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

 

 

Analyses of Pooled Field Data: Descriptive Statistics

Descriptive circular statistics of the pooled directional data for the 1987 Monarch butterfly (Danaus plexippus) migrations in Northwest Georgia.

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left arrowarrow leftTable III

Mean Bearings of migrating Danaus plexippus for eight wind conditions

Directional data were grouped according to wind direction at the time of the observation.

Wind

N

Mean Bearing

r

A.D.

95% C.I.

North

 121           186° (S) 0.92873*** ±21.4° ±4°

Northeast

 12           216° (SW) 0.74847*** ±41.3° ±28°

East

   7           272° (W) 0.98433*** ±11.5° -

Southeast

 49           275° (W) 0.87853*** ±28.1° ±8°

South

 44           265° (W) 0.80478*** ±36.2° ±13°

Southwest

 15           272° (W) 0.66117*** ±47.3° ±30°

West

 17           156° (S) 0.51947**   ±56.7° ±38°

Northwest

 35           149° (SE) 0.82952*** ±28.1° ±10°

Population

 300            xxx° (x) 0.xxx ±xx°

±xx°

Definitions of abbreviations and symbols:  N = number in sample, S = South, SW = Southwest, WSW = West-Southwest, etc., r = length of mean vector, A.D. = Angular deviation, C.I. = Confidence Intervals.   Asterisks indicate significance level for Rayleigh tests (* =  P< 0.05, ** =  P< 0.01,   and *** =  P< 0.001)   

Comments

  1. The significance levels of the Rayleigh test for N, NE, E, SE, S, and NW winds meant that the probability that the population being sampled (e.g. all monarch butterflies flying in North winds in southern Ontario during late summer and fall) from which the sample (i.e. 53  vanishing bearings of monarch butterflies that I observed flying in North winds) was taken actually has no directional bias (i.e. vanishing bearings are randomly distributed in the population) is less than one in a thousand.    In other words, the chance was less than one in a thousand chance that the directional bias of my samples of monarchs were simply runs of (good? bad?) luck.

  2. The above discussion also applies to the directional data for monarch butterflies flying in W winds, except that the results are a little less convincing.   Because P was less than 0.01, but greater than 0.001, the probability that the butterflies were actually flying about in random directions was less than one in a hundred, but greater than one in a thousand.  Therefore, we are slightly less confident of the results for West winds than the results for the other seven wind conditions.   The high value for the Confidence Intervals for West winds is a further indication that it may be a good idea to get more information (i.e. increase the sample size for this wind condition) before we are feel comfortable about accepting the results as representative of the population.