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 1987 Monarch Butterfly Migration in Calhoun, Georgia

left arrowarrow leftTable XII k
Descriptive statistics of the October 9, 1987 Observations of the Danaus plexippus migration in Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

28

 Eleven observation of D. plexippus* and ten  observations of other species were not included in the analysis. 

2)       Sum of sines        

-24.82740  

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

3)       Sum of cosines

-2.24120

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

4)       Mean sine

-0.88669 

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

5)       Mean cosine

-0.08004 

6)       Length of mean vector  

0.89030

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

7)       Sine of mean vector      

-0.99595  

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  

-0.08991  

9)       Angular deviation         

±26.9°

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

10)     Magnetic mean bearing

265° ±26.9°
(West)

 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          

263° ±26.9°
(West)

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

13)     95% confidence intervals

± 10°

 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 406, 409, 411, 422, 431, 436, 442, 444, 445, 446, and 447.  

Comments

Wind was South in the morning, Southeast by mid-afternoon, and East by late afternoon.