Details: Relative Abundance Maps

Many investigators have used bird survey data to develop contour maps of bird abundance based on mean counts on survey routes. Root (1988) provided a grid of smoothed relative abundances for species observed on Christmas Bird Counts. Sauer and Droege (1989) mapped relative abundances of Eastern Bluebirds (Sialia sialis) just after severe winters in the mid 1970's and after their populations returned to pre-winter levels. We have also used relative abundance maps to document the ranges of several species (e.g., Droege and Sauer 1990). See Sauer et al. (In Press a, b, and c) for applications and discussions regarding mapping of survey data.

Preparation of Maps from BBS Data

We developed a map of starting locations of BBS routes. Latitude and longitude (degree-minute) of the starting locations were taken from topographic maps of the route path. Of course, the route is 24.5 miles in length, hence any point used to characterize the route is arbitrary.

We estimated average counts from the interval 1966 -1994 (old maps) or 1982 - 1996 (new version of maps) on each route for each species, and copied them into database files. We developed contour maps of bird relative abundances, using the route relative abundances as input to smoothing procedures (Isaaks and Srivastava 1989, Cressie 1992).

We used inverse distancing (Isaaks and Srivastava 1989) to prepare a smooth of the data. This procedure estimates the abundance at a location as a distance-weighted average of counts from nearby survey routes. We used inverse distancing to estimate abundances for a grid of points overlaid on the survey area, then used Arc/Info to make a contour map from the estimated abundances (Environmental Systems Research Institute 1991). See below for more datails of the analysis.

Arc/Info provided an arc coverage of contours that connect points having the same value. Depending on the maximum relative abundance of the species, we used levels of 1, 3, 10, 30, and 100 for contours. The maps end at a minimum level of 0.1, which was chosen as a possible edge-of-range index after some comparisons of contours with known edges of ranges (S. Droege and D. Bystrak, Personal Communication), and the larger cutpoints were chosen as a series of powers of 3, rounded up for ease of presentation.

The maps presented here are quite similar to the maps in the those of earlier versions of the Home Page, but several differences exist between the procedures used to prepare the earlier maps and these maps. To make the 1966 - 1992 maps, we used Kriging, a procedure in which a variogram is estimated for the species and is used to define the distance-covariance relationship for the smooth (Cressie 1992). In theory, the Kriging should provide a more accurate surface than a procedure such as inverse distancing, which never uses information from the data to adjust the weighting. However, in our experience the variograms were not particularly informative, suggesting that at the scale of the BBS there is little advantage in using Kriging.

We acknowledge, however, that the maps provided here are designed to provide a large-scale summary of the data, and if a species is of particular interest, a more intensive analysis should be conducted using Kriging or some other smoothing procedure. Kriging is a model-based estimation procedure, and if the model is appropriate for the data we can put confidence intervals on the resulting surface. By developing a semivariogram model that more accurately portrays the spatial covariance among routes, the resulting Kriged surface will better reflect the patterns of change among the routes. Often features such as directionality of the semivariogram and trend in the data will require the use of more complex models. See Isaaks and Srivastava (1989) for a useful discussion of the technical details of fitting semivariograms to data, and Cressie (1991) for a more technical discussion of all aspects of spatial modelling.

Technical Details of 1982-1996 Maps

These are based on 82-96 averages of counts on routes. If a route was not counted in that interval, but had data from earlier years, the 66 - 96 average was used as the index to relative abundance. This allowed for the largest possible sample of routes.

Smoothing was conducted by inverse distancing. A systematic grid of points was placed over the map area, and abundances of each species was predicted for each point on the grid as a distance-weighted average of data from adjacent survey routes. The starting point of the route was used as the index to the route location. In this averaging, an initial radius of 100Km was considered. If more than 5 routes occurred within that radius, and the species did not occur on those routes, then the route was given a zero abundance estimate. If the species did occur within the 100Km radius, but there were fewer than 5 routes in the area, a larger search radius was selected (350Km) to allow a larger sample size for the averaging. However, only the closest 15 routes were used in the inverse-distanced average.

This procedure was adaptive, in that it minimized the problems of overestimating the edges of ranges, and it allowed for regional differences in sample intensity by extending the search radius where necessary.

Literature Cited

Cressie, N.  1992.  Statistics for spatial data.
     Wiley, New York. 900pp.

Droege, S., and J. R. Sauer.  1990. Northern bobwhite, Gray
     partridge, and ring-necked pheasant population trends
     (1966-1988) from the North American Breeding Bird Survey.
     Pages 2-20 in K. E. Church, R. E. Warner, and S. J. Brady, 
     eds. Perdix V: Gray partridge and ring-necked pheasant
     workshop, Kans. Dept. Wildl. and Parks, Emporia. 

Environmental Systems Research Institute.  1991.  Surface Modeling
      with TIN. Environmental Systems Research
     Institute, Inc., Redlands, CA.  

Isaaks, E. H., and R. M. Srivastava.  1989. An introduction to 
     applied geostatistics. Oxford University Press, New York.

Root, T.  1988.  Atlas of wintering North American birds. 
     University of Chicago Press, Chicago, Il.

Sauer, J. R., and S. Droege.  1990.  Recent population trends
     of the eastern bluebird.  Wilson Bull 102:239-252.

Sauer, J. R., S. Orsillo, and B. G. Peterjohn.  Using GIS to
     model bird distributions from the North American Breeding
     Bird Survey. Proc IV U. S. Fish and Wildlife Service GIS
     Workshop, In Press a.

Sauer, J. R., S. Orsillo, and B. G. Peterjohn.  Geographic 
     patterns in relative abundances and population trends 
     of breeding and wintering Loggerhead Shrikes in North
     America. Proc. Int. Shrike Symp. In Press b. 

Sauer, J. R., G. W. Pendleton, and S. Orsillo.  Mapping of bird 
     distributions from point count surveys.  Proc. Point Count 
     Workshop, In Press c.