Tactics and Vectors 98/99
                           

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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 1988 Monarch Butterfly Migration in Resaca and Calhoun, Georgia

left arrowarrow leftTable XIV a
Mean Vanishing Bearing for Danaus plexippus Flying above the Radiation Inversion (SE wind)

Descriptive statistics for the September 26 to October 2, 1988, observations in Resaca and Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

56

 Records with non-numerical records for vanishing bearing or  wind (e.g. N instead of 360°) were not included in the analysis. 

2)       Sum of sines        

-53.87313 Divide by sample size to get mean sine (line 4).  Also needed when pooling data from other studies.

3)       Sum of cosines

 -0.89907 Divide by sample size to get mean cosine (line 5).  Also needed when pooling data from other studies.

4)       Mean sine

 -0.96202 Values for  lines 4 and 5 are used with sample size (line 1) to calculate length of mean vector (line 6).

5)       Mean cosine

 -0.01605

6)       Length of mean vector  

0.96215 An index of  dispersal of  bearings.    Used to determine values for lines 9 and 13. 

7)       Sine of mean vector      

-0.99986 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  

-0.01669

9)       Angular deviation         

±16.2°

 Determined from Tables that convert mean vector length (line 6) into angular deviation (or circular standard deviation).

10)     Magnetic mean bearing

°269±16.2°
(West)

 Descriptive statistic for the True mean bearing and the dispersion around the mean for the sample. 

11)     Magnetic declination     

-2°W

 Subtract magnetic declination (variation) to obtain True bearing

12)     True mean bearing          

°267±16.2°
(West)

 Descriptive statistic for the True mean bearing and the dispersion around the mean for the sample.  

13)     95% confidence intervals

±5°

 95% Confidence Intervals (C.I.) are extrapolated from a chart using values from lines 1 and 6.

Comments: