Perspective on statistical power and equivalence tests.

The use of both sexes or genders should be considered in experimental design, analysis, and reporting. Since there is no requirement to double the sample size or to have sufficient power to study sex differences, challenges for the statistical analysis can arise. In this article, we focus on the topics of statistical power and ways to increase this power. We also discuss the choice of an appropriate design and statistical method and include a separate section on equivalence tests needed to show the absence of a relevant difference.

Virtual prey with Lévy motion are preferentially attacked by predatory fish.

Of widespread interest in animal behavior and ecology is how animals search their environment for resources, and whether these search strategies are optimal. However, movement also affects predation risk through effects on encounter rates, the conspicuousness of prey, and the success of attacks. Here, we use predatory fish attacking a simulation of virtual prey to test whether predation risk is associated with movement behavior. Despite often being demonstrated to be a more efficient strategy for finding resources such as food, we find that prey displaying Lévy motion are twice as likely to be targeted by predators than prey utilizing Brownian motion. This can be explained by the predators, at the moment of the attack, preferentially targeting prey that were moving with straighter trajectories rather than prey that were turning more. Our results emphasize that costs of predation risk need to be considered alongside the foraging benefits when comparing different movement strategies.

Evaluating the power of a recent method for comparing two circular distributions: an alternative to the Watson U2 test.

Some data are collected on circular (rather than linear) scales. Often researchers are interested in comparing two samples of such circular data to test the hypothesis that they came from the same underlying population. Recently, we compared 18 statistical approaches to testing such a hypothesis, and recommended two as particularly effective. A very recent publication introduced a novel statistical approach that was claimed to outperform the methods that we had indicated were highest performing. However, the evidence base for this claim was limited. Here we perform simulation studies to offer a more detailed comparison of the new "Angular Randomisation Test" (ART) with existing tests. We expand previous evaluations in two ways: exploring small and medium sized samples, and exploring a range of different shapes for the underlying distribution(s). We find that the ART controls type I error rates at the nominal level. The ART had greater power than established methods in detecting a difference in underlying distribution caused by a shift around the circle. Its performance advantage in this case was strongest when samples where small and unbalanced in size. When the difference between underlying unimodal distributions was in shape rather than central tendency, then the ART was at least as good (and sometimes considerably more powerful) than the established methods, except when distributions samples were small and uneven in size, and the smaller sample came from a more concentrated underlying distribution. In such cases its power could be markedly inferior to established alternatives. The ART was also inferior to alternatives in dealing with axially distributed data. We conclude that under widely-encountered circumstances the ART test can be recommended for its simplicity of implementation, but researchers should be aware of situations where it cannot be recommended.

Evolutionarily stable levels of aposematic defence in prey populations.

Our understanding of aposematism (the conspicuous signalling of a defence for the deterrence of predators) has advanced notably since its first observation in the late nineteenth century. Indeed, it extends the scope of a well-established game-theoretical model of this very same process both from the analytical standpoint (by considering regimes of varying background mortality and colony size) and from the practical standpoint (by assessing its efficacy and limitations in predicting the evolution of prey traits in finite simulated populations). The nature of the manuscript at hand is more mathematical and its aim is two-fold: first, to determine the relationship between evolutionarily stable levels of defence and signal strength under various regimes of background mortality and colony size. Second, to compare these predictions with simulations of finite prey populations that are subject to random local mutation. We compare the roles of absolute resident fitness, mutant fitness and stochasticity in the evolution of prey traits and discuss the importance of population size in the above.

Investigating and preventing scientific misconduct using Benford's Law.

Integrity and trust in that integrity are fundamental to academic research. However, procedures for monitoring the trustworthiness of research, and for investigating cases where concern about possible data fraud have been raised are not well established. Here we suggest a practical approach for the investigation of work suspected of fraudulent data manipulation using Benford's Law. This should be of value to both individual peer-reviewers and academic institutions and journals. In this, we draw inspiration from well-established practices of financial auditing. We provide synthesis of the literature on tests of adherence to Benford's Law, culminating in advice of a single initial test for digits in each position of numerical strings within a dataset. We also recommend further tests which may prove useful in the event that specific hypotheses regarding the nature of data manipulation can be justified. Importantly, our advice differs from the most common current implementations of tests of Benford's Law. Furthermore, we apply the approach to previously-published data, highlighting the efficacy of these tests in detecting known irregularities. Finally, we discuss the results of these tests, with reference to their strengths and limitations.

The price of defence: toxins, visual signals and oxidative state in an aposematic butterfly.

