Every year, the Journey North Project tracks sightings of the first Monarch butterflies (Danaus plexippus) of spring, and produces maps like this one.

The legend shows the first sightings in given two-week periods, but uses overlaid dots, which become a little confusing. The choice of colors is not the best; I had to get very close to my monitor to tell early and late May apart. It could do with some improvement, and Leland Wilkinson in The Grammar of Graphics produces a far superior version, though for an earlier year.

Could this be further improved? Wilkinson uses the “Scientist’s Rainbow” in his legend. But since the data are associated with increasing spring temperatures, and the lines are in a definite order, a legend using increasingly warm colors (different saturations of orange, for example) would work better; the original graph does this to some extent. Wilkinson uses colder colors as summer arrives, which seems counter-intuitive. The lines could easily be labelled directly, since the legend is sitting right beside them. Since most of the sightings are Eastern, half the map is blank and could be cropped.

Instead of ranges, I used a date for the advancing front. Wilkinson’s lines are nonparametrically smoothed contours through the concentration of points in each date range, rather than across the leading edge, because of “random error in the dataset”. The effect is to retard the contour, and it implies that all the points in advance of it are mistakes. Remember, these points are not a population sample from which we’re discerning a mean value, but the edge of a range.

This raises a bigger issue: what’s the purpose of this graphic, anyway? If the goal is to answer the question “When will the Monarchs appear in my state?” then averaging the lines for several successive years would be best—instead of two-week ranges, a less precise time interval would be better like “early April” and “late April”. The data are all online, and the graph is left as an exercise for the reader. Think how useful such a graph will be to our grandchildren, when they’re jaded from seeing Monarchs flitting around in February.

There was a very good article in the October 3rd New York Times science section on Monarch migration. They use a color palette similar to one I suggested above (though these butterflies are heading south), and dots for sightings like the Journey North project. The dotted line is not the wave front of butterflies, as you might think, but a 60°F isotherm—Monarchs can’t fly when the temperature drops below 55°F. The isotherm is labeled a little way offscreen, and I missed the label on my first reading of the map, so that would be my only criticism.

References. The Journey North Project archives can be found at at Annenberg/CPB Learner Online (www.learner.org). Wilkinson’s thorough and analytical book The Grammar of Graphics (Springer, 1999) is also worth a look if you’re interested in programming graph-generating applications.