Eastern Ecological Science Center (formerly Patuxent Wildlife Research Center) (EESC)    Migratory Bird Research (MBR)    Comments/FAQ(comments)

# Details: Trend Estimation

## Introduction

We estimated population trends for the entire survey interval for which we had data (1959 - 1988), For the interval, 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 circles on which trends were estimated. We also present the 95 % confidence interval of the trend estimate, and the weighted regional abundance of the species (average birds/100 party hours).

Regions include States and Provinces and the Entire survey region (SUR).

### 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 circle) 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 circles. Circle trends are estimated from linear regression of the natural logarithm of effort-adjusted counts (plus 0.5 to accommodate 0 counts) on year of survey. The slope estimate for year, when transformed back to the multiplicative scale, provides the trend estimate for the circle.

Regional trends are found as weighted averages of circle trends. Regardless of variability in the counts on the circle, missing counts (from years when the circle was not surveyed) tend to make circle data less reliable. Consequently, it is necessary to weight the circle trends by a measure of the consistency of counting on the circle. We do this by weighting the circle 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, but because it does not contain the MSE of the count data it provides no information on variation in counts. We also weight circle trend estimates by mean circle 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.

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 are preliminary, and should not be published until they have received proper peer review. 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).

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