In a variety of aposematic species, the conspicuousness of an individual's warning signal and the quantity of its chemical defence are positively correlated. This apparent honest signalling is predicted by resource competition models which assume that the production and maintenance of aposematic defences compete for access to antioxidant molecules that have dual functions as pigments and in protecting against oxidative damage. To test for such trade-offs, we raised monarch butterflies (Danaus plexippus) on different species of their milkweed host plants (Apocynaceae) that vary in quantities of cardenolides to test whether (i) the sequestration of cardenolides as a secondary defence is associated with costs in the form of oxidative lipid damage and reduced antioxidant defences; and (ii) lower oxidative state is associated with a reduced capacity to produce aposematic displays. In male monarchs conspicuousness was explained by an interaction between oxidative damage and sequestration: males with high levels of oxidative damage became less conspicuous with increased sequestration of cardenolides, whereas those with low oxidative damage became more conspicuous with increased levels of cardenolides. There was no significant effect of oxidative damage or concentration of sequestered cardenolides on female conspicuousness. Our results demonstrate a physiological linkage between the production of coloration and oxidative state, and differential costs of sequestration and signalling in monarch butterflies.

A synthesis of deimatic behaviour.

Deimatic behaviours, also referred to as startle behaviours, are used against predators and rivals. Although many are spectacular, their proximate and ultimate causes remain unclear. In this review we aim to synthesise what is known about deimatic behaviour and identify knowledge gaps. We propose a working hypothesis for deimatic behaviour, and discuss the available evidence for the evolution, ontogeny, causation, and survival value of deimatic behaviour using Tinbergen's Four Questions as a framework. Our overarching aim is to direct future research by suggesting ways to address the most pressing questions in this field.

Artificial light at night may decrease predation risk for terrestrial insects.

Artificial light at night (ALAN) is thought to be detrimental for terrestrial insect populations. While there exists evidence for lower abundance under ALAN, underlying mechanisms remain unclear. One mechanism by which ALAN may contribute to insect declines may be through facilitating increased predation. We investigated this by experimentally manipulating insect-substitute abundance under differential levels of light. We used insect-containing birdfeed placed at varying distances from streetlights as a proxy for terrestrial insects, inspecting the rate of predation before and after dusk (when streetlights are, respectively, off and on). We found that there was a significantly greater effect of increasing distance on predation after dusk, suggesting that predation was actually reduced by greater levels of artificial light. This may occur because ALAN also increases the vulnerability of insectivores to their own predators. Implications for foraging behaviour and alternative explanations are discussed.

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

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.

The Effects of Local Enhancement on Mean Food Uptake Rate.

AbstractA forager searching for food can cue on a distant feeding group to infer the location of a food patch it could share. This behavior, known as local enhancement, reduces variance in time between meals, but its effect on long-term uptake rate is less resolved. An influential simulation study concluded that benefits through reduced variance would be mitigated by reduced long-term uptake rate. This cost comes about through spatial clumping of foragers, leading to overlapping search paths and, thus, reduced aggregate patch finding. Here, we revise the previous model and submit it to more extensive investigation. Our simulations reveal that local enhancement can increase mean uptake rates but only when food patches are scarce in the environment. Contrary to previous speculations, we do not find that high-value patches or strong heterogeneity in patch quality strengthens this potential added benefit to local enhancement. As such, our simulations delineate situations where selection pressures based on maximizing long-term uptake rate act antagonistically or synergistically with starvation-avoidance through reduced temporal variance in feeding.

Incorporating thermodynamics in predator-prey games predicts the diel foraging patterns of poikilothermic predators.

Models of foraging behaviour typically assume that prey do not adapt to temporal variation in predation risk, such as by avoiding foraging at certain times of the day. When this behavioural plasticity is considered-such as in predator-prey games-the role of abiotic factors is usually ignored. An abiotic factor that exerts strong influence on the physiology and behaviour of many animals is ambient temperature, although it is often ignored from game models as it is implicitly assumed that both predators and prey are homothermic. However, poikilotherms' performance may be reduced in cold conditions due to reduced muscle function, limiting the prey-capture ability of predators and the predator-avoidance and foraging abilities of prey. Here, we use a game-theoretic predator-prey model in which diel temperature changes influence foraging gains and costs to predict the evolutionarily stable diel activity of predators. Our model predicts the range of patterns observed in nature, including nocturnal, diurnal, crepuscular and a previously unexplained post-sunset crepuscular pattern observed in some sharks. In general, smaller predators are predicted to be more diurnal than larger ones. The safety of prey when not foraging is critical, explaining why predators in coral reef systems (with safe refuges) may often have different foraging patterns to pelagic predators. We make a range of testable predictions that will enable the further evaluation of this theoretical framework for understanding diel foraging patterns in poikilotherms.

An ecological perspective on water shedding from leaves.

