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, Georgia

left arrowarrow leftTable III i
Descriptive statistics of the September 28, 1988 Observations of the Danaus plexippus migration in Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

47

 Observations 85, 110, and 123 for D. plexippus* were not included in the analysis.

2)       Sum of sines        

-43.89105 

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

3)       Sum of cosines

+3.46891

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

4)       Mean sine

-0.93385

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

5)       Mean cosine

+0.07386 

6)       Length of mean vector  

0.93676

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

7)       Sine of mean vector      

-0.99689

 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  

+0.07879

9)       Angular deviation         

±19.9°

 This value is determined from Tables that convert mean vector length (line 6) into angular deviation (or circular standard deviation).

10)     Magnetic mean bearing

275° ±19.9°
(West)

 Descriptive statistic of  the Magnetic 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          

273° ±19.9°
(West)

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

13)     95% confidence intervals

±6°

 Values from lines 1 and 6 are used to extrapolate 95% (or 99%) Confidence Intervals (C.I.) from appropriate Tables.

* No numerical data was recorded for  vanishing bearing.   

Comments

Wind was calm at surface and SE above the nocturnal (radiation) invesion until about 8:45 AM, then mainly S to SE for rest of day.