously unrec-
ognized sources of variation inherent in counts
during the annual Snail Kite survey. Failure to
account for this variation can result in misin-
terpretation of most of the parameters estimat-
ed from the unadjusted counts.
Our results are consistent with previous con-
clusions that the overall population has in-
creased over the 26-year period, reflecting res-
toration of long-hydroperiod marshes in sev-
eral areas previously influenced by drainage
programs (e.g. Sykes 1983). However, the pat-
tern of population change we estimate within
the period is quite different from that shown by
simple total counts. In particular, the large in-
crease in counts from 1978 to 1980 also coin-
cides with a substantial increase in effort. The
use of the unadjusted counts to evaluate year-
to-year change is especially problematic when
the primary observer differed. For example, the
difference in counts between the 1980 and 1981
surveys, although widely interpreted as change
in population size owing to a drought in 1981
(e.g. Beissinger 1986, 1988; Takekawa and Beis-
singer 1989), may also be explained by differ-
ences in detection rates related to effort and ob-
servers. The observer in 1980 was substantially
more experienced, and more effort was ex-
pended on the survey in 1980 than in 1981.
Without accounting for these factors, inferences
about year-to-year changes in these data are
not likely to be reliable.
Observer differences may reflect differences
in experience (Kendall et al. 1996) or inherent
ability attributable to such things as visual acu-
ity (Sauer et al. 1994). They may also reflect dif-
ferences in the way individual observers con-
ducted the surveys. For example, Sykes often
conducted his surveys alone and often over a
period exceeding one month because the dis-
tribution of Snail Kites in Florida was poorly
known at the time he initiated the survey. In
contrast, Rodgers tried to keep the duration of
the survey shorter (about 10 days) and more
consistent among years, and he often used sev-
eral different observers (J. A. Rodgers, Jr. pers.
comm.). Another difference among observers
was that Bennetts had prior knowledge of the
distribution of numerous radio-tagged kites
just prior to conducting his surveys. We believe
that these differences are substantial enough to
require the inclusion of observer effects in an-
alyses of these data. Unfortunately, because
there was no overlap in the periods counted by
distinct observers, it is impossible to test for
differences among observers using a year-ef-
fects model. Such a test requires modeling a
smooth pattern of population change across pe-
riods of observer change. The results of such
tests (which are not reported here) also suggest
that differences among observers exist. The
lack of overlap in periods covered by distinct
observers is a critical deficiency of these data
that limits their usefulness for estimating long-
term trends.
A tendency also existed for each consecutive
observer to include sites not surveyed by the
previous observer. For example, Rodgers in-
cluded three lakes within the Kissimmee wa-
tershed, only one of which had been previously
included by Sykes during one year. Bennetts in-
cluded portions of the Big Cypress National
Preserve, which had not been included by ei-
ther Rodgers or Sykes. Consequently, site ef-
fects were confounded with observer effects.
Under these circumstances, we were able to fit
a model with interactions of observer and site
effects, but not an additive model of these ef-
fects. This feature of the data, along with the
absence of overlap among observers, necessi-
tated our approach of estimating population
change within, but not between, the time pe-
riods corresponding to different observers.
Patterns of population change can be extract-
ed from count data provided that researchers
adequately control for factors that produce ir-
relevant variation in the data. The year effects
that we estimated reflect patterns in counts that
remain after having controlled for sources of
variation known to influence detection. In at-
tributing such patterns to population change,
we assume that we have neither neglected tem-
porally varying factors related to detection nor
inadvertently removed variation related to ac-
tual population change. Often it is not clear
whether these assumptions are legitimate. For
example, although we are fairly confident that
effort affects detection (and hence the count
data) and is unrelated to population size, we
are less confident in our treatment of water lev-
el as a factor that affects only detection.
Our results are consistent with previous
studies indicating that counts are positively
correlated with water levels, although the fitted
year effects were less sensitive to our choice of
whether to include water level effects than
whether to include observer or effort effects. In
our analysis, we treated water level as an effect
on detection. This perspective is based on
knowledge that kites disperse widely during
droughts (Beissinger and Takekawa 1983, Take-
kawa and Beissinger 1989), often to areas not
included in the annual survey (Bennetts and
Kitchens 1997a). Thus, temporary emigration
of birds to these peripheral habitats is an im-
portant component of detection (Bennetts and
Kitchens 1997a, Valentine-Darby et al. 1998). In
contrast, most previous investigators interpret-
ed unadjusted counts (e.g. Sykes 1983; Beissin-
ger 1988, 1995) and have assumed that water
levels affect only population size, thus ignoring
temporary emigration. In reality, water levels
probably affect both detection rates and pop-
ulation size. Bennetts and Kitchens (1997b)
suggested that the response of Snail Kites to
droughts depends on the spatial extent of the
drought. Rainfall patterns across Florida are
quite variable, and small localized droughts
occur at a relatively high frequency (McVicar
and Lin 1984). In contrast, widespread
droughts that encompass the entire range of
Snail Kites in Florida are relatively rare
(MacVicar and Lin 1984, Duever et al. 1994,
Bennetts and Kitchens 1997a). During these
more localized droughts the response of kites
may be largely behavioral: birds simply move
to a different location (Bennetts and Kitchens
1997a, b). However, as droughts become in-
creasingly widespread, both survival and re-
production may decrease as local food resourc-
es and refugia become less available (Sykes
1983, Beissinger 1986, Takekawa and Beissin-
ger 1989). Without a reliable estimate of the de-
tection probability of individuals in the entire
population, it is virtually impossible to distin-
guish temporary emigration from real popu-
lation change during droughts.
