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 V h
Descriptive statistics of the September 30, 1988 Observations of the Danaus plexippus migration in Calhoun, Georgia

Statistic  

Value

Comments

1)       Sample size     

41

 Observation 238 for D. plexippus* was not included in the analysis.

2)       Sum of sines        

-35.93375 

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

3)       Sum of cosines

+14.88798   

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

4)       Mean sine

-0.87643

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

+0.36312 

6)       Length of mean vector  

0.94867

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

7)       Sine of mean vector      

-0.92384

 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  

+0.38277

9)       Angular deviation         

±18.1°

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

10)     Magnetic mean bearing

292° ±18.1°
(Northwest)

 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          

290° ±18.1°
(West)

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

13)     95% confidence intervals

±8°

 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 shortly after 8:00 AM, then mainly SE for rest of day.