Tactics and Vectors analses of data of butterfly migration in southern Ontario Table II

Tactics and Vectors 98/99

Compass Bearings Hypothesis

Suns' Azimuth Hypothesis

Expansion-Contraction Hypothesis

Never Go Back Hypothesis

Analyses of Pooled Field Data: Descriptive Statistics

Descriptive circular statistics of the pooled directional data for the 1978, 1979, and 1981 Monarch butterfly (Danaus plexippus) migrations in Southern Ontario. Ś Up Ś Tables: Ś I, II, III, IV, V, VI, VII, VIII a, VIII b, IX, X, XI, XII Ś
Table II* 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	53	185° (S)	0.90***	ą26°	ą8°
Northeast	64	229° (SW)	0.90***	ą26°	ą7°
East	150	247° (WSW)	0.84***	ą32°	ą5°
Southeast	131	257° (WSW)	0.86***	ą30°	ą5°
South	15	237° (WSW)	0.51*	ą57°	ą39°
Southwest	35	143° (SE)	0.30*	ą68°	ą52°
West	20	128° (SE)	0.59***	ą52°	ą29°
Northwest	107	153° (SSE)	0.83***	ą33°	ą5°
Population	575	222° (SW)	0.60***	ą47°	ą5°

* Adapted from Gibo, D. L., 1986, 1990

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

The significance levels of the Rayleigh test for N, NE, E, W, 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.
The above discussion also applies to the directional data for monarch butterflies flying in S or SW winds, except that the results are less convincing. Because P was less than 0.05, but greater than 0.01, the probability that the butterflies were actually flying about in random directions was less than one in twenty but greater than one in a hundred. Therefore, we are less confident of the results for South winds and Southwest winds than the results for the other six wind conditions. The high values for the Confidence Intervals for South and Southwest winds are further indications that it would be best to get more information (i.e. increase the sample size for these two wind conditions) before we accept the results as representative of the two populations.