Estimating genetic benefits of polyandry from experimental studies: a meta‐analysis

The consequences of polyandry for female fitness are controversial. Sexual conflict studies and a meta‐analysis of mating rates in insects suggest that there is a longevity cost when females mate repeatedly. Even so, compensatory material benefits can elevate egg production and fertility, partly because polyandry ensures an adequate sperm supply. Polyandry can therefore confer direct benefits. The main controversy surrounds genetic benefits. The argument is analogous to that surrounding the evolution of conventional female mate choice, except that with polyandry it is post‐copulatory mechanisms that might bias paternity towards males with higher breeding values for fitness. Recent meta‐analyses of extra‐pair copulations in birds have cast doubt on whether detectable genetic benefits exist. By contrast, another meta‐analysis showed that polyandry elevates egg hatching success (possibly due to a fertilization bias towards sperm with paternal genes that elevate embryo survival) in insects. A detailed summary of whether polyandry elevates other components of offspring performance is lacking. Here we present a comprehensive meta‐analysis of 232 effect sizes from 46 experimental studies. These experiments were specifically designed to try to quantify the potential genetic benefits of polyandry by controlling fully for the number of matings by females assigned to monandry and polyandry treatments. The bias‐corrected 95% confidence intervals for egg hatching success (d = ?0.01 to 0.61), clutch production (d = 0.07 to 0.45) and fertility (d = 0.04 to 0.40) all suggest that polyandry has a beneficial effect (although P values from parametric tests were marginally non‐significant at P = 0.075, 0.052 and 0.058, respectively). Polyandry was not significantly beneficial for any single offspring performance trait (e.g. growth rate, survival, adult size), but the test power was low due to small sample sizes (suggesting that many more studies are still needed). We then calculated a composite effect size that provides an index of general offspring performance. Depending on the model assumptions, the mean effect of polyandry was either significantly positive or marginally non‐significant. A possible role for publication bias is discussed. The magnitude of the reported potential genetic benefits (d = 0.07 to 0.19) are larger than those from two recent meta‐analyses comparing offspring sired by social and extra‐pair mates in birds (d = 0.02 to 0.04). This difference raises the intriguing possibility that cryptic, post‐copulatory female choice might be more likely to generate ‘good gene’ or ‘compatible gene’ benefits than female choice of mates based on the expression of secondary sexual traits.     

Formalizing the definition of meta‐analysis in Molecular Ecology

Meta‐analysis, the statistical synthesis of pertinent literature to develop evidence‐based conclusions, is relatively new to the field of molecular ecology, with the first meta‐analysis published in the journal Molecular Ecology in 2003 (Slate & Phua 2003). The goal of this article is to formalize the definition of meta‐analysis for the authors, editors, reviewers and readers of Molecular Ecology by completing a review of the meta‐analyses previously published in this journal. We also provide a brief overview of the many components required for meta‐analysis with a more specific discussion of the issues related to the field of molecular ecology, including the use and statistical considerations of Wright's F_ST and its related analogues as effect sizes in meta‐analysis. We performed a literature review to identify articles published as ‘meta‐analyses’ in Molecular Ecology, which were then evaluated by at least two reviewers. We specifically targeted Molecular Ecology publications because as a flagship journal in this field, meta‐analyses published in Molecular Ecology have the potential to set the standard for meta‐analyses in other journals. We found that while many of these reviewed articles were strong meta‐analyses, others failed to follow standard meta‐analytical techniques. One of these unsatisfactory meta‐analyses was in fact a secondary analysis. Other studies attempted meta‐analyses but lacked the fundamental statistics that are considered necessary for an effective and powerful meta‐analysis. By drawing attention to the inconsistency of studies labelled as meta‐analyses, we emphasize the importance of understanding the components of traditional meta‐analyses to fully embrace the strengths of quantitative data synthesis in the field of molecular ecology.     

Variable reporting and quantitative reviews: a comparison of three meta-analytical techniques

Variable reporting of results can influence quantitative reviews by limiting the number of studies for analysis, and thereby influencing both the type of analysis and the scope of the review. We performed a Monte Carlo simulation to determine statistical errors for three meta‐analytical approaches and related how such errors were affected by numbers of constituent studies. Hedges’d and effect sizes based on item response theory (IRT) had similarly improved error rates with increasing numbers of studies when there was no true effect, but IRT was conservative when there was a true effect. Log response ratio had low precision for detecting null effects as a result of overestimation of effect sizes, but high ability to detect true effects, largely irrespective of number of studies. Traditional meta‐analysis based on Hedges’d are preferred; however, quantitative reviews should use various methods in concert to improve representation and inferences from summaries of published data.     

