FACTORS INFLUENCING COUNTS IN AN ANNUAL SURVEY OF SNAIL KITES IN FLORIDA

--Snail Kites (Rostrhamus ociabilis) 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 amodel 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 uch as capture-recapture. Received 29 April 1997, accepted 24 July 1998. COUNT DATA have been widely used to monitor changes in bird populations (Barker and Sauer 1992, Johnson 1995). Counts are observation-based surveys in which an observer records some unknown portion of the birds actually present at a site. A complete census of a bird population is seldom feasible (Lancia et al. 1994), and alternative approaches (e.g. capturerecapture) often are too expensive or are logistically impractical (Link and Sauer 1997, 1998). However, count-based inferences about changes 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 (Burnham 1981, Nichols 1992, Johnson 1995, Link

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 variation 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 analyses 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).
Here Sites at which the annual survey was conducted have been •escribed by Sykes (1984), Rodgers et al. (1988), and Bennetts and Kitchens (1997a).The surveyed area of these sites ranged in size from approximately 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 distribution of kites became better known, and/or changed over time, the wetlands included in the survey changed accordingly.Thus, sites tended to be added over time, which generally corresponded with changes in observers.However, there was also considerable 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 accounted for a small percentage (f = 1.7%) of the total num- 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 surveys.We then used the number of standard deviations 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- 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 acuity (Sauer et al. 1994).They may also reflect differences in the way individual observers conducted the surveys.For example, Sykes often conducted his surveys alone and often over a period exceeding one month because the distribution 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 several 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 analyses 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-effects model.Such a test requires modeling a smooth pattern of population change across periods 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-

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FIG. 1. Central and southern Florida showingwetland sites surveyed for Snail Kites and included in our analysis.
ber of birds counted.Modeling population change.--Acommon and frequently reasonable assumption for analyses of count data is that counts have Poisson distributions.The family of overdispersed Poisson distributions was [Auk, detection rates; thus, the models we used included parameters describing site and observer 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 represented 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 overlap.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 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 observer days to the nearest 0.25 days (assuming a 12h day) that we could reasonably determine from the original records of each observer.Each principal ob-server had from one to eight observers assisting, particularly during simultaneous counts at multiple roosts.We modeled the effect of effort as proportional to exp(-c/•o) for some c > 0; thus, 1/•o was treated as an additive variable in the loglinear model.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 function of effort for high levels of effort, leading to a finite asymptote (i.e. more effort leads to proportionately 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 interaction 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 included 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 Management District, U.S. Army Corps of Engineers, U.S. Geological Survey, and the city of West Palm Beach.

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FIG. 2. Total number of Snail Kites counted dur-ing each annual survey by each observer from 1969 through 1994, plotted with amount of effort expended in each survey year.Line denotes effort as measured by the total number of observer days for a given year.
not an additive model of these effects.This feature of the data, along with the absence of overlap among observers, necessitated our approach of estimating population change within, but not between, the time periods corresponding to different observers.Patterns of population change can be extracted from count data provided that researchers adequately control for factors that produce irrelevant 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 attributing such patterns to population change, we assume that we have neither neglected temporally varying factors related to detection nor inadvertently removed variation related to actual 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 level 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, Takekawa 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 important component of detection (Bennetts and Kitchens 1997a, Valentine-Darby et al. 1998).In contrast, most previous investigators interpreted unadjusted counts (e.g.Sykes 1983; Beissin-the response of kites may be largely behavioral: birds simply move to a different location (Bennetts and Kitchens 1997a, b).However, as droughts become increasingly widespread, both survival and reproduction may decrease as local food resources and refugia become less available (Sykes 1983, Beissinger 1986, Takekawa and Beissinger 1989).Without a reliable estimate of the detection probability of individuals in the entire population, it is virtually impossible to distinguish temporary emigration from real population change during droughts.We have not included all factors that affect detection rates.Our analysis includes several such covariates but does not include other potential 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 presence of an evening roost, which was then used as a check on the accuracy (and often a replacement) 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 radio-tagged birds known to have been in a particular 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 roosted 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 temporal 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 variation in covariates known to influence detection.Our analysis suggests that standardization of site selection, the amount of effort expended, survey dates, and search strategies (transects) would lead to less variation in detection rates.Distance-based sampling (Buckland 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 violated (Bennetts and Kitchens 1997a).Although the use of different observers is inevitable over time, these changes should not occur concurrent 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 resuits can be calibrated against those of the observer being replaced.During the change in obdata are considerably more reliable 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 [Auk,