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

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 for pooled directional data for 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 IV* Mean Headings 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 headings recorded for the subgroup of individuals that were flying straight.
Wind	N	Mean Heading	r	A.D.	95% C.I.

North	9	244° (WSW)	0.67*	ą47°	ą42°
Northeast	12	207° (SSW)	0.68**	ą46°	ą33°
East	48	180° (S)	0.81***	ą35°	ą11°
Southeast	50	190° (S)	0.89***	ą27°	ą8°
South	1	208° (SSW)	-	-	-
Southwest	13	167° (SSE)	0.83***	ą33°	ą21°
West	8	238° (WSW)	0.70*	ą44°	ą41°
Northwest	46	230° (SW)	0.83***	ą33°	ą11°

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

Definitions of abbreviations and symbols: N = number in sample, WSW = West-Southwest, SSW = South-Southwest, S = South, 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 E, SE, SW, 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. 48 headings that I observed for monarch butterflies flying in East winds) was taken has no directional bias (i.e. the true headings are randomly distributed in the population) is less than one in a thousand. In other words, the chance that the directional biases observed for headings in my sample of monarchs was due to a run of (good? bad?) luck was less than one in a thousand.
The same argument applies to the significance levels for the Rayleigh test of the directional data for monarch butterflies flying in NE winds except that the probability that it the observed results were was due to chance was less than one in a hundred.
The same argument also applies to the significance levels for the Rayleigh test of the directional data for monarch butterflies flying in North winds or W winds, except that the results are not as encouraging. Because P is less than 0.05 and greater than 0.01, the probability may be almost as high as 1 in 20 that the headings for D. plexippus flying in N winds and W winds are distributed at random . Therefore, we are less confident about the results for South and West winds. The very high value for the Confidence Intervals for South and Southwest winds is a further warning that we should increase sample size for these two wind conditions before drawing any further conclusions.