Details: Trend Estimation


We estimated population trends for 3 time periods: the entire survey interval (1966 - 1994), an early period (1966 - 1979), and a recent period (1980 - 1994). For all periods, we provide the estimated population trend (in %/year), a measure of its statistical significance (*: P < 0.10, **: P < 0.05, ***: P < 0.01), and the number of routes on which trends were estimated. For the entire survey interval results, we also present the 95 % confidence interval of the trend estimate, and the weighted regional abundance of the species (average birds/route).

These results are presented for regions with < 14 samples. Regions include States and Provinces, physiographic strata (indexed by number, e.g. S05 is the Mississippi Alluvial Valley), BBS regions (Eastern, Central, and Western), Fish and Wildlife Service Administrative Regions (RE1-RE6), The United States, Canada, and the Entire survey region (1CO).

The Route-regression method

Trends are estimated using the route-regression method. In this analysis, we estimate population trends and annual indices using the methods described by Geissler and Sauer (1990). In this analysis, trend (or a consistent change in counts of birds on a route) is the quantity that is estimated, and annual indices of abundance are used to assess higher levels of pattern in the data in the context of the trend.

Regional trends are estimated as a weighted average of trends on individual routes. Route trends are estimated using the estimating equations estimator described by Link and Sauer (1994), in which a multiplicative trend is estimated. As in earlier analyses, observer effects are incorporated in the model to prevent bias associated with increases in observer quality over time (Sauer et al. 1994). See Link and Sauer (1994) for a detailed discussion of the advantages of the estimating equations estimator over the linear regression-based estimates used in earlier analyses.

Regional trends are found as weighted averages of route trends. Regardless of variability in the counts on the route, missing counts (from years when the route was not surveyed) and observer changes (that modify the quality of the data) both tend to make route data less reliable. Consequently, it is necessary to weight the route trends by a measure of the consistency of counting on the route. We do this by weighting the route trends with the inverse of the part of the variance of the slope estimate associated with these factors (which is the appropriate element of the (X'X)-1 matrix). This variance weight is proportional to number of years run and number of observer changes, but because it does not contain the MSE of the count data it provides no information on variation in counts. We also weight route trend estimates by mean route counts (Geissler and Sauer 1990) and by areas of the physiographic strata within states. Combination of entire strata is not conducted because of geographic variation in sampling intensity within the strata. Bootstrapping is used to estimate variances of trends. See Geissler and Sauer (1990) for details of the route-regression trend estimation procedure.

Data Selection Criteria

We caution all users of BBS trend and annual index results that there exist species, regions, and time periods for which trends should not be estimated. In this analysis, we only used data from observers that we felt provided consistent results. Although any standards tend to be arbitrary, we feel that the results may not be reliable when the number of samples in the analysis is less than 14. A positive bias in the trend may occur with small samples and low counts, and the variances are imprecise. Of course, if the trend is unreliable the indices must also be unreliable, as they are conditional on the trends. We also note that, although we do our best to assure the quality of the results, no data analysis is ever error free. Users of these data are therefore cautioned to carefully inspect the results for consistency. If errors are found, please inform us.

Finally, these trend results were produced by NBS researchers and managers. While the data are clearly public domain, results of analyses must be considered a research product of the analyst. Any publications based on our analyses should acknowledge that they are collaborative efforts. And, if the paper is based primarily on the results of unpublished NBS trend analysis, we suggest that you involve us with the writing and review of the manuscript.

Literature Cited

Geissler, P. H. and J. R. Sauer. 1990.  Topics in route-regression
     analysis. Pages 54-57 in J. R. Sauer and S. Droege, editors.
     Survey Designs and Statistical Methods for the estimation of
     Avian Population Trends.  U. S. Fish and Wildlife Service,   
     Biological Report 90(1).

Link, W. A., and J. R. Sauer.  1994.  Estimating equations
     estimates of trend.  Bird Populations 2:23-32.

Sauer, J. R., B. G. Peterjohn, and Link, W. A.  1994.  Observer
     differences in the North American Breeding Bird Survey.  Auk