I have done an analysis of 11 years' worth of data in my birding database to determine the statistical peak of warblers in spring migration in the southeast Michigan area. I am defining "peak" on the basis of number of warbler 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 migration dates for southeast Michigan will lag dates for Magee Marsh (northwest Ohio) by a day or two.

[I have done a similar analysis for total species count instead of warbler 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).]

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 birds 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 warblers 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 warblers 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.

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 for warblers of a single primary migration waveform without superimposed local waves. Both sets of results are shown in the table. I will comment primarily on the results for five-day smoothing. The three-day results are not fundamentally different in nature.

The five-day moving average shows a single, primarily flat peak. The center of the plateau is indicated in the table by a "P" notation. The three-day moving average differs in that it includes some local peaks. Related local valleys are indicated by "(-m/-n)", where m and n are depths of the valley relative to adjacent local peaks.

The level, overall peak of 17-18 warblers (five-day average) is from May 11 to May 17--in approximation, the middle eight days of May. The center of the plateau is at May 14. Day-by-day average warbler counts increase more or less uniformly beginning in the middle of April up to the May 11-17 plateau and then, from the plateau, decline uniformly through the end of May at about the same rate as the April-May rise. These characteristics of the data are perhaps seen more easily in the accompanying graphical data than in the tabular data.

A similar but earlier plateau has been found in an analysis for total species count, viz., a five-day moving average of 61-62 species from April 29 to May 10. Therefore, to maximize both warbler count and total species 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 warblers          # of warblers  
           5-day moving avg       3-day moving avg (not used)

April 23            3                      4
      24            2                      3
      25            3                      2
      26            3                      2
      27            3                      4 
      28            8                      6 
      29           10                     12   
      30           13                     14  P
 May   1           13                     14        
       2           12                     12
       3           13                     12  (-2/-6)      
       4           13                     12  
       5           12                     13
       6           13                     15
       7           15                     13
       8           15                     15        
       9           16                     16
      10           16                     18
      11           17                     17        
      12           17                     16
      13           17                     16  P (center of
      14           17  P (center of       17   16-18 plateau)
      15           17   17-18 plateau)    18        
      16           18                     18        
      17           17                     17        
      18           16                     14        
      19           14                     10  (-8/-5)
      20           13                     13        
      21           13                     14        
      22           14                     15  P     
      23           14                     13        
      24           14                     14        
      25           11                     13        
      26           11                      9        
      27           10                     10       
      28            8                      9        
      29            -                      -
      30            -                      -
      31            -                      -

Actual highs were 

  25 on 5-11-2003 (average=17, 5-day moving average=17) 
  23 on 5-10-2005 (average=18, 5-day moving average=16)
  23 on 5-14-2005 (average=18, 5-day moving average=17)
  21 on 5-09-1999 (average=18, 5-day moving average=16)
  20 on 5-10-2003 (average=18, 5-day moving average=16)
  20 on 5-16-2002 (average=18, 5-day moving average=18) 
  20 on 5-17-2003 (average=17, 5-day moving average=17) 

Eighteen-warbler days came as early as April 30 and as late as 
May 28.


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
   |----|----|----|----|----|----|----|----|----|----|----|----|----|
 18                                              *
 17                                         ***** *
 16                                       **       *
 15                                     **
 14                                                 *  ***
 13                              ** ** *             **
 12                                *  *
 11                                                       **
 10                             *                           *
  9 
  8                            *                             ***
  7 
  6                                                             ***
  5 
  4 
  3                  ****** ***
  2                 *      *
  1               **
   |----|----|----|----|----|----|----|----|----|----|----|----|----|
        5   10   15   20   25   30    5   10   15   20   25   30
                April                          May

            Five-day moving average warblers 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

  Data
       May 2, 2001:  16
       May 2, 2003:  19
       May 2, 2005:   7
       May 3, 2001:   9
       May 4, 2002:  18
       May 4, 2003:   7
       May 4, 2005:   6
       May 5, 2002:  16
       May 5, 2004:  17
       May 6, 2000:  14
       May 6, 2005:  11

  Five-day moving average for May 4

    [(16+19+7) + 9 + (18+7+6) + (16+17) + (14+11)] / 11 
                                                    = 12.7 = 13

    The value 13 (smoothed data) is used instead of the 
    average value for May 4 (which would be (18+7+6)/3 = 10).

Bruce M. Bowman
Ann Arbor, Michigan
bbowman99@comcast.net
http://www.umich.edu/~bbowman/birds/

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