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. LITERATURE CITED BARKER, R. J., AND J. R. SAUER. 1992. Modelling pop- ulation change from time series data. Pages 182- 193 in Wildlife 2001: Populations (D. R. Mc- Cullough and R. H. Barrett, Eds.). Elsevier Ap- plied Science, New York. BEISSINGER, S. R. 1986. Demography, environmental uncertainty, and the evolution of mate desertion in the Snail Kite. Ecology 67:1445-1459. BEISS1NGER, S. g. 1988. The Snail Kite. 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