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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 II c
Preferred Mean Direction for Monarchs Flying Within 3 m of the Ground :
Calculations using selected observations
Second round of calculations of preferred mean direction and other descriptive
statistics for the Sept. 28 - Oct. 10 Observations of the Danaus
plexippus migration in Calhoun, Georgia
|
Statistic |
Value |
Comments |
1)
Sample size |
31 |
Based on Category II Vanishing Bearings.
Analysis restricted to observations for which the following had been recorded: a
numerical value for bearing, maximum altitude, straight flight, and no interactions with
other butterflies, predators, etc. |
2) Sum of
sines |
-21.99343 |
Divide by sample size to get mean sine (line 4). Also
needed when pooling data from other studies. |
3) Sum of
cosines |
-9.42349 |
Divide by sample size to get mean cosine (line 5).
Also needed when pooling data from other studies. |
4) Mean sine |
-0.70947 |
Values for lines 4 and 5 are used with
sample size (line 1) to calculate length of mean vector (line 6). |
5) Mean cosine |
-0.30398 |
6)
Length of mean vector |
0.77185 |
An index of dispersal of
bearings. Used to determine values for lines 9 and 13. |
7) Sine of
mean vector |
-0.91917 |
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 |
-0.39384 |
9) Angular
deviation |
±38.9° |
Determined from Tables that convert mean vector length
(line 6) into angular deviation (or circular standard deviation). |
10)
Magnetic mean bearing |
247° ±38.9° |
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
|
245° ±38.9° |
Descriptive statistic for the True mean bearing and the
dispersion around the mean for the sample. |
13) 95%
confidence intervals |
±16° |
95% Confidence Intervals (C.I.) are
extrapolated from a chart using values from lines 1 and 6. |
Comments
Preferred Direction for the Georgia, 1987, also differed
from that of southern Ontario migrants (232° ±46°, and CI = ±16°).
However, a two-sample statistical test is necessary to see if observed difference is
significant.
The 95% Confidence Intervals for the Preferred Direction
(245 - 16 = 229°) came close but did not include the 226.2° Great Circle direction to
the overwintering sites from Calhoun.
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