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Table of Contents
Great Circle Hypotheis
Magnetoclinic Hypothesis
Magnetic-Latitude Hypothesis
Compass Bearings Hypothesis
Suns' Azimuth Hypothesis
Expansion-Contraction Hypothesis
Always Advance Hypothesis
Never Go Back Hypothesis
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Analysis of Field Data for the 1987 Monarch
Butterfly Migration in Calhoun, Georgia
 Table IX i
Descriptive statistics of the October
6, 1987 Observations of the Danaus plexippus migration in Calhoun, Georgia
|
Statistic |
Value |
Comments |
1)
Sample size |
16 |
Seven observation of D.
plexippus* were not included in the analysis. |
2) Sum of
sines |
+2.71612 |
Divide by sample size to get mean sine (line 4). Also
needed when pooling data from other studies. |
3) Sum of
cosines |
-1.50900 |
Divide by sample size to get mean cosine (line 5).
Also needed when pooling data from other studies. |
4) Mean sine |
+0.16976 |
Values for lines 4 and 5 are used with
sample size (line 1) to calculate length of mean vector (line 6). |
5) Mean cosine |
-0.09431 |
6)
Length of mean vector |
0.19420 |
An index of dispersal of
bearings. Used to determine values for lines 9 and 13. |
7) Sine of
mean vector |
+0.87415 |
Values for lines 7 and 8 are obtained by
dividing the values from lines 4 and 5 by the value for line 6. The resulting
sine and cosine are used with a Trigonometry Table of sines and cosines to
extrapolate the angle of the mean vector, in this case the Magnetic mean bearing (line10
). |
8) Cosine of
mean vector |
-0.48565 |
9) Angular
deviation |
±72.9° |
Determined from Tables that convert mean vector length
(line 6) into angular deviation (or circular standard deviation). |
10)
Magnetic mean bearing |
119° ±72.9°
(Southeast) |
Descriptive statistic for the True mean
bearing and the dispersion around the mean for the sample. |
11) Magnetic declination
|
-2ºW |
Subtract magnetic declination (variation) to obtain True
bearing |
12) True
mean bearing |
117° ±72.9°
(Southeast) |
Descriptive statistic for the True mean
bearing and the dispersion around the mean for the sample. |
13) 95% confidence
intervals |
± >90° |
95% Confidence Intervals (C.I.) are extrapolated from a
chart using values from lines 1 and 6. |
* Either no numerical records for bearing, or butterfly landed, or both
for observations 307, 309, 312, 316, 319, 320, and 324.
Comments
Wind was South to South- Southeast in morning, swung to
Southwest by mid morning, West -Northwest by midday, then was mainly West-Southwest
for rest of day. The Rayleigh test showed that the mean angle (bearing) was not
significant. In other words, there was no evidence of a bias towards a particular
direction.
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