In the wake of Rachel Carson's 1962 book Silent Spring suspicions emerged that DDT, which came into agricultural use in the US in 1945 and was eventually banned in 1972, contributed to eggshell thinning and a collapse in the populations of some birds of prey. This is a look at the population trajectories of a few of these birds. All data here come from the Audubon Society's annual Christmas Bird Count (CBC). We'll go back to the mid 1940's; before then the CBC data are erratic, sometimes counting 0 occurrences of a species for decades.

Note that it makes no sense to study raw CBC counts. The number of observers has trended higher over the years, which alone should yield increasing counts. They observe in groups, and the group sizes fluctuate. Weather affects counting as well. And the skill of different observers is variable. Not surprisingly then, a naive glance at the data reveals fluctuations, but a marked population growth trend for nearly every species:

A simple antidote for these problems is to normalize counts of a species by dividing by the counts for another species; this produces a measure of the relative population trajectory of two species. For example, by normalizing the counts of peregrine falcons by the counts of blue jays, we get a picture of how peregrine falcons have fared relative to a species whose numbers are ostensibly unaffected by known environmental factors. To help visualize the results, here's a bilinear regression on the log of this population ratio. (A bilinear regression consists of minimizing non-linear least squares of a model consisting of two straight line segments.)

This model pinpoints the bottom of a peregrine falcon decline to 1971. Here are the analogous results for four other species popularly linked to significant population declines:

It's widely believed that osprey populations collapsed because of DDT (see, for example, this summary or this paper), so it's worth noting that neither the model nor the underlying data points above validate such a conclusion. Regardless of whether populations collapsed or not, the analysis here supports the consensus view that osprey populations (as well as the populations of the other birds above) have soared since the 1970s.

The technique here is *descriptive* so the lines above should be considered only as visual aids. It is inappropriate to ascribe a causal relationship between DDT and bird populations from this study alone. Moreover there is nothing authoritative about the particular lines the bilinear modeling selected; note for example that the actual low population points occur later than the modeled turning point for bald eagles, brown pelicans, and Cooper's hawks; for all three species the low occurs in the decade from 1970 to 1980.

Do the results above depend on the choice of normalizing species? Certainly. Although the shapes of the trajectories are similar, turning points selected by the bilinear model can vary by several years. A precaution against using an anomalous species for the normalization divisor is a cointegration test. It turns out, for example, that hairy woodpeckers, blue jays, spotted sandpipers, northern cardinals, and northern mockingbirds all cointegrate pairwise. This means that for any pair of them, some linear combination of their population trajectories does not drift over time, so one can expect similar results using any of them as normalizing species. As an aside, the Carolina wren and common loon cointegrate with one another, but **not** with the aforementioned species. You can see these relationships visually here:

Note the hockey stick shape of all the cointegrating species, with the exception of the Carolina wren ("carwre") and common loon ("comloo"), whose trajectories do not markedly flatten at the end.

Finally, here are plots of the peregrine falcon population pattern in each of 24 states, using the nationwide count of northern cardinals as the normalizing species. The dashed lines are the same in each plot -- they portray the nationwide pattern -- so you can compare each state's trajectory with the national trajectory. (The turning point for the national population normalized by cardinals is about a year later than by blue jays, making 1972 the bottom year.)