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Altogether, we found that, while traffic volume declined by  > 7% during the pandemic year (with a maximum monthly decline of nearly 40%), the absolute number of annual WVCs was largely unchanged. This resulted in significant increases of  > 8% in collision rates between vehicles and wildlife during the pandemic year, peaking at a  > 27% nationwide increase in April 2020. Other studies from the first several months of the pandemic documented similar transient declines in the number of WVCs when the pandemic began which then reversed in many jurisdictions as the pandemic progressed and traffic rebounded26,27. We observed a similar pattern over the first five months of the pandemic at the national scale (Fig. 2): WVCs initially declined during the pandemic in step with declines in traffic volume, but then started to increase to baseline levels at a faster rate than traffic, possibly due to behavioral lags by wildlife following traffic-mediated increases in wildlife road use. Though based on coarse-scale data, our research aligns with assertions from studies during27 and prior to the pandemic3,15,16,28,29 that the relationship between traffic volume and WVCs is non-linear.We postulate that the observed non-linear relationship between traffic volume and WVCs is the result of greater use of roads and roadsides by certain wildlife species, namely large mammals (Table S1), in response to decreasing traffic volume, as prior research has suggested3,14,15,16. This explanation is consistent with accounts of various wildlife species making increased use of human spaces during the pandemic17,20,21: with less cars on the roads, wildlife might be less deterred from roads by the noise and light pollution that accompany high traffic volumes9,10,11,20 and perceive roads as less risky, thereby increasing their willingness to attempt road crossings3,8,15,16. Beyond incidentally crossing roads while moving about the landscape8,9, wildlife might be attracted to roads for travel, mates, or other resources8,10,11. Many animals are shown to utilize roads to move efficiently across the landscape11,12, and roads and the surrounding areas are comparatively open, such that wildlife might select roads and roadsides for enhanced visibility to find mates, detect predators, or locate prey10,13. Roadsides also can provide foraging opportunities and essential nutrients for wildlife via abundant, high-quality early successional vegetation and high salt concentrations10,11. As such, decreased road traffic during the pandemic might have caused certain wildlife species to tolerate the risks associated with roads in order to access the benefits of roads and roadsides.An alternative explanation for the observed increases in collision rates is that human driving behavior, rather than animal behavior, changed during the pandemic. With fewer cars on the road, people might drive faster35, rendering it more difficult for both humans and wildlife to avoid collisions3. Preliminary studies from throughout the United States have indeed suggested changes to human driving behavior during the pandemic, with several jurisdictions reporting increased vehicle speeds35,36. Despite reported increases in vehicle speeds, however, the total number of vehicle collisions (the sum of both wildlife and non-wildlife collisions) mirrored trends in traffic volume and declined considerably during the pandemic37,38. Thus, because changes to human behavior appear to have had a minimal effect on vehicle collisions overall, it is unlikely that the observed changes in collision rates are due to increased vehicle speeds alone. Still, we cannot discount the possibility that changes to human driving behavior contributed to the patterns documented here, and future work should more explicitly test the relative effects of changes in traffic volume on both human driving behavior and wildlife space-use, as well as the resultant impacts on WVCs.A greater understanding of human driving behavior would also help explain our findings regarding changes in traffic patterns during the pandemic. Nationwide, the severity of COVID-19 restrictions accounted for a large amount of the variation in changes in monthly traffic volume (R2 = 0.968), but the severity of restrictions was less influential on changes in yearly traffic across states (Tables S3 and S4). Restrictions implemented throughout the pandemic were largely enacted for the purpose of minimizing travel, and other research has demonstrated that these restrictions were effective at reducing human mobility18,21. Our state-level findings, however, imply that it was not only the restrictions themselves that reduced travel, but possibly also the associated anxiety regarding the risk of contracting the SARS-CoV-2 virus, as has been suggested in other studies21,22,23,24; although we observed the greatest declines in traffic volume early in the pandemic (Fig. 2A) when restrictions were most stringent (Fig. S2)21, there was widespread anxiety about the risks posed by SARS-CoV-2 during this time22,23, which likely motivated people to stay home independent of restrictions24. Indeed, anxiety and risk perception might explain the relationship between traffic volume and the other covariates in our top models (Table S4). Declines in traffic were greatest in the most densely populated states (Fig. 4A) and in states that had the highest and the lowest disease burdens (Fig. 4B). The risk of SARS-CoV-2 transmission is greater in more densely populated states due to the close proximity