1. Trend detection- birds Marian Scott Dept of Statistics, University of Glasgow Glasgow, Sept 2007

2. Native wintering waders- another approach What is the trend in the numbers of birds?

3. The data

4. some other species

5. Step 1 Exploring the data Normally, if comparison across the species was of interest, it would be best to plot each species data on the same scale. However, the data for the Black Tailed Godwit, the Sanderling and the Grey Plover is quite different to the rest. Therefore these three should be plotted separately. This means that extra care must be taken when drawing conclusions from data on different scales.

6. what do they show? some variation, some extremely high values (outliers?) but also some evidence of increasing numbers over the time period. All seem to show an increase in percentages over the period, with the Godwit rising to around 5000% of its 1974 numbers by 1994. The sudden peak in the Sanderling data could even suggest that the 1983 value has been entered incorrectly. The plots seem to display a significant upward trend though, even when spike in the Sanderling plot is disregarded. However, we also need to ask if a non-linear trend may be more suitable given the non-monotonic nature of the increases.

7. Simple linear trends

8. from the linear trends The high points (outliers?) have some influence on the fitted lines, so we also need to question how robust the analysis is. For some species it seems that they could be better explained by a non-linear fit. eight of the eleven species have exhibited some sort of an upward trend relative to the 1974 baseline, the most pronounced of which seems to be in the Black Tailed Godwit. Only the Bar Tailed Godwit, the Redshank and the Dunlin have seen falling numbers since 1974,

9. Non-linear trends The models fit in the earlier section assume monotonicity, (i.e. always increasing or always decreasing) and some of the plots show a more complex structure. A loess curve has been fitted to each species and included on the plots. The loess curve is useful as an exploratory tool, since it smooths out some of the roughness.

10. non-linear trends

11. results The LOESS plots tracks the data more closely, but show more complex patterns, including periods of increase and decrease for many of the species, which would argue that the simple monotonic trends do not capture the full story. Is it important to know that the rate of increase from 1974 to 2004 is not described by a simple linear trend?