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

Bruce M. Bowman

June 1, 2005 (old)

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 11 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 (25 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 2005 I made 66 spring migration birding trips to Magee Marsh. Fifty-six were in May; ten were in April. After tabulating number of birds recorded for each date for all trips, I calculated five-day moving averages for all dates in May and the last half of April. Note that these are five-DAY moving averages, not five-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 four years contributing to some dates (May 8, May 15, and May 16--e.g., May 15 in 1999, 2002, 2003, and 2004). [There is, of course, a SINGLE species count for each particular birding day--e.g., May 24, 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 below. Calculation of five-day moving averages is described 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 66 data points, while representing a lot of birding, are insufficient for simple date-by-date averages over a month and a half (in several years) 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 11 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 five-day moving averages are more reasonable for processing my data than three- day moving averages, but I believe them to be more realistic because they illustrate better my expectation of relatively small local waves (three or so?) superimposed on the overall primary migration waveform. Both sets of results are shown in the table. I will comment on only the results for five-day smoothing. The three-day results are not fundamentally different in nature.

The five-day moving average shows three local peaks. These are indicated in the table by "P" notations. Related local valleys are indicated by "(-m/-n)", where m and n are depths of the valley relative to adjacent local peaks. Asterisks (*) indicate numbers that are uncertain because of sparseness of data and/or end effects from the smoothing procedure.

The level, overall peak of 61-62 (five-day average) is at April 29 to May 10--in approximation, the first week of May. The center of the plateau is at May 5. More broadly, near-peak numbers of 58 to 62 occur over the 19-day period April 28 to May 16. The most significant secondary peak is at May 16, but day-by-day average species counts decline more or less uniformly after May 10. 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 accompanying graphical data than in the tabular data.

A similar but later plateau has been found in an analysis for warblers count alone, viz., a five-day moving average of 17-18 species from May 11 to May 17. Therefore, to maximize both total species count and warblers count, the optimal time to bird at Magee Marsh Wildlife Area is May 10-11.

Actual peaks from my database are listed after the table.

# of species # of species 5-day moving avg 3-day moving avg (not used) April 27 47 50 28 58 58 29 62 65 P 30 61 64 May 1 61 63 2 61 57 (-8/-7) 3 61 60 4 61 62 5 61 P (center of 63 6 61 61-62 plateau) 64 P 7 62 58 (-6/-5) 8 62 61 9 61 63 P 10 61 62 11 59 61 12 59 53 (-10/-8) 13 57 (-5/-4) 57 14 58 57 15 59 60 16 61 P 60 17 57 61 P 18 55 56 19 55 34 (-27/-23) 20 49 (-12/-6) 48 21 51 53 22 54 57 P 23 55 P 53 24 53 53 25 48 49 26 46 41 27 44* 44 28 42* 43* 29 - - 30 - - 31 - - Actual highs were 81 on 4-30-2004 (5-day moving average=61) 79 on 5-05-2002 (average=71, 5-day moving average=61) 79 on 5-10-2005 (average=68, 5-day moving average=61) 72 on 5-14-2005 (average=64, 5-day moving average=58) 72 on 5-15-2002 (average=58, 5-day moving average=59) 70 on 5-02-2003 (average=62, 5-day moving average=61) 70 on 5-10-2003 (average=68, 5-day moving average=61) The five-day moving average data are plotted in the graphs below. April May 5 10 15 20 25 30 5 10 15 20 25 30 |----|----|----|----|----|----|----|----|----|----|----|----|----| 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 Five-day moving average species count data for birding at Magee Marsh Wildlife Area
Definition - The "five-day moving average" count for a particular day is calculated as the average of all data points from that day, the two days before, and the two days after. The actual field data for each day are replaced by the five-day moving average value. The effect is to smooth the data. Three-day moving average data are calculated similarly by using the data points for a particular day plus the day before and the day 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 - five-day moving average for May 4

       May 2, 2001:  61
       May 2, 2003:  70
       May 2, 2005:  56
       May 3, 2001:  44
       May 4, 2002:  62
       May 4, 2003:  67
       May 4, 2005:  58
       May 5, 2002:  79
       May 5, 2004:  63
       May 6, 2000:  45
       May 6, 2005:  69

  Five-day moving average for May 4

    [(61+70+56) + 44 + (62+67+58) + (79+63) + (45+69)] / 11 
                                                     = 61.3 = 61

    The value 61 (smoothed data) is used instead of the 
    average value for May 4 (which would be (62+67+58)/3 = 62).

Bruce M. Bowman
Ann Arbor, Michigan

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