Experienced Migratory Bats Integrate the Sun’s Position at Dusk for Navigation at Night

2021

Preprint

A broad range of scientific studies involve taking measurements on a circular rather than linear scale (often times or orientations). For linear measures there is a well-established statistical toolkit based on linear modelling to explore the associations between this focal variable and potentially several explanatory factors and covariates. However, most statistical testing of circular statistics is much simpler: often involving either testing whether variation in the focal measurements departs from circular uniformity, or whether a single explanatory factor with two levels is supported. Here we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as effective as the most-commonly used tests in these simple situations, while additionally it offers extension to multi-factorial modelling that these conventional tests do not. This, in combination with recent developments in Bayesian approaches, offers a substantial broadening of the scientific questions that can be addressed statistically with circular data.

Section: Real Data Examplessupporting

confidence: 92%

“…The second data set is from Lindecke et al (2019) involving migratory bats (Pipistrella pygmaeus). The expectation was a difference between two treatment groups (with a 180° switch in preferred direction) and an effect of age on the treatment effect (interaction between age and treatment).…”

Section: Simulation Testsmentioning

confidence: 99%

The multivariate analysis of variance as a powerful approach for circular data

2021

Preprint

“…The third data set is taken from a recent paper on bat navigation by Lindecke et al 21 . They investigated if migratory bats ( Pipistrellus pygmaeus ) use the sun’s position at dusk to calibrate their navigational compass.…”

Section: Methodsmentioning

confidence: 99%

Advice on comparing two independent samples of circular data in biology

2021

Sci Rep

Many biological variables are recorded on a circular scale and therefore need different statistical treatment. A common question that is asked of such circular data involves comparison between two groups: Are the populations from which the two samples are drawn differently distributed around the circle? We compared 18 tests for such situations (by simulation) in terms of both abilities to control Type-I error rate near the nominal value, and statistical power. We found that only eight tests offered good control of Type-I error in all our simulated situations. Of these eight, we were able to identify the Watson’s U2 test and a MANOVA approach, based on trigonometric functions of the data, as offering the best power in the overwhelming majority of our test circumstances. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Hence, we recommend the routine use of either Watson’s U2 test or MANOVA approach when comparing two samples of circular data.

“…The third data set is taken from a recent paper on bat navigation by Lindecke and colleagues (2019). They investigated if migratory bats ( Pipistrellus pygmaeus ) use the sun’s position at dusk to calibrate their navigational compass.…”

Section: Methodsmentioning

confidence: 99%

Comparing two circular distributions: advice for effective implementation of statistical procedures in biology

2021

Preprint

Many biological variables, often involving timings of events or directions, are recorded on a circular rather than linear scale, and need different statistical treatment for that reason. A common question that is asked of such circular data involves comparison between two groups or treatments: Are the populations from which the two samples drawn differently distributed around the circle? For example, we might ask whether the distribution of directions from which a stalking predator approaches its prey differs between sunny and cloudy conditions; or whether the time of day of mating attempts differs between lab mice subject to one of two hormone treatments. An array of statistical approaches to these questions have been developed. We compared 18 of these (by simulation) in terms of both abilities to control type I error rate near the nominal value, and statistical power. We found that only eight tests offered good control of type I error in all our test situations. Of these eight, we are able to identify Watsons U^2 test and MANOVA based on trigonometric functions of the data as offering the best power in the overwhelming majority of our test circumstances. There was often little to choose between these tests in terms of power, and no situation where either of the remaining six tests offered substantially better power than either of these. Hence, we recommend the routine use of either Watsons U^2 test or MANOVA when comparing two samples of circular data.