Water shedding from leaves is a complex process depending on multiple leaf traits interacting with rain, wind, and air humidity, and with the entire plant and surrounding vegetation. Here, we synthesize current knowledge of the physics of water shedding with implications for plant physiology and ecology. We argue that the drop retention angle is a more meaningful parameter to characterize the water-shedding capacity of leaves than the commonly measured static contact angle. The understanding of the mechanics of water shedding is largely derived from laboratory experiments on artificial rather than natural surfaces, often on individual aspects such as surface wettability or drop impacts. In contrast, field studies attempting to identify the adaptive value of leaf traits linked to water shedding are largely correlative in nature, with inconclusive results. We make a strong case for taking the hypothesis-driven experimental approach of biomechanical laboratory studies into a real-world field setting to gain a comprehensive understanding of leaf water shedding in a whole-plant ecological and evolutionary context.

Why Students Cheat and How Understanding This Can Help Reduce the Frequency of Academic Misconduct in Higher Education: A Literature Review.

Academic integrity is fundamental to effective education and learning yet cheating continues to occur in diverse forms within the higher education sector. It is essential that students are educated about, and understand the importance of, good academic practice. Strict standards of academic integrity help to ensure that knowledge is acquired in an honest and ethical manner, creating fairness and equity for students, ultimately enriching the student experience at university and the wider society's trust in the value of university education. This literature review synthesizes the many varied reasons why students cheat, as presented in a large body of existing literature. We then turn our attention to what we can do as educators to help reduce the rates of academic misconduct. Factors influencing the propensity of students to cheat are diverse but relatively well understood. Whilst policing and applying appropriate punishments should be part of institutional responses to academic misconduct, it is clear that this is only part of the solution. We emphasize the need for a much broader range of proactive activities to be brought to bear. Many of these are educational in nature and should have benefits for students, staff and institutions beyond discouraging academic misconduct. Resource implication should not be a barrier to their implementation.

Advice on comparing two independent samples of circular data in biology.

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.

Turn alternation and the influence of environmental factors on search routes through branched structures by ladybirds (Coccinella septempunctata and Adalia bipunctata).

Turn alternation is a locomotory behaviour wherein an animal makes consecutive turns in opposite directions (left-then-right or right-then-left). It has been suggested that its adaptive function is to maintain locomotion in a relatively constant general direction while negotiating obstacles. Previous work has focussed on the use of turn alternation in prey species in artificial horizontal mazes. In the first study presented here, we tested whether predatory seven-spot ladybirds (Coccinella septempunctata) exhibit turn alternation when repeatedly presented with consecutive choice turning decisions on vertically oriented twigs. Our findings suggest that turn alternation occurs vertically as well as horizontally, on plant structures as well as terrestrially, and in a type of animal (predatory insect) in which turn alternation has received little attention. In the second study presented here, we tested whether characteristics of branched structures explored by two-spot ladybirds (Adalia bipunctata) influence turning decisions. Our findings suggest that ladybirds exhibit preferences for thicker over thinner, straighter over more deviating headings, and higher over lower turning choice options at bifurcations. These exploratory studies indicate that while turn alternation is an observable phenomenon in ladybirds, it is not the only predictor of searching behaviour on branched structures.

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

ABSTRACT: 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. SIGNIFICANCE STATEMENT: Circular data are widespread across biological disciplines, e.g. in orientation studies or circadian rhythms. Often these data are rounded to the nearest 1-10 degrees. We have shown previously that this leads to an inflation of false-positive results when testing whether the data is significantly different from a random distribution using the Rao test. Here we present a modification that avoids this increase in false-positives for rounded data while retaining statistical power for a variety of tests. In sum, we provide comprehensive guidance on how best to test for departure from uniformity in non-continuous data.

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

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.

Camouflage in predators.

Camouflage - adaptations that prevent detection and/or recognition - is a key example of evolution by natural selection, making it a primary focus in evolutionary ecology and animal behaviour. Most work has focused on camouflage as an anti-predator adaptation. However, predators also display specific colours, patterns and behaviours that reduce visual detection or recognition to facilitate predation. To date, very little attention has been given to predatory camouflage strategies. Although many of the same principles of camouflage studied in prey translate to predators, differences between the two groups (in motility, relative size, and control over the time and place of predation attempts) may alter selection pressures for certain visual and behavioural traits. This makes many predatory camouflage techniques unique and rarely documented. Recently, new technologies have emerged that provide a greater opportunity to carry out research on natural predator-prey interactions. Here we review work on the camouflage strategies used by pursuit and ambush predators to evade detection and recognition by prey, as well as looking at how work on prey camouflage can be applied to predators in order to understand how and why specific predatory camouflage strategies may have evolved. We highlight that a shift is needed in camouflage research focus, as this field has comparatively neglected camouflage in predators, and offer suggestions for future work that would help to improve our understanding of camouflage.