of and frequent interactions amongst people21. As such, people may have altered their road use more in densely populated states as compared to sparsely populated ones due to differing perceptions of disease transmission risk23—though differences in infrastructure in relation to population density likely contributed to this pattern as well39. Similarly, declines in traffic volume in states with larger outbreaks of SARS-CoV-2 might have been driven by increases in the perceived risk of contracting the virus21,23. Alternatively, traffic reductions in states with low disease burdens might reflect increased compliance with stay-at-home orders, and therefore less opportunity for disease spread40,41; essentially, reductions in traffic volume might be the cause of locally low disease burdens therein, rather than a consequence. Altogether, we posit that the observed heterogeneity in traffic volume between states is, at least in part, attributed to differences in the perceived risk posed by the SARS-CoV-2 virus.Regardless of the mechanisms underlying changes in traffic volume and WVCs, our observation that the annual number of WVCs was largely unchanged despite substantive declines in traffic volume has implications for mitigating WVCs going forward. Most directly, the lack of a directional change in WVCs suggests that road traffic levels in the United States are currently such that even large decreases in traffic volume would have minimal long-term effects on the absolute number of WVCs. As such, decreasing collisions by reducing traffic volume would require even larger and longer-lasting changes in traffic than those observed during the pandemic. Since such massive and sustained reductions in traffic are unlikely4,5,6, WVCs in the United States essentially represent a fixed cost as of now, both for human society and wildlife populations. As such, these transient decreases in traffic likely provided minimal reprieve to large mammals from collision-induced mortality, in contrast to speculation that changes in human mobility during the COVID-19 pandemic had substantial positive effects for wildlife populations by freeing wildlife from the pervasive direct and indirect effects of humans17,18,19,20,26,27,42.Indeed, it is possible that short-term decreases in traffic volume might ultimately be harmful to those wildlife species that increased their road use. Although the increases in collision rates we observed at the beginning of the pandemic were rapid and corresponded to nationwide declines in traffic volume (see also26,27), collision rates remained elevated even as traffic approached baseline levels in July (Fig. 2B). If wildlife responses to changes in traffic are asymmetric (i.e., increases in wildlife road use following declines in traffic occur more rapidly than decreases in wildlife road use in response to increased traffic), then short-term declines in traffic volume might lead to net increases in the number WVCs over longer timeframes, ultimately proving detrimental to certain wildlife populations1,3. Future work should evaluate the long-term effects of the pandemic on wildlife populations, specifically with regards to collision-induced mortality17,20,26,27,42.Although the COVID-19 pandemic provided an opportunity to examine the short-term effects of transient decreases in traffic volume on WVCs, the longer-term effects of expanding human populations, greater road densities, and altogether higher traffic volumes on WVCs are less clear. Similar to the increases in wildlife road use in response to decreases in traffic volume theorized here, steady increases in traffic might reduce wildlife road use long-term3,14,15,16; since road traffic is indeed increasing through time4,5,6, we might therefore see declines in WVCs as roads become more effective at repelling wildlife1,3,14. Although these reductions in vehicle-induced wildlife mortality are welcome, this would see roads increasingly serve as barriers to animal movement and gene flow43, further fragmenting already disconnected wildlife populations8. Thus, policy makers and urban planners should invest in infrastructure such as overpasses, underpasses, and fencing that enables wildlife to cross high-traffic roads safely or directs wildlife towards low-risk areas8,9. Even substantive short-term declines in road traffic are not sufficient to mitigate wildlife-vehicle conflict on their own. More

Gene Expression and Therapy Group, King’s College London, Faculty of Life Sciences & Medicine, Department of Medical and Molecular Genetics, Guy’s Hospital, London, UKRobin Mesnage & Michael N. AntoniouCentre for Ecology, Evolution & Behaviour, Department of Biological Sciences, School of Life Sciences and the Environment, Royal Holloway University of London, Egham, UKEdward A. Straw, Mark J. F. Brown & Ellouise LeadbeaterHeartland Health Research Alliance, Port Orchard, WA, USACharles BenbrookANSES, Sophia Antipolis Laboratory, Unit of Honey Bee Pathology, Sophia Antipolis, FranceMarie-Pierre ChauzatAgricultural Economics and Policy Group, ETH Zürich, Zürich, SwitzerlandRobert FingerSchool of Life Sciences, University of Sussex, Brighton, UKDave GoulsonBC3 — Basque Centre for Climate Change, Scientific Campus of the University of Basque Country, Leioa, SpainAna López-BallesterosCentre D’Études Biologiques de Chizé, UMR 7372, CNRS & La Rochelle Université, Villiers-en-bois, FranceNiklas MöhringInstitute of Bee Health, Vetsuisse Faculty, University of Bern, Bern, SwitzerlandPeter NeumannSchool of Agriculture and Food Science, University College Dublin, Dublin, IrelandEdward A. Straw, Dara Stanley & Linzi J. ThompsonDepartment of Botany, School of Natural Sciences, Trinity College Dublin, Dublin, IrelandJane C. Stout & Elena ZiogaDepartment of Ecoscience, Aarhus University, Aarhus, DenmarkChristopher J. ToppingSchool of Chemical Sciences, Glasnevin Campus, Dublin City University, Dublin, IrelandBlánaid WhiteInstitute of Zoology, University of Natural Resources and Life Sciences, Vienna, Vienna, AustriaJohann G. ZallerCorrespondence to
