DECADAL DECLINE ( )OF LOGGERHEAD SHRIKES ON CHRISTMAS BIRD COUNTS IN ALABAMA, MISSISSIPPI, AND TENNESSEE

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1 DEPARTMENT OF MATHEMATICS TECHNICAL REPORT DECADAL DECLINE ( )OF LOGGERHEAD SHRIKES ON CHRISTMAS BIRD COUNTS IN ALABAMA, MISSISSIPPI, AND TENNESSEE DR. STEPHEN J. STEDMAN AND DR. MICHAEL ALLEN AUGUST 23 No TENNESSEE TECHNOLOGICAL UNIVERSITY Cookevlle, TN 3855

2 Decadal Declne ( ) of Loggerhead Shrkes on Chrstmas Brd Counts n Alabama, Msssspp, and Tennessee Stephen J. Stedman, Department of Englsh, Box 553, Tennessee Technologcal Unversty, Cookevlle, TN 3855 Mchael R. Allen, Department of Mathematcs, Box 554, Tennessee Technologcal Unversty, Cookevlle, TN 3855 Introducton Most major works dscussng the populaton status of the Loggerhead Shrke (Lanus ludovcanus) n North Amerca ndcate that ths predatory songbrd has declned n populaton numbers at a rate of >2%/year snce at least the md-196s through the md-198s or later (Root 1988; Prce et al. 1995; Yosef 1996; Lefranc 1997; Pardeck and Sauer 2). The most recent major works dscussng the status of the shrke n Alabama (Imhof 1976) and Tennessee (Robnson 199; Ncholson 1997) also refer to ts declnng populaton numbers; the major work for Msssspp (Toups and Jackson 1987) does not deal wth the speces populaton status as a focal pont and so does not menton ths matter. Nearly all the aforementoned works offerng dscussons about the populaton status of ths speces base comments on varous populaton data, manly from Breedng Brd Surveys (BBS) and Chrstmas Brd Counts (CBC), acqured no later than the md-199s; only one source (Pardeck and Sauer 2) provdes commentary based on data acqured durng the late 199s, and n ths case the data are derved from the BBS. Therefore, an update of the shrke s status n Alabama, Msssspp, and Tennessee based on the most recent CBC data appears warranted, especally n lght of the contnung declne n the shrke s populaton numbers. Methods To provde a bass for statstcal analyss, CBC data from each these states were collected from the Hstorcal Results secton of the Natonal Audubon Socety (22) webste. Data were used from counts that were conducted every year from 1992 to 22, resultng n a dataset derved from 11 years of counts from 11 stes n Alabama, 11 n Msssspp, and 15 n Tennessee. The total number of shrkes counted durng each year for each state and for the three states combned was obtaned (Table 1). Statstcal Analyss The statstcal objectve of ths study was to determne f there was a sgnfcant downward trend n Loggerhead Shrke populaton counts for the years 1992 through 22. These 11 years of count data were collected from 11 stes n Alabama, 15 n Tennessee and 11 n

3 Msssspp for a total of 37 stes and 47 overall observatons. Although the yearly counts per ste resemble a tme seres both graphcally (Fgure 1) and ntutvely, ths tme dependent structure was weak enough to avod the use of a more complcated tme seres model. Hence, multple regresson analyss was the method of choce because of ts smplcty and robustness. Also, combnng all the stes from the three states nto one data set ncreased the power of the resultant hypothess test, and the dagnostcs showed that the assumptons of normalty and ndependence were only slghtly volated, f at all. Second, the orgnal count data Y was transformed usng the natural log to allevate the problem of explodng varance and non-normalty (Neter et al. 1996). Fnally, the multple regresson model used n ths study to test for the possble downward trend n Loggerhead Shrke populatons s gven as Y = + β1 X1 + β2x 2 + β3x 3 + β4x1 X 2 + β5x 1 X 3 β + ε where Y s the log of the number of shrkes recorded at each ste, β s the y ntercept β 1 s the change per year of the average of Y, called E( Y ) β 2 s the change n β for stes n Tennessee β 3 s the change n β for stes n Msssspp β s the change n E Y ) for stes n Tennessee 4 5 ( β s the change n E Y ) for stes n Msssspp X 1 s the year, ( X 2 s 1 f a Tennessee ste, otherwse, X 3 s 1 f a Msssspp ste, otherwse, ε s the error term for the th data pont, and = 1,...,47. In the above model t s obvous that no parameters seem assocated wth Alabama. Ths, n fact, s not the case. If any of the extra parameters ( β2 - β 5) are found to be sgnfcant, then β and β 1 would represent the ntercept and slope for Alabama. Conversely, f all of the extra parameters are not found to be sgnfcant, then β and β 1 smply represent the overall ntercept and slope. Results Graphcally, the data ndcate a downward trend n the shrke populaton sampled by Alabama CBCs (Fgures 1 and 2). Although smlar trends were realzed n the graphs for the Tennessee data and slghtly less so for the Msssspp data, those fgures are not presented here

