Waveform in Spring Migration Statistics
for Magee Marsh Wildlife Area (NW Ohio)
("Crane Creek State Park")

Bruce M. Bowman

June 1, 2009


I have always supposed that the statistical peak in spring migration in the southeast Michigan area was around May 10-14, but it was never more than an assumption. In part to test this assumption I have done an analysis of 15 years' worth of data in my birding database. I am defining "peak" on the basis of number of species, not number of individuals. For an analysis of this sort all data need to be for a particular, defined birding region or location. I have a large amount of data for Magee Marsh Wildlife Area (20 miles east of Toledo; with, and sometimes called, Crane Creek State Park), so I used that rather than data for, say, Nichols Arboretum (Ann Arbor), for this analysis. It can be expected that spring migration dates for southeast lower Michigan will lag dates for Magee Marsh (northwest Ohio) by a couple of days.


One reason for using Magee Marsh data is that Magee Marsh has sufficiently varied habitat that passerines, waterfowl, wading birds, shorebirds, and others are all represented. I used only Magee Marsh data for this analysis; i.e., I did not include additional species found at Ottawa National Wildlife Refuge, Metzger Marsh, Maumee Bay State Park, and other places that I regularly visit along with Magee Marsh Wildlife Area on my trips to Ohio. All data were collected in morning birding (7:45am and after) with continuation into the afternoon on most days. On most days I was with one to three other birders. I have included in the data all species that the group found, not just my own birds. Needless to say, I was never birding when it was pouring rain, but I never let light rain or cold weather stop me. That is, the data are not particularly constrained by weather conditions except that it is undoubtedly true that fewer of the birds present are found when the weather is bad. Predicted fallouts had little bearing on whether or not I was birding on any particular day. That said, there is a greater density of data for the first two and a half weeks of May than for any other period.

From 1995 through May 2009 I made 123 spring migration birding trips to Magee Marsh. Ninety-six were in May; twenty-seven were in April. After tabulating number of birds recorded for each date for all trips, I calculated three-day moving averages for all dates in May and the last half of April. Note that these are three-DAY moving averages, not three-POINT moving averages. Multiple data points for particular calendar dates were used if available, and all data points were given full and equal weight. There were, for example, as many as six years contributing to one date; e.g., May 16--1999, 2002, 2004, 2005, 2006, and 2008). [There is, of course, a SINGLE species count for each particular birding day--e.g., May 16, 2004. If at some time in the future I supplement my data with data from other birders, there would still be a single value used for any particular birding day; I would probably use the largest of available values rather than an average.] The results are shown in a table and a graph in the Appendix. Calculation of three-day moving averages is described there in a footnote.

[I have done a similar analysis for warbler species count instead of total species count. Another analysis has determined first arrival and last departure dates for 36 warbler species found in April and May in the Magee Marsh region (not limited to Magee Marsh Wildlife Area).]

Smoothing, done here by calculating moving averages, was deemed necessary because 123 data points, while representing a lot of birding, are insufficient for simple date-by-date averages over a month and a half to have great meaning. I.e., the plotted data show unrealistic amplitudes and numbers of peaks and valleys. If I had 40 years' worth of data, smoothing might not be needed at all--but the long-term decline in some species and effects of changes in climate would complicate the analysis. It is certain, in fact, that these factors affect even my 15 years' worth of data to some unknown degree.

I calculated both three-day and five-day moving averages. I cannot argue on any theoretical basis that one or the other is more reasonable for processing my data. However, while in analyses done prior to 2007 I used the five-day moving averages, I believe that I now have sufficient data that adequate smoothing is done with the three-day method and that processing with the five-day method may now oversmooth the data. Only three-day smoothed results are shown in Table 1, and I will comment on only the results for three-day smoothing. The five-day results are not fundamentally different in nature.


The three-day moving average shows four local peaks and three deep valleys. The peaks are indicated in the Table 1 by "P" notations. Related local valleys are indicated by "V (-m/-n)", where m and n are depths of the valley relative to adjacent local peaks.

The primary, overall peak of 67 species (three-day average) is at May 9 and May 10. Immediately before and after that central peak are valleys of significant depth--10 species. These are at May 7 and May 12. The May 7 valley follows an initial local peak of 63 species at May 1; the May 12 valley precedes a clearly identified, 64-species secondary peak at May 17. After the May 17 peak there is a day-by-day average species count decline that is more or less uniform through the end of the month except for a 13-species-deep valley at May 19 and another secondary peak at May 22. The fastest rise in number of species occurs over the last week of April. These characteristics of the data are perhaps seen more easily in the graphical data of Figure 1 than in the tabular data.


