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: Hypothesis Testing

Hypothesis Testing:  Comparsions of Mean Bearings to theoretical bearings, or theoretical directions, for the pooled data for the 1978, 1979, and 1981 Monarch butterfly (Danaus plexippus) migrations in southern Ontario 

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left arrowarrow leftTable VIII a*

Hypothesis:  Mean Bearings of migrating D. plexippus cannot be distinguished from the downwind direction for each wind condition.

Confidence intervals were used to compare mean bearings for migrants to the Downwind Bearing and the Downwind Sector for eight wind conditions 

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

Mean Bearing ± 95% Confidence Intervals overlap with the Downwind:

Wind

Number

Mean Bearing

95% C.I.

Bearing
(direction)

Sector
(range)

North

  53  

          185° (S)

±8°

YES
(S = 180°)

YES

Northeast

  64 

          229° (SW)

±7°

YES
(SW = 225°)

YES
(>202.5° to 247.5 °)

East

150 

          247° (WSW)

±5°

NO
(W = 270°)

YES
(>247.5° to 292.5°)

Southeast

131 

          257° (WSW)

±5°

NO
(NW = 315°)

NO
(>292.5° to 337.5°)

South

  15  

          237° (WSW)

   ±39°

NO
(N = 360°)

NO
(>337.5° to 022.5°)

Southwest

  35  

          143° (SE)

   ±52°

NO
(NE = 045°)

NO
(>022.5° to 067.5°)

West

  20  

          128° (SE)

  ±29°

NO
(E = 090°)

YES
(>067.5° to 112.5°)

Northwest

107 

          153° (SSE)

±5°

NO
(SE = 135°)

YES
(>112.5° to 157.5°)

Population

575  

          222° (SW)

±5°

* Adapted from Gibo, D. L.,  1990

Definitions of abbreviations and symbols:  N = North, NE = Northeast,  E = East,  S = South, SW = Southwest, WSW = West-Southwest, etc., C.I. = Confidence Intervals. 

Conclusions

  1. The null hypothesis is rejected for downwind bearings of the E, SE, S, SW, W, and NW wind conditions, but is not rejected for the N and NE wind conditions.  The direction of displacement of the butterflies is not aligning with the downwind bearing for most wind conditions.

  2. The null hypothesis is rejected for downwind sectors (compass arcs) of the SE, S, and SW wind conditions, but not for W, NW, N, NE, and E wind conditions.  The direction of displacement of the butterflies cannot be distinguished from the downwind sector for most wind conditions.  The exceptions are the three wind conditions with a S component (i.e. SE, S, and SW winds).

Comments

  1. The results were mixed. Migrating D. plexippus in southern Ontario were likely to be displaced toward the downwind sector for five of the eight wind conditions.  On the other hand, the butterflies were unlikely to be displaced directly downwind except when winds were N or NW. 

  2. The length of a compass arc defining a wind sector was 45°.  The downwind bearing was the bearing at the midpoint of the downwind sector.  For example, the Bearing of a South wind was 180° and the downwind sector extended 22.5° on either size, or from 157.5° to 202.5°.    

  3. The results for South wind and West wind groups should be considered to be tentative because each has a small sample size,  large angular variance, and wide Confidence Intervals.

  4. Testing the Hypothesis, either by using the midpoint bearing for the the wind, or by using wind sectors, results in a reduction of precision.  Ideally, the data would have been grouped according to wind sector for each observation, and the vanishing bearing for each observation would be compared to the upwind bearing as determined at the time of the observation.