Robin Mesnage or Edward A. Straw. More

Type-I errorIn the case of two identical unimodal von Mises distributions, seven tests did not maintain Type-I error near the nominal 5% level, at least when sample sizes were small. These tests were the Kuiper two-sample test, the non equal concentration parameters approach ANOVA, the P-test, the Watson’s large-sample nonparametric test, the Watson–Williams test and the Rao dispersion test (Fig. 2). The Type-I error results were similar for the unimodal wrapped skew-normal distribution, except that the Wallraff test and Fisher’s method also showed Type-I error inflation (Fig. S1). No other methods showed evidence of failure to control Type-I error rate across different testing situations (Figs. S2–S5), except for the Log-likelihood ratio ANOVA in the case of two identical asymmetrical bimodal distributions (Fig. S3). In summary, only eight out of 18 tests reliably controlled the Type-I error rate near the nominal 5% level across all the situations investigated. These included five tests for identical distribution, the Watson’s U2 test, the Large-sample Mardia–Watson–Wheeler test, the Watson-Wheeler test, the embedding approach ANOVA, the MANOVA approach, the Rao polar test for differences in mean direction, and two tests for differences in concentration, the Levene’s test and the concentration test. We focus only on these tests in our explorations of statistical power.Figure 2Type-I error of all tests using von Mises distributions for different sample sizes: 10 and 10 (A), 20 and 20 (B), 50 and 50 (C), 20 and 30 (D) and 10 and 50 (E). Concentration (κ, kappa) increases for both distributions from 0 to 8. Tests are grouped according to their null hypotheses.Full size imagePower to detect differences in concentrationThe most powerful test to detect concentration differences between two von Mises distributions was the MANOVA approach, which offered superior power especially at lower sample sizes (Fig. 3). The Watson’s U2 test was also very powerful, followed by the Watson–Wheeler and the Large-sample Mardia–Watson–Wheeler tests with only marginally lower power. The embedding approach ANOVA had lower power, but, notably, was still more powerful than the Concentration test and Levene’s test, both specifically designed to detect differences in concentration. As expected, the Rao polar test was not sensitive to differences in concentration. The general results for two unimodal wrapped skew-normal distributions were comparable to the results for unimodal von Mises distributions, with the only exception of superior performance of Levene’s test in situations with highly asymmetric samples sizes (Fig. S6).Figure 3Power of all included tests when comparing von Mises distributions of differing concentrations using different sample sizes: 10 and 10 (A), 20 and 20 (B), 50 and 50 (C), 20 and 30 (D) and 10 and 50 (E). The first distribution is fixed at κ = 0, the second increases from 0 towards 8.Full size imageWhen comparing axial von Mises distributions, only the Watson’s U2 test offered acceptable power (Fig. S7). For the symmetrical trimodal distributions, overall power was very low, and again, only the Watson’s U2 providing some power (Fig. S8). The asymmetrical bimodal (Fig. S9) situation showed acceptable power of the MANOVA approach and Watson’s U2, however, for the asymmetrical trimodal distribution power was low with the Watson’s U2 providing the best results (Fig. S10).Power to detect differences in the mean/medianThe power to detect angular differences between two von Mises distributions was highest for the MANOVA approach at small sample sizes (n = 10), followed by the Watson’s U2, Watson-Wheeler test and the Large-sample Mardia-Watson-Wheeler test (Fig. 4). Notably, the Levene’s test also showed acceptable power levels, clearly failing to detect specifically concentration differences (to which it was less sensitive, see Fig. 4). The concentration test was not sensitive to the differences in mean direction. Special cases were the embedding approach ANOVA and the Rao polar test. The ANOVA approach showed, with the exception of very unequal sample sizes (n = 10/50), a unimodal response, with increasing power levels from 0° to 90° difference, but then rapidly decreasing power towards 180° difference. The Rao polar test showed an even stranger pattern, with, at higher sample sizes, very good power when the difference was either around 45° or 135°, but with power levels dropping to 0.05 in between these two peaks (at 90°). The results were similar for the wrapped skew-normal distribution, with the exceptions that the Rao polar test showed strongly reduced power and switched from a bimodal to a unimodal power curve with a peak around 60°, and the Levene’s test completely lost its power (Fig. S11).Figure 4Power of all included tests when comparing von Mises distributions (kappa for both = 2) of differing directions using different sample sizes: 10 and 10 (A), 20 and 20 (B), 50 and 50 (C), 20 and 30 (D) and 10 and 50 (E). The first distribution is fixed at 0°, the second increases from 0° towards 180.Full size imageFor axial distributions, only the Watson’s U2 test offered acceptable power levels, although large sample sizes (~ n = 100) were required for the power to reach over 50% (Fig. S12). All other tests failed to detect the difference in mean direction between two axial distributions. For symmetric trimodal distributions none of the tests used was sensitive to differences in mean direction (Fig. S13).When comparing asymmetrical bimodal distributions, the general trends were similar to the unimodal case. However, over all sample sizes the MANOVA approach offered the best power. The Watson–Wheeler test was considerably less powerful in this situation, as were the Watson’s U2 test and the Large-sample Mardia–Watson–Wheeler test (Fig. S14). The Levene’s test showed a unimodal-shaped power curve. The asymmetrical trimodal situation was, again, similar to the asymmetrical bimodal situation (Fig. S15), with the exception of the Levene’s test, which showed steady power increase with angular difference (instead of the hump-shaped curve).Power to detect differences in distribution typeWhen comparing a unimodal and an axial bimodal distribution, which increased similarly in concentration, we found that the MANOVA approach again offered the best power in particular at low samples sizes, followed by the Watson’s U2 test, the Large-sample Mardia–Watson–Wheeler test and Watson–Wheeler test (Fig. 5). While the embedding approach ANOVA and the Levene’s test had varying but usable power levels, the concentration test was only sensitive to such differences at low concentration values. The Rao polar test was not sensitive to such differences.Figure 5Power of all included tests when comparing von Mises distributions of differing number of modes (unimodal and axially bimodal) using different sample sizes: 10 and 20 (A), 20 and 40 (B), 50 and 100 (C), 20 and 60 (D) and 10 and 100 (E). The concentration (κ) of both increases from 0 to 8.Full size imageThe picture was only marginally different when comparing a von Mises with a wrapped skew-normal distribution (Fig. S16). For low sample sizes (n = 10) the MANOVA approach offered great power, followed by the embedding approach ANOVA. The latter offered good power throughout the range of sample sizes tested, followed by the Watson’s U2 test, the Large-sample Mardia–Watson–Wheeler test and Levene’s test. Also, the Rao polar test showed lower, but acceptable sensitivity to distribution type. The concentration test only showed very low power, that (as expected) increased with increasing concentrations of the respective distributions.We summarize the results obtained in the power analysis in Table 2. In all situations, either the Watson’s U2 test or the MANOVA approach offered the best power.Table 2 Ranking of tests based on the power comparisons for the main scenarios encountered in potential data sets (using different distributions: unimodal, axial, asymmetrical bimodal, symmetrical trimodal, asymmetrical trimodal), in cases were only one test performed acceptable the others ranks were left blank (see Table 1 for abbreviations).Full size tableReal data examplesTesting the performance of the robust tests on real data sets revealed, predominantly, the expected test behavior. In the example of homing pigeons where a difference in concentration was expected, all tests, with the exception of the Rao polar test and, notably, the concentration test, showed a significant difference between the distributions (Fig. 6A). Therefore, we can conclude, in accordance with the respective publication19, that sectioning of the olfactory nerve disrupted the homing behavior of pigeons.Figure 6Results from example data. Shown are results of pigeon (A), ant (B) and bat orientations (C). Control groups are on the left panels and experimental groups on the right. The tests are abbreviated according to Table 1, significant test results are indicated in red with asterisk and non-significant in blue. For each circular plot directional data is shown as dots on the circle (each dot is one individual), the arrows represent the mean direction and the dashed line the 95% confidence interval.Full size imageIn the ant example, where no difference between the groups was expected, there was no significant difference between the distributions detected by most of the tests (Fig. 6B). Only the concentration test showed a significant difference. Based on the other tests we would conclude that there was no biological meaningful difference between the two distributions. Therefore, ants appear to be able to transfer visual information from one eye to the other.In the bat example, where a difference in mean direction was expected, the Watson’s U2, the Mardia–Watson–Wheeler, Watson-Wheeler test and the MANOVA approach showed a significant difference (Fig. 6C). Notably, the Rao polar, Levene’s, and concentration tests and the embedding approach ANOVA failed to show a significant difference. At least for the Rao polar test, one would have expected a significant difference, as the two distributions are clearly 180° apart. This outcome concurs with our simulation results where the Rao polar test failed to distinguish distributions on the same and orthogonal axes (Fig. 4). As the results of the tests where quite mixed this example highlights the need for choosing a test with appropriate power to detect the expected differences. Based on the results of the most powerful tests, we conclude that the bats showed a mirrored orientation, as expected in the experimental design. More