4 because the Alabama set was a good representatve. Data from all three states are plotted along wth the lne of best ft and a 95% confdence band (Fgure 3). Statstcally, the above model as appled to the data gave these results: Parameter Estmate Standard Error p-value Dropped from the model? β No β No β Yes 2 β Yes 3 β Yes 4 β Yes 5 In summary, the results ndcate that for the years 1992 through 22 there s no sgnfcant dfference among the three states (.e., the three states have about the same shrke populaton szes and f any trend n the sze of the shrke populaton exsts, all three states reflect roughly the same trend). Second and most mportantly, there appears to be a slght downward trend n the average populaton count, gvng an estmated decrease of 6% per year after untransformng the data. In fact, when parameters β2 - β 5 n the above table are removed from the model, the p-value for β 1 becomes.7, ndcatng substantally stronger statstcal sgnfcance than f they reman. Dscusson Data were analyzed for years begnnng n 1992, but t should not be assumed that the shrke populaton n these states n 1992 represented a baselne of populaton abundance. Rather, ths year was selected because the number of counts wth contnuous coverage was greatest f the data were derved from that pont n tme onward. Shrkes have been decreasng n populaton numbers for many decades; the current analyss covers only the decrease occurrng wthn the past decade. Concluson The wnterng Loggerhead Shrke populaton sampled by CBCs n Alabama, Msssspp, and Tennessee showed, roughly, a 6% decrease per year from1992 through 22. As for any future populaton counts, regresson analyss of ths type does not lend tself well to predcton beyond the range of the explanatory varables. Hence, the above decrease cannot be reled upon as a good estmate of future populaton counts but does show cause for contnung concern about ths predatory songbrd.

5 Lterature Cted Imhof, T. A Alabama Brdlfe. Unversty of Alabama Press, Unversty, Alabama. Lefranc, N Shrkes: A Gude to the Shrkes of the World. Yale Unversty Press, New Haven, Connectcut. Natonal Audubon Socety (22). The Chrstmas Brd Count Hstorcal Results [Onlne]. Avalable [15 Aprl 23]. Neter, J., M. H. Kutner, C. J. Natchshem, and W. Wasserman Appled Lnear Statstcal Models. 4 th ed., Irwn, Chcago. Ncholson, C. P Atlas of the Breedng Brds of Tennessee. Unversty of Tennessee Press, Knoxvlle, Tennessee. Pardeck, K. L., and J. R. Sauer. 2. The Summary of the North Amercan Breedng Brd Survey. Brd Populatons 5: Robnson, J. C An Annotated Checklst of the Brds of Tennessee. Unversty of Tennessee Press, Knoxvlle, Tennessee. Root, T Atlas of Wnter North Amercan Brds: An Analyss of Chrstmas Brd Count Data. Unversty of Chcago Press, Chcago. Prce, J. S. Droege, and A. Prce The Summer Atlas of North Amercan Brds. Academc Press, New York. Toups, J. A., and J. A. Jackson Brds and Brdng on the Msssspp Coast. Unversty Press of Msssspp, Jackson, Msssspp. Yosef, R Loggerhead Shrke (Lanus ludovcanus). In The Brds of North Amerca, No. 231 (A. Poole and F. Gll, eds.). The Academy of Natural Scences, Phladelpha, and the Amercan Ornthologsts Unon, Washngton, D.C. Table 1. Total Loggerhead Shrkes recorded on Chrstmas Brd Counts n Alabama, Msssspp, and Tennessee Tennessee Msssspp Alabama State Total

6 Fgures 1a-k. Lne graphs presentng Loggerhead Shrke data for all Alabama CBCs conducted n all years

7 Fgure 2. Multple lne graph for all Alabama CBC Loggerhead Shrke data

8 Fgure 3. Scatter plot presentng all CBC Loggerhead Shrke data for Alabama, Msssspp, and Tennessee wth regresson lne estmate and 95%-confdence band.