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

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 pooled directional data for the 1978, 1979, and 1981 Monarch butterfly (Danaus plexippus) migrations in Southern Ontario. Ś Up Ś Tables: I, II, III, IV, V, VI, VII, VIII a, VIII b, IX, X, XI, XII Ś
Table III* Mean Bearings of straight-flying, migrating, Danaus plexippus for eight wind conditions Directional data were grouped according to wind direction at the time of the observation. The analysis was restricted to the subgroup of individuals for each wind condition that were flying straight.
Wind	N	Mean Bearing	r	A.D.	95% C.I.

North	21	196° (SSW)	0.93***	ą21°	ą10°
Northeast	21	224° (SW)	0.79***	ą37°	ą18°
East	81	235° (SW)	0.89***	ą27°	ą5°
Southeast	86	247° (WSW)	0.90***	ą26°	ą5°
South	10	219° (SW)	0.73***	ą42°	ą33°
Southwest	30	156° (SSE)	0.35*	ą65°	ą45°
West	11	175° (S)	0.55*	ą54°	ą48°
Northwest	58	164° (SSE)	0.77***	ą39°	ą11°
Population	318	223° (SW)	0.63***	ą49°	ą7°

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

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

Comments

The significance level of the Rayleigh test for N, NE, E, SE, S, and NW winds means that the probability that the population (e.g. all monarch butterflies flying straight in North winds in southern Ontario during late summer and fall) from which the sample (i.e. 21 vanishing bearings of monarch butterflies that I observed for North winds) was taken has no directional bias (i.e. true vanishing bearings are randomly distributed in the population ) is less than one in a thousand. In other words, the probability is less than one in a thousand that the directional bias of my samples of monarchs were simply runs of (good? bad?) luck.
The above argument applies to the significance levels for the Rayleigh test of the directional data for monarch butterflies flying in South or Southwest winds, except that the results are not as encouraging. Because P is less than 0.05, but greater than 0.01, the probability that the population in southern Ontario is actually flying about in random directions may be a high as about 1 in 20. Therefore, we are less confident that the results for South winds and Southwest winds. The very high value for the Confidence Intervals for South winds and Southwest winds are another reason to be skeptical of the results. We need to increase sample size and see if this reduces the P value and the Confidence Intervals, before we accept that the results for S winds and SW winds are representative of the flight tactics of the butterflies in these wind conditions.