Annual indices of abundance are estimated as residuals from the route-regressions. Using the regional trend estimate and a regional average count, a line can be drawn that depicts the predicted trend in counts over time. We define annual indices as deviations from this regional predicted trend. These annual indices can be thought of as residual variation remaining after trend is modeled. For each route in the region, we estimate observer effects on each route using the regression described above, but with the slope parameter fixed as the regional estimate.
Residuals are calculated for each year the route was run. Residuals from all routes are averaged by year, and the yearly averages are then added to the yearly counts from the predicted trend line. Resulting estimates of annual indices are then exponentiated to produce the yearly annual indices on the linear scale. This procedure produces both a smooth trend line and a yearly index of abundance. The indexes are smoothed using a procedure such as LOESS to allow observation of patterns in the data. For more discussion of the method, see Sauer and Geissler (1990).
Sauer, J. R., and P. H. Geissler. 1990. Annual indices from
route regression analyses. Pages 58-62 in J. R. Sauer
and S. Droege, eds. Survey designs and statistical
methods for the estimation of avian population trends.
U. S. Fish. Wildl. Serv., Biol. Rept. 90(1).