We have not included all factors that affect
detection rates. Our analysis includes several
such covariates but does not include other po-
tential influences of detection for which we had
no measure of the covariate. For example,
Rodgers et al. (1988) suggested that transect
counts of more than 10 birds indicated the pres-
ence of an evening roost, which was then used
as a check on the accuracy (and often a replace-
ment) of the transect counts. In areas where the
survey relies on roost counts, failure to locate
all roosts could result in a substantially lower
count of birds. Bennetts and Kitchens (1997a)
used radio telemetry to verify that all of the ra-
dio-tagged birds known to have been in a par-
ticular wetland were in known roosts. They
found that they overlooked at least 64% of the
birds in the area that had used other roosts. In
addition, Darby et al. (1996) found that 57% of
the Snail Kites that they observed either roost-
ed solitarily (20%) or in roosts of fewer than 10
birds (37%). The effect of neglecting to include
these covariates in analyses of population
change depends on the magnitude of the tem-
poral component of their variation.
Some of the difficulties related to identifying
and modeling variability in detection of birds
could be reduced by standardizing the survey
protocol and hence limiting the range of vari-
ation in covariates known to influence detec-
tion. Our analysis suggests that standardiza-
tion of site selection, the amount of effort ex-
pended, survey dates, and search strategies
(transects) would lead to less variation in de-
tection rates. Distance-based sampling (Buck-
land et al. 1993) also may improve estimates
derived from transects for some species, but a
pilot study indicated that the assumptions of
this approach would have been severely violat-
ed (Bennetts and Kitchens 1997a). Although the
use of different observers is inevitable over
time, these changes should not occur concur-
rent with major environmental events (e.g.
droughts). Moreover, whenever possible count
years during which a new observer is present
should overlap so that the new observer's re-
suits can be calibrated against those of the ob-
server being replaced. During the change in ob-
servers that occurred from 1980 to 1981, the
new observer accompanied the previous ob-
server for much of the survey. Although this
step may help reduce the variability between
the two observers, it does not provide indepen-
dent surveys from which an observer effect can
be estimated.
Statistical calibration is also an intuitively
appealing way to improve the reliability of
counts. However, such calibration requires an
independent benchmark for comparison. For an
absolute calibration, this benchmark would be
a known number of animals in the population
(Osborne 1991), although comparative calibra-
tions are possible using multiple counts or in-
dependent estimates of population size (Pol-
lock and Kendall 1987, Rodgers et al. 1995). Ex-
cept in strictly controlled settings, a known
population size is highly unlikely. Multiple
counts and independent estimates of popula-
tion size are possible for Snail Kites but would
require considerable effort and expense. Con-
sequently, methods that estimate detection
probability (e.g. capture-recapture) may be
preferred for estimation of demographic pa-
rameters. These data are considerably more re-
liable than count data (Nichols 1992) and are
obtainable for many species, including Snail
Kites (Bennetts and Kitchens 1997a). For many
species of birds in which no feasible way exists
to obtain reliable estimates of population size
or other demographic parameters, count data
may provide the most reasonable substitute
(Link and Sauer 1998). In such situations, sur-
veys should be standardized as much as pos-
sible, should incorporate explicit tests for
sources of variation in detection, and then
should account for such variation.
ACKNOWLEDGMENTS
James A. Rodgers, Jr. generously provided us with
unpublished data on effort from his Snail Kite sur-
veys. We appreciate the helpful comments of Jona-
than Bart, Brian Collins, Kathy Martin, B. Riley
McClelland, James A. Rodgers, Jr., Graham W. Smith,
and Len Thomas. Financial support for REB was pro-
vided by the National Park Service, the U.S. Fish and
Wildlife Service, the U.S. Army Corps of Engineers,
the U.S.G.S. Biological Resources Division, South
Florida Water Management District, and St. Johns
River Water Management District through the Flor-
ida Cooperative Fish and Wildlife Research Unit co-
operative agreement 14-16-0007-1544, RWO90. This
is contribution number R-06364 of the Florida Agri-
cultural Experiment Station Journal Series, Institute
of Food and Agricultural Sciences, University of
Florida.
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