Model selection versus traditional hypothesis testing in circular statistics : a simulation study

L.L. was partially funded by the Austrian Science Fund [FWF, grant number: P32586].Many studies in biology involve data measured on a circular scale. Such data require different statistical treatment from those measured on linear scales. The most common statistical exploration of circular data involves testing the null hypothesis that the data show no aggregation and are instead uniformly distributed over the whole circle. The most common means of performing this type of investigation is with a Rayleigh test. An alternative might be to compare the fit of the uniform distribution model to alternative models. Such model-fitting approaches have become a standard technique with linear data, and their greater application to circular data has been recently advocated. Here we present simulation data that demonstrate that such model-based inference can offer very similar performance to the best traditional tests, but only if adjustment is made in order to control type I error rate.Publisher PDFPeer reviewe

Grouped circular data in biology : advice for effectively implementing statistical procedures

Open access funding provided by Austrian Science Fund (FWF). LL was partially funded by the Austrian Science Fund (FWF, Grant Number: P32586).The most common statistical procedure with a sample of circular data is to test the null hypothesis that points are spread uniformly around the circle without a preferred direction. An array of tests for this has been developed. However, these tests were designed for continuously distributed data, whereas often (e.g. due to limited precision of measurement techniques) collected data is aggregated into a set of discrete values (e.g. rounded to the nearest degree). This disparity can cause an uncontrolled increase in type I error rate, an effect that is particularly problematic for tests that are based on the distribution of arc lengths between adjacent points (such as the Rao spacing test). Here, we demonstrate that an easy-to-apply modification can correct this problem, and we recommend this modification when using any test, other than the Rayleigh test, of circular uniformity on aggregated data. We provide R functions for this modification for several commonly used tests. In addition, we tested the power of a recently proposed test, the Gini test. However, we concluded that it lacks sufficient increase in power to replace any of the tests already in common use. In conclusion, using any of the standard circular tests (except the Rayleigh test) without modifications on rounded/aggregated data, especially with larger sample sizes, will increase the proportion of false-positive results—but we demonstrate that a simple and general modification avoids this problem.Publisher PDFPeer reviewe

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

LL is supported by the Austrian Science Fund (FWF, Grant Number: P32586). EPM receives funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 948728).Background A broad range of scientific studies involve taking measurements on a circular, rather than linear, scale (often variables related to 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. In contrast, statistical testing of circular data 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. Methods We use simulations and example data sets to investigate the usefulness of a MANOVA approach for circular data in comparison to commonly used statistical tests. Results Here we demonstrate that a MANOVA approach based on the sines and cosines of the circular data is as powerful as the most-commonly used tests when testing deviation from a uniform distribution, while additionally offering extension to multi-factorial modelling that these conventional circular statistical tests do not. Conclusions The herein presented MANOVA approach offers a substantial broadening of the scientific questions that can be addressed statistically using circular data.Publisher PDFPeer reviewe

Advice on comparing two independent samples of circular data in biology

LL is supported by the Austrian Science Fund (FWF, Grant Number: P32586). EPM receives funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No 948728). This research was funded in whole, or in part, by the Austrian Science Fund (FWF) P32586.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.Publisher PDFPeer reviewe

Cryptochromes in mammals: a magnetoreception misconception?

Cryptochromes are flavoproteins related to photolyases that are widespread throughout the plant and animal kingdom. They govern blue light-dependent growth in plants, control circadian rhythms in a light-dependent manner in invertebrates, and play a central part in the circadian clock in vertebrates. In addition, cryptochromes might function as receptors that allow animals to sense the Earth’s magnetic field. As cryptochromes are also present in mammals including humans, the possibility of a magnetosensitive protein is exciting. Here we attempt to provide a concise overview of cryptochromes in mammals. We briefly review their canonical role in the circadian rhythm from the molecular level to physiology, behaviour and diseases. We then discuss their disputed light sensitivity and proposed role in the magnetic sense in mammals, providing three mechanistic hypotheses. Specifically, mammalian cryptochromes could form light-induced radical pairs in particular cellular milieus, act as magnetoreceptors in darkness, or as secondary players in a magnetoreception signalling cascade. Future research can test these hypotheses to investigate if the role of mammalian cryptochromes extends beyond the circadian clock

Circular data in biology : advice for effectively implementing statistical procedures

