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 1998
Monarch Butterfly Migration
at UTM, Mississauga, Ontario, Canada

Table I c
Descriptive Stastics of the September 1, 1998 Observations of Danaus plexippus migration at the Mississauga Campus of the University of Toronto

Statistic  

Value

Comments

1)       Sample size (= N)

5

Observations  2* and 5** were not included in the analysis.

2)       Sum of sines        

-4.20833

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

3)       Sum of cosines

-0.63748

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

4)       Mean sine

-0.84167

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

5)       Mean cosine

-0.12750

6)       Mean vector length (= r)

+0.85127

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

7)       Sine of mean vector       

-0.98872

Values for lines 7 and  8 are used with a Trigonometry Table of  sines and cosines to extrapolate the mean angle, in this case the Magnetic mean bearing (line10 ).

8)       Cosine of mean vector  

-0.14977

9)       Angular deviation         

±63º

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

10)     Magnetic mean bearing

261.5º ±63º
(West)

Descriptive statistic of the  Magnetic mean bearing and the dispersion around the mean  for the  5  butterflies  in the sample.

11)     Magnetic declination     

-10ºW

Subtract magnetic declination (variation) to obtain True bearing

12)     True mean bearing          

251.5° ±63º
(West)

Descriptive statistic for the True mean bearing and the dispersion around the mean for the 5 butterflies in the sample. 

13)     95% Confidence Intervals

A sample size of 5 is
too small to determine
confidence intervals.

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

* Butterfly was in a strong thermal and vanished straight up - no vanishing bearing could be taken. **Butterfly was one of a pair that were apparently involved in mating behavior.  The pair flew behind a building well before reaching their vanishing point.

Comments

The significance of the mean direction for this study is limited because of the small sample size.  Nevertheless, it is encouraging that the True mean direction (252° ±63º) calculated for monarch butterflies  was similar to the mean direction (257° ±30º, N = 131,   r = 0.86, C.I. ±5°) calculated for field data recorded for SE winds in 1978, 1979, and 1981 in a field (now a parking lot) on the Campus of UTM, another field (now a car dealership) within 2.5 km of the campus, and my front yard (still my front yard), also within 2.5 km of the campus (Gibo 1986).   There apparently has been little change in tactics over the past two decades.