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.Electronic supplementary materialThe online version of this article (10.1007/s00265-018-2538-y) contains supplementary material, which is available to authorized users.
The biophysical and molecular mechanisms that enable animals to detect magnetic fields are unknown. It has been proposed that birds have a light-dependent magnetic compass that relies on the formation of radical pairs within cryptochrome molecules. Using spectroscopic methods, we show that pigeon cryptochrome clCRY4 is photoreduced efficiently and forms long-lived spin-correlated radical pairs via a tetrad of tryptophan residues. We report that clCRY4 is broadly and stably expressed within the retina but enriched at synapses in the outer plexiform layer in a repetitive manner. A proteomic survey for retinal-specific clCRY4 interactors identified molecules that are involved in receptor signaling, including glutamate receptor–interacting protein 2, which colocalizes with clCRY4. Our data support a model whereby clCRY4 acts as an ultraviolet-blue photoreceptor and/or a light-dependent magnetosensor by modulating glutamatergic synapses between horizontal cells and cones.
a b s t r a c tMagnetic alignment (MA) constitutes the simplest directional response to the geomagnetic field. In contrast to magnetic compass orientation, MA is not goal directed and represents a spontaneous, fixed directional response. Because animals tend to align their bodies along or perpendicular to the magnetic field lines, MA typically leads to bimodal or quadrimodal orientation, although there is also growing evidence for a fixed unimodal orientation not necessarily coinciding with the magnetic cardinal directions. MA has been demonstrated in diverse animals including insects, amphibians, fish, and mammals. Alignment can be expressed by animals during resting as well as on the move (e.g. while grazing, hunting, feeding, etc.). Here, we briefly survey characteristic features and classical examples of MA and review the current knowledge about the occurrence of MA in mammals. In addition, we summarize what is known about mechanisms underlying MA and discuss its prospective biological functions. Finally, we highlight some physiological effects of alignment along the magnetic field axes reported in humans. We argue that the phenomenon of MA adds a new paradigm that can be exploited for investigation of magnetoreception in mammals.
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. Electronic supplementary material The online version of this article (10.1186/s12898-019-0246-8) contains supplementary material, which is available to authorized users.
The mammalian magnetic sense is predominantly studied in species with reduced vision such as mole-rats and bats. Far less is known about surface-dwelling (epigeic) rodents with well-developed eyes. Here, we tested the wood mouse Apodemus sylvaticus for magnetoreception using a simple behavioural assay in which mice are allowed to build nests overnight in a visually symmetrical, circular arena. The tests were performed in the ambient magnetic field or in a field rotated by 90°. When plotted with respect to magnetic north, the nests were bimodally clustered in the northern and southern sectors, clearly indicating that the animals used magnetic cues. Additionally, mice were tested in the ambient magnetic field with a superimposed radio frequency magnetic field of the order of 100 nT. Wood mice exposed to a 0.9 to 5 MHz frequency sweep changed their preference from north-south to east-west. In contrast to birds, however, a constant frequency field tuned to the Larmor frequency (1.33 MHz) had no effect on mouse orientation. In sum, we demonstrated magnetoreception in wood mice and provide first evidence for a radical-pair mechanism in a mammal.
Cryptochromes are a ubiquitous group of blue-light absorbing flavoproteins that in the mammalian retina have an important role in the circadian clock. In birds, cryptochrome 1a (Cry1a), localized in the UV/violet-sensitive S1 cone photoreceptors, is proposed to be the retinal receptor molecule of the light-dependent magnetic compass. The retinal localization of mammalian Cry1, homologue to avian Cry1a, is unknown, and it is open whether mammalian Cry1 is also involved in magnetic field sensing. To constrain the possible role of retinal Cry1, we immunohistochemically analysed 90 mammalian species across 48 families in 16 orders, using an antiserum against the Cry1 C-terminus that in birds labels only the photo-activated conformation. In the Carnivora families Canidae, Mustelidae and Ursidae, and in some Primates, Cry1 was consistently labeled in the outer segment of the shortwave-sensitive S1 cones. This finding would be compatible with a magnetoreceptive function of Cry1 in these taxa. In all other taxa, Cry1 was not detected by the antiserum that likely also in mammals labels the photo-activated conformation, although Western blots showed Cry1 in mouse retinal cell nuclei. We speculate that in the mouse and the other negative-tested mammals Cry1 is involved in circadian functions as a non-light-responsive protein.
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