Open access funding provided by Research Institute of Molecular Pathology (IMP) / IMBA - Institute of Molecular Biotechnology / Gregor Mendel Institute of Molecular Plant Biology.Circular data are common in biological studies. The most fundamental question that can be asked of a sample of circular data is whether it suggests that the underlying population is uniformly distributed around the circle, or whether it is concentrated around at least one preferred direction (e.g. a migratory goal or activity phase). We compared the statistical power of five commonly used tests (the Rayleigh test, the V-test, Watson’s test, Kuiper’s test and Rao’s spacing test) across a range of different unimodal scenarios. The V-test showed higher power for symmetrical distributions, Rao’s spacing performed worst for all explored unimodal distributions tested and the remaining three tests showed very similar performance. However, the V-test only applies if the hypothesis is restricted to one (pre-specified) direction of interest. In all other unimodal cases, we recommend using the Rayleigh test. Much less explored is the multimodal case with data concentrated around several directions. We performed power simulations for a variety of multimodal situations, testing the performance of the widely used Rayleigh, Rao’s, Watson, and Kuiper’s tests as well as the more recent Bogdan and Hermans-Rasson tests. Our analyses of alternative statistical methods show that the commonly used tests lack statistical power in many of multimodal cases. Transformation of the raw data (e.g. doubling the angles) can overcome some of the issues, but only in the case of perfect f-fold symmetry. However, the Hermans-Rasson method, which is not yet implemented in any software package, outcompetes the alternative tests (often by substantial margins) in most of the multimodal situations explored. We recommend the wider uptake of the powerful but hitherto neglected Hermans-Rasson method. In summary, we provide guidance for biologists helping them to make decisions when testing circular data for single or multiple departures from uniformity.Publisher PDFPeer reviewe

The Hermans–Rasson test as a powerful alternative to the Rayleigh test for circular statistics in biology

Background:  Circular data are gathered in diverse fields of science where measured traits are cyclical in nature: such as compass directions or times of day. The most common statistical question asked of a sample of circular data is whether the data seems to be drawn from a uniform distribution or one that is concentrated around one or more preferred directions. The overwhelmingly most-popular test of the null hypothesis of uniformity is the Rayleigh test, even though this test is known to have very low power in some circumstances. Here we present simulation studies evaluating the performance of tests developed as alternatives to the Rayleigh test. Results:  The results of our simulations demonstrate that a single test, the Hermans and Rasson test is almost as powerful as the Rayleigh test in unimodal situations (when the Rayleigh test does well) but substantially outperforms the Rayleigh test in multimodal situations. Conclusion:  We recommend researchers switch to routine use of the new Hermans and Rasson test. We also demonstrate that all available tests have low power to detect departures from uniformity involving more than two concentrated regions: we recommend that where researchers suspect such complex departures that they collect substantially-sized samples and apply another recent test due to Pycke that was designed specifically for such complex cases. We provide clear textual descriptions of how to implement each of these recommended tests and encode them in R functions that we provide.Publisher PDFPeer reviewe

Circular statistics meets practical limitations : a simulation-based Rao’s spacing test for non-continuous data

Background: For data collected on a circular rather than linear scale, a very common procedure is to test whether the underlying distribution appears to deviate from circular uniformity. Rao’s spacing test is often used to evaluate the support the data offers for the null hypothesis of uniformity. Here we demonstrate that the traditional version of this test fails to adequately control type I error rate when the data is non-continuous (i.e. is rounded/grouped to a finite number of discrete values, e.g. to the nearest degree, a common situation). To overcome this issue, we provide a numerically-intensive simulation version of the test. Methods: We use a simulation study to explore the performance of the traditional and our novel variant on Rao’s spacing test, both in terms of control of type I error rate and statistical power. Results: When data is measured on a continuous circular scale then both methods offer good control of type I error and similar statistical power. If the data is rounded (even to a relatively fine scale such as to the nearest degree – giving 360 possible values), however, the traditional method produces highly inflated type I error rates, particularly with high sample sizes, that make it inappropriate for application to such data. In contrast, our simulation method retains good control of type I error while offering levels of statistical power similar to the traditional Rao test. Conclusions: The traditional method of applying Rao’s spacing test should be replaced by the simulation-based variant introduced here. The two methods offer similar performance but only the simulation method retains good control of the type I error rate when circular data is rounded to a finite set of values (likely due to limited precision of measuring equipment). Adoption of the simulation variant will substantially improve the reliability of this regularly-used test in the commonplace situation where data values are rounded.Publisher PDFPeer reviewe

Risk to pollinators from anthropogenic electro-magnetic radiation (EMR): evidence and knowledge gaps

Worldwide urbanisation and use of mobile and wireless technologies (5G, Internet of Things) is leading to the proliferation of anthropogenic electromagnetic radiation (EMR) and campaigning voices continue to call for the risk to human health and wildlife to be recognised. Pollinators provide many benefits to nature and humankind, but face multiple anthropogenic threats. Here, we assess whether artificial light at night (ALAN) and anthropogenic radiofrequency electromagnetic radiation (AREMR), such as used in wireless technologies (4G, 5G) or emitted from power lines, represent an additional and growing threat to pollinators. A lack of high quality scientific studies means that knowledge of the risk to pollinators from anthropogenic EMR is either inconclusive, unresolved, or only partly established. A handful of studies provide evidence that ALAN can alter pollinator communities, pollination and fruit set. Laboratory experiments provide some, albeit variable, evidence that the honey bee Apis mellifera and other invertebrates can detect EMR, potentially using it for orientation or navigation, but they do not provide evidence that AREMR affects insect behaviour in ecosystems. Scientifically robust evidence of AREMR impacts on abundance or diversity of pollinators (or other invertebrates) are limited to a single study reporting positive and negative effects depending on the pollinator group and geographical location. Therefore, whether anthropogenic EMR (ALAN or AREMR) poses a significant threat to insect pollinators and the benefits they provide to ecosystems and humanity remains to be established