Thus, the waveform for total species count can be characterized as one with three primary peaks. The central and highest peak is short in duration--67 species--for May 9 and 10. Significant 10-species valleys separate the central peak from secondary peaks of about 63 species a week earlier and a week later. A significant late-May valley (May 19) is followed by another local peak at 58 species on May 22. An analysis for warblers count alone shows a waveform with a single peak preceded by and followed by nearly monotonic rise and fall. The long, one-week central plateau (peak) of about 19 warbler species per day extends from May 10 to 17.

To maximize both total species count and warbler count, the optimal time to bird at Magee Marsh Wildlife Area is May 9-11. May 17 stands out as a date nearly as good.


Actual peaks from my database are listed at the bottom of Table 1.

TABLE 1 # of species 3-day moving avg April 15 49 16 50 17 47 18 48 19 46 20 47 21 46 22 46 23 47 24 45 V (-5/-18) 25 45 26 50 27 54 28 58 29 58 30 60 May 1 63 P 2 61 3 61 4 62 5 61 6 59 7 57 V (-6/-10) 8 60 9 67 10 67 P 11 65 12 57 V (-10/-7) 13 60 14 59 15 60 16 63 17 64 P 18 62 19 51 V (-13,-7) 20 52 21 57 22 58 P 23 56 (beginning of linear decline) 24 55 25 53 26 48 27 49 28 47 29 47 30 41 31 40 (end of linear decline) Actual highs were 84 on 5-10-2006 (average=74, 3-day moving average=67) 82 on 5-10-2007 (average=74, 3-day moving average=67) 81 on 4-30-2004 (average=69, 3-day moving average=60) 80 on 5-13-2009 (average=56, 3-day moving average=60) 79 on 5-10-2005 (average=74, 3-day moving average=67) 79 on 5-05-2002 (average=71, 3-day moving average=61) 77 on 5-22-2007 (average=57, 3-day moving average=58) 75 on 5-10-2009 (average=74, 3-day moving average=67) 75 on 5-09-2008 (average=69, 3-day moving average=67) 74 on 5-17-2006 (average=68, 3-day moving average=64) 72 on 5-17-2007 (average=68, 3-day moving average=64) 72 on 5-14-2005 (average=62, 3-day moving average=59) 72 on 5-15-2002 (average=59, 3-day moving average=60) 72 on 5-03-2008 (average=58, 3-day moving average=61) The three-day moving average data are plotted in Figure 1. FIGURE 1 April May 5 10 15 20 25 30 5 10 15 20 25 30 |----|----|----|----|----|----|----|----|----|----|----|----|----| 67 ** 66 65 * 64 * 63 * * 62 * * 61 ** * 60 * * * * 59 * * 58 ** * 57 * * * 56 * 55 * 54 * 53 * 52 * 51 * 50 ************** * * 49 * * 48 * * 47 * * * ** 46 * ** 45 ** 44 43 42 41 * 40 *** |----|----|----|----|----|----|----|----|----|----|----|----|----| 5 10 15 20 25 30 5 10 15 20 25 30 April May Three-day moving average species count data for birding at Magee Marsh Wildlife Area
Definition - The "three-day moving average" count for a particular day is calculated as the average of all data points from that day, the day before, and the day after. The actual field data for each day are replaced by the three-day moving average value. The effect is to smooth the data. Five-day moving average data are calculated similarly by using the data points for a particular day plus the two days before and the two days after. For any year there is a single data point for any birding day. Data points for all years for which data are available are used.

Example calculation - three-day moving average for May 4

       May 3, 2001:  44
       May 3, 2008:  72
       May 4, 2002:  62
       May 4, 2003:  67
       May 4, 2005:  58
       May 4, 2006:  58
       May 4, 2007:  57
       May 5, 2002:  79
       May 5, 2004:  63

  Three-day moving average for May 4

  [ (44+72) + (62+67+58+58+57) + (79+63) ] / 9 = 62.2 = 62

    The value 62 (smoothed data) is used instead of the
    average value for May 4 (which would be (62+67+58+58+57)/5 = 60).

Bruce M. Bowman
Ann Arbor, Michigan

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