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.

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.

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.

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.

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.

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.

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.

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.

The dicey dinner dilemma: Asymmetry in predator-prey risk-taking, a broadly applicable alternative to the life-dinner principle.

Forty years ago, the 'life-dinner principle' was proposed as an example of an asymmetry that may lead prey species to experience stronger selection than their predators, thus accounting for the high frequency with which prey escape alive from interaction with a predator. This principle remains an influential concept in the scientific literature, despite several works suggesting that the concept relies on many under-appreciated assumptions and does not apply as generally as was initially proposed. Here, we present a novel model describing a very different asymmetry to that proposed in the life-dinner principle, but one that could apply broadly. We argue that asymmetries between the relative costs and benefits to predators and prey of selecting a risky behaviour during an extended predator-prey encounter could lead to an enhanced likelihood of escape for the prey. Any resulting advantage to prey depends upon there being a behaviour or choice that introduces some inherent danger to both predator and prey if they adopt it, but which if the prey adopts the predator must match in order to have a chance of successful predation. We suggest that the circumstances indicated by our model could apply broadly across diverse taxa, including both risky spatial or behavioural choices.

A theory for investment across defences triggered at different stages of a predator-prey encounter.

We introduce a general theoretical description of a combination of defences acting sequentially at different stages in the predatory sequence in order to make predictions about how animal prey should best allocate investment across different defensive stages. We predict that defensive investment will often be concentrated at stages early in the interaction between a predator individual and the prey (especially if investment is concentrated in only one defence, then it will be in the first defence). Key to making this prediction is the assumption that there is a cost to a prey when it has a defence tested by an enemy, for example because this incurs costs of deployment or tested costs as a defence is exposed to the enemies; and the assumption that the investment functions are the same among defences. But if investment functions are different across defences (e.g. the investment efficiency in making resources into defences is higher in later defences than in earlier defences), then the contrary could happen. The framework we propose can be applied to other victim-exploiter systems, such as insect herbivores feeding on plant tissues. This leads us to propose a novel explanation for the observation that herbivory damage is often not well explained by variation in concentrations of toxic plant secondary metabolites. We compare our general theoretical structure with related examples in the literature, and conclude that coevolutionary approaches will be profitable in future work.

Adaptive suicide: is a kin-selected driver of fatal behaviours likely?

While several manipulated host behaviours are accepted as extended phenotypes of parasites, there remains debate over whether other altered behaviours in hosts following parasitic invasion represent cases of parasite manipulation, host defence or the pathology of infection. One particularly controversial subject is 'suicidal behaviour' in infected hosts. The host-suicide hypothesis proposes that host death benefits hosts doomed to reduced direct fitness by protecting kin from parasitism and therefore increasing inclusive fitness. However, adaptive suicide has been difficult to demonstrate conclusively as a host adaptation in studies on social or clonal insects, for whom high relatedness should enable greater inclusive fitness benefits. Following discussion of empirical and theoretical works from a behavioural ecology perspective, this review finds that the most persuasive evidence for selection of adaptive suicide comes from bacteria. Despite a focus on parasites, driven by the existing literature, the potential for the evolution of adaptive suicidal behaviour in hosts is also considered to apply to cases of infection by pathogens, provided that the disease has a severe effect on direct fitness and that suicidal behaviour can affect pathogen transmission dynamics. Suggestions are made for future research and a broadening of the possible implications for coevolution between parasites and hosts.

Underestimation of Pearson's product moment correlation statistic.

Pearson's product moment correlation coefficient (more commonly Pearson's r) tends to underestimate correlations that exist in the underlying population. This phenomenon is generally unappreciated in studies of ecology, although a range of corrections are suggested in the statistical literature. The use of Pearson's r as the classical measure for correlation is widespread in ecology, where manipulative experiments are impractical across the large spatial scales concerned; it is therefore vital that ecologists are able to use this correlation measure as effectively as possible. Here, our literature review suggests that corrections for the issue of underestimation in Pearson's r should not be adopted if either the data deviate from bivariate normality or sample size is greater than around 30. Through our simulations, we then aim to offer advice to researchers in ecology on situations where both distributions can be described as normal, but sample sizes are lower than around 30. We found that none of the methods currently offered in the literature to correct the underestimation bias offer consistently reliable performance, and so we do not recommend that they be implemented when making inferences about the behaviour of a population from a sample. We also suggest that, when considering the importance of the bias towards underestimation in Pearson's product moment correlation coefficient for biological conclusions, the likely extent of the bias should be discussed. Unless sample size is very small, the issue of sample bias is unlikely to call for substantial modification of study conclusions.

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.

Optimizing countershading camouflage.

Countershading, the widespread tendency of animals to be darker on the side that receives strongest illumination, has classically been explained as an adaptation for camouflage: obliterating cues to 3D shape and enhancing background matching. However, there have only been two quantitative tests of whether the patterns observed in different species match the optimal shading to obliterate 3D cues, and no tests of whether optimal countershading actually improves concealment or survival. We use a mathematical model of the light field to predict the optimal countershading for concealment that is specific to the light environment and then test this prediction with correspondingly patterned model "caterpillars" exposed to avian predation in the field. We show that the optimal countershading is strongly illumination-dependent. A relatively sharp transition in surface patterning from dark to light is only optimal under direct solar illumination; if there is diffuse illumination from cloudy skies or shade, the pattern provides no advantage over homogeneous background-matching coloration. Conversely, a smoother gradation between dark and light is optimal under cloudy skies or shade. The demonstration of these illumination-dependent effects of different countershading patterns on predation risk strongly supports the comparative evidence showing that the type of countershading varies with light environment.

Why war is a man's game.

Interest in the evolutionary origins and drivers of warfare in ancient and contemporary small-scale human societies has greatly increased in the last decade, and has been particularly spurred by exciting archaeological discoveries that suggest our ancestors led more violent lives than previously documented. However, the striking observation that warfare is an almost-exclusively male activity remains unexplained. Three general hypotheses have been proposed, concerning greater male effectiveness in warfare, lower male costs, and patrilocality. But while each of these factors might explain why warfare is more common in men, they do not convincingly explain why women almost never participate. Here, we develop a mathematical model to formally assess these hypotheses. Surprisingly, we find that exclusively male warfare may evolve even in the absence of any such sex differences, though sex biases in these parameters can make this evolutionary outcome more likely. The qualitative observation that participation in warfare is almost exclusive to one sex is ultimately explained by the fundamentally sex-specific nature of Darwinian competition-in fitness terms, men compete with men and women with women. These results reveal a potentially key role for ancestral conditions in shaping our species' patterns of sexual division of labour and violence-related adaptations and behavioural disorders.

The evolutionary stability of attenuators that mask information about animals that social partners can exploit.

Signals and cues are fundamental to social interactions. A well-established concept in the study of animal communication is an amplifier, defined as a trait that does not add extra information to that already present in the original cue or signal, but rather enhances the fidelity with which variation in the original cue or signal is correctly perceived. Attenuators as the logical compliment of amplifiers: attenuators act to reduce the fidelity with which variation in a signal or cue can be reliably evaluated by the perceivers. Where amplifiers reduce the effect of noise on the perception of variation, attenuators add noise. Attenuators have been subject to much less consideration than amplifiers; however, they will be the focus of our theoretical study. We utilize an extension of a well-established model incorporated signal or cue inaccuracy and costly investments by emitter and perceiver in sending and attending to the signal or cue. We present broad conditions involving some conflict of interest between emitter and perceiver where it may be advantageous for emitters to invest in costly attenuators to mask cues from potential perceivers, and a subset of these conditions where the perceiver may be willing to invest in costly anti-attenuators to mitigate the loss of information to them. We demonstrate that attenuators can be evolutionary stable even if they are costly, even if they are sometimes disadvantageous and even if a perceiver can mount counter-measures to them. As such, we feel that attenuators of cues may be deserving of much more research attention.

Statistical model specification and power: recommendations on the use of test-qualified pooling in analysis of experimental data.

A common approach to the analysis of experimental data across much of the biological sciences is test-qualified pooling. Here non-significant terms are dropped from a statistical model, effectively pooling the variation associated with each removed term with the error term used to test hypotheses (or estimate effect sizes). This pooling is only carried out if statistical testing on the basis of applying that data to a previous more complicated model provides motivation for this model simplification; hence the pooling is test-qualified. In pooling, the researcher increases the degrees of freedom of the error term with the aim of increasing statistical power to test their hypotheses of interest. Despite this approach being widely adopted and explicitly recommended by some of the most widely cited statistical textbooks aimed at biologists, here we argue that (except in highly specialized circumstances that we can identify) the hoped-for improvement in statistical power will be small or non-existent, and there is likely to be much reduced reliability of the statistical procedures through deviation of type I error rates from nominal levels. We thus call for greatly reduced use of test-qualified pooling across experimental biology, more careful justification of any use that continues, and a different philosophy for initial selection of statistical models in the light of this change in procedure.