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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 1998
Monarch Butterfly Migration
at UTM, Mississauga, Ontario, Canada
Table I c
Descriptive Stastics of the September
1, 1998 Observations of Danaus plexippus migration at the
Mississauga Campus of the University of Toronto |
Statistic |
Value |
Comments |
1)
Sample size (= N) |
5 |
Observations 2* and 5** were not
included in the analysis. |
2) Sum of
sines |
-4.20833 |
Divide by sample size to get mean sine (line 4). Also
needed when pooling data from other studies. |
3) Sum of
cosines |
-0.63748 |
Divide by sample size to get mean cosine (line 5).
Also needed when pooling data from other studies. |
4) Mean sine |
-0.84167 |
Values for lines 4 and 5 are used with
sample size (line 1) to calculate length of mean vector (line 6). |
5) Mean cosine |
-0.12750 |
6)
Mean vector length (= r) |
+0.85127 |
An index of dispersal of
bearings. Used to determine values for lines 9 and 13. |
7) Sine of
mean vector |
-0.98872 |
Values for lines 7 and 8 are used with a
Trigonometry Table of sines and cosines to extrapolate the mean angle, in this case
the Magnetic mean bearing (line10 ). |
8) Cosine of
mean vector |
-0.14977 |
9) Angular
deviation |
±63º |
This value is determined from Tables that convert
mean vector length (line 6) into angular deviation (or circular standard deviation). |
10)
Magnetic mean bearing |
261.5º ±63º
(West) |
Descriptive statistic of the
Magnetic mean bearing and the dispersion around the mean for the 5
butterflies in the sample. |
11) Magnetic declination
|
-10ºW |
Subtract magnetic declination (variation) to obtain True
bearing |
12) True
mean bearing |
251.5° ±63º
(West) |
Descriptive statistic for the True mean
bearing and the dispersion around the mean for the 5 butterflies in the sample. |
13) 95%
Confidence Intervals |
A sample size of 5 is
too small to determine
confidence intervals. |
Values from lines 1 and 6 are used
to extrapolate 95% Confidence Intervals (C.I.) from appropriate Tables. |
* Butterfly was in a strong thermal and vanished straight up - no
vanishing bearing could be taken. **Butterfly was one of a pair that were apparently
involved in mating behavior. The pair flew behind a building well before reaching
their vanishing point.
Comments
The significance of the mean direction for this study is limited
because of the small sample size. Nevertheless, it is encouraging that the True mean
direction (252° ±63º) calculated for monarch butterflies was similar to the
mean direction (257° ±30º, N = 131, r = 0.86, C.I. ±5°) calculated for field
data recorded for SE winds in 1978, 1979, and 1981 in a field (now a parking lot) on the
Campus of UTM, another field (now a car dealership) within 2.5 km of the campus, and my
front yard (still my front yard), also within 2.5 km of the campus (Gibo 1986). There apparently has been
little change in tactics over the past two decades.
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