Georgia 87 II c prefered direction 2

Tactics and Vectors 98/99

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

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.