Tactics and Vectors analysis of field data georgia 87 IX i

Tactics and Vectors 98/99

Compass Bearings Hypothesis

Suns' Azimuth Hypothesis

Expansion-Contraction Hypothesis

Never Go Back Hypothesis

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.