Ignoring non‐English‐language studies may bias ecological meta‐analyses

Meta‐analysis plays a crucial role in syntheses of quantitative evidence in ecology and biodiversity conservation. The reliability of estimates in meta‐analyses strongly depends on unbiased sampling of primary studies. Although earlier studies have explored potential biases in ecological meta‐analyses, biases in reported statistical results and associated study characteristics published in different languages have never been tested in environmental sciences. We address this knowledge gap by systematically searching published meta‐analyses and comparing effect‐size estimates between English‐ and Japanese‐language studies included in existing meta‐analyses. Of the 40 published ecological meta‐analysis articles authored by those affiliated to Japanese institutions, we find that three meta‐analysis articles searched for studies in the two languages and involved sufficient numbers of English‐ and Japanese‐language studies, resulting in four eligible meta‐analyses (i.e., four meta‐analyses conducted in the three meta‐analysis articles). In two of the four, effect sizes differ significantly between the English‐ and Japanese‐language studies included in the meta‐analyses, causing considerable changes in overall mean effect sizes and even their direction when Japanese‐language studies are excluded. The observed differences in effect sizes are likely attributable to systematic differences in reported statistical results and associated study characteristics, particularly taxa and ecosystems, between English‐ and Japanese‐language studies. Despite being based on a small sample size, our findings suggest that ignoring non‐English‐language studies may bias outcomes of ecological meta‐analyses, due to systematic differences in study characteristics and effect‐size estimates between English‐ and non‐English languages. We provide a list of actions that meta‐analysts could take in the future to reduce the risk of language bias.     

Detecting and avoiding likely false‐positive findings – a practical guide

Recently there has been a growing concern that many published research findings do not hold up in attempts to replicate them. We argue that this problem may originate from a culture of ‘you can publish if you found a significant effect’. This culture creates a systematic bias against the null hypothesis which renders meta‐analyses questionable and may even lead to a situation where hypotheses become difficult to falsify. In order to pinpoint the sources of error and possible solutions, we review current scientific practices with regard to their effect on the probability of drawing a false‐positive conclusion. We explain why the proportion of published false‐positive findings is expected to increase with (i) decreasing sample size, (ii) increasing pursuit of novelty, (iii) various forms of multiple testing and researcher flexibility, and (iv) incorrect P‐values, especially due to unaccounted pseudoreplication, i.e. the non‐independence of data points (clustered data). We provide examples showing how statistical pitfalls and psychological traps lead to conclusions that are biased and unreliable, and we show how these mistakes can be avoided. Ultimately, we hope to contribute to a culture of ‘you can publish if your study is rigorous’. To this end, we highlight promising strategies towards making science more objective. Specifically, we enthusiastically encourage scientists to preregister their studies (including a priori hypotheses and complete analysis plans), to blind observers to treatment groups during data collection and analysis, and unconditionally to report all results. Also, we advocate reallocating some efforts away from seeking novelty and discovery and towards replicating important research findings of one's own and of others for the benefit of the scientific community as a whole. We believe these efforts will be aided by a shift in evaluation criteria away from the current system which values metrics of ‘impact’ almost exclusively and towards a system which explicitly values indices of scientific rigour.     

Dissemination biases in ecology: effect sizes matter more than quality

Publication and citation decisions in ecology are likely influenced by many factors, potentially including journal impact factors, direction and magnitude of reported effects, and year of publication. Dissemination bias exists when publication or citation of a study depends on any of these factors. We defined several dissemination biases and determined their prevalence across many sub‐disciplines in ecology, then determined whether or not data quality also affected these biases. We identified dissemination biases in ecology by conducting a meta‐analysis of citation trends for 3867 studies included in 52 meta‐analyses. We correlated effect size, year of publication, impact factor and citation rate within each meta‐analysis. In addition, we explored how data quality as defined in meta‐analyses (sample size or variance) influenced each form of bias. We also explored how the direction of the predicted or observed effect, and the research field, influenced any biases. Year of publication did not influence citation rates. The first papers published in an area reported the strongest effects, and high impact factor journals published the most extreme effects. Effect size was more important than data quality for many publication and citation trends. Dissemination biases appear common in ecology, and although their magnitude was generally small many were associated with theory tenacity, evidenced as tendencies to cite papers that most strongly support our ideas. The consequences of this behavior are amplified by the fact that papers reporting strong effects were often of lower data quality than papers reporting much weaker effects. Furthermore, high impact factor journals published the strongest effects, generally in the absence of any correlation with data quality. Increasing awareness of the prevalence of theory tenacity, confirmation bias, and the inattention to data quality among ecologists is a first step towards reducing the impact of these biases on research in our field.     

Facultative adjustment of the offspring sex ratio and male attractiveness: a systematic review and meta‐analysis

Females can benefit from mate choice for male traits (e.g. sexual ornaments or body condition) that reliably signal the effect that mating will have on mean offspring fitness. These male‐derived benefits can be due to material and/or genetic effects. The latter include an increase in the attractiveness, hence likely mating success, of sons. Females can potentially enhance any sex‐biased benefits of mating with certain males by adjusting the offspring sex ratio depending on their mate's phenotype. One hypothesis is that females should produce mainly sons when mating with more attractive or higher quality males. Here we perform a meta‐analysis of the empirical literature that has accumulated to test this hypothesis. The mean effect size was small (r = 0.064–0.095; i.e. explaining <1% of variation in offspring sex ratios) but statistically significant in the predicted direction. It was, however, not robust to correction for an apparent publication bias towards significantly positive results. We also examined the strength of the relationship using different indices of male attractiveness/quality that have been invoked by researchers (ornaments, behavioural displays, female preference scores, body condition, male age, body size, and whether a male is a within‐pair or extra‐pair mate). Only ornamentation and body size significantly predicted the proportion of sons produced. We obtained similar results regardless of whether we ran a standard random‐effects meta‐analysis, or a multi‐level, Bayesian model that included a correction for phylogenetic non‐independence. A moderate proportion of the variance in effect sizes (51.6–56.2%) was due to variation that was not attributable to sampling error (i.e. sample size). Much of this non‐sampling error variance was not attributable to phylogenetic effects or high repeatability of effect sizes among species. It was approximately equally attributable to differences (occurring for unknown reasons) in effect sizes among and within studies (25.3, 22.9% of the total variance). There were no significant effects of year of publication or two aspects of study design (experimental/observational or field/laboratory) on reported effect sizes. We discuss various practical reasons and theoretical arguments as to why small effect sizes should be expected, and why there might be relatively high variation among studies. Currently, there are no species where replicated, experimental studies show that mothers adjust the offspring sex ratio in response to a generally preferred male phenotype. Ultimately, we need more experimental studies that test directly whether females produce more sons when mated to relatively more attractive males, and that provide the requisite evidence that their sons have higher mean fitness than their daughters.     

What determines species richness of parasitic organisms? A meta‐analysis across animal,plant and fungal hosts

Although a small set of external factors account for much of the spatial variation in plant and animal diversity, the search continues for general drivers of variation in parasite species richness among host species. Qualitative reviews of existing evidence suggest idiosyncrasies and inconsistent predictive power for all proposed determinants of parasite richness. Here, we provide the first quantitative synthesis of the evidence using a meta‐analysis of 62 original studies testing the relationship between parasite richness across animal, plant and fungal hosts, and each of its four most widely used presumed predictors: host body size, host geographical range size, host population density, and latitude. We uncover three universal predictors of parasite richness across host species, namely host body size, geographical range size and population density, applicable regardless of the taxa considered and independently of most aspects of study design. A proper match in the primary studies between the focal predictor and both the spatial scale of study and the level at which parasite species richness was quantified (i.e. within host populations or tallied across a host species' entire range) also affected the magnitude of effect sizes. By contrast, except for a couple of indicative trends in subsets of the full dataset, there was no strong evidence for an effect of latitude on parasite species richness; where found, this effect ran counter to the general latitude gradient in diversity, with parasite species richness tending to be higher further from the equator. Finally, the meta‐analysis also revealed a negative relationship between the magnitude of effect sizes and the year of publication of original studies (i.e. a time‐lag bias). This temporal bias may be due to the increasing use of phylogenetic correction in comparative analyses of parasite richness over time, as this correction yields more conservative effect sizes. Overall, these findings point to common underlying processes of parasite diversification fundamentally different from those controlling the diversity of free‐living organisms.     

Relationships fade with time: a meta-analysis of temporal trends in publication in ecology and evolution.

Both significant positive and negative relationships between the magnitude of research findings (their 'effect size') and their year of publication have been reported in a few areas of biology. These trends have been attributed to Kuhnian paradigm shifts, scientific fads and bias in the choice of study systems. Here we test whether or not these isolated cases reflect a more general trend. We examined the relationship using effect sizes extracted from 44 peer-reviewed meta-analyses covering a wide range of topics in ecological and evolutionary biology. On average, there was a small but significant decline in effect size with year of publication. For the original empirical studies there was also a significant decrease in effect size as sample size increased. However, the effect of year of publication remained even after we controlled for sampling effort. Although these results have several possible explanations, it is suggested that a publication bias against non-significant or weaker findings offers the most parsimonious explanation. As in the medical sciences, non-significant results may take longer to publish and studies with both small sample sizes and non-significant results may be less likely to be published.     

Irreproducible text‐book “knowledge”: The effects of color bands on zebra finch fitness

Many fields of science—including behavioral ecology—currently experience a heated debate about the extent to which publication bias against null findings results in a misrepresentative scientific literature. Here, we show a case of an extreme mismatch between strong positive support for an effect in the literature and a failure to detect this effect across multiