Tactics and Vectors 98/99
                           

Home

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

left arrowarrow leftTable X o
Descriptive statistics of the October 7, 1987 Observations of the Danaus plexippus migration in Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

46

 Eleven  observation of D. plexippus* were not included in the analysis. 

2)       Sum of sines        

+17.82636

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

3)       Sum of cosines

-32.15475

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

4)       Mean sine

+0.38753 

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

5)       Mean cosine

-0.69902

6)       Length of mean vector  

0.79925

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

7)       Sine of mean vector      

+0.48487

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  

-0.87459 

9)       Angular deviation         

±36.2°

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

10)     Magnetic mean bearing

151° ±36.2°
(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          

149° ±36.2°
(Southeast)

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

13)     95% confidence intervals

± 12°

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

* Either no numerical record for bearing, or butterfly landed, or both for observations 329, 333, 334, 336, 339, 355, 356, 360, 319, 366, and 370.  

Comments

Wind was South in morning and had swung to Northwest  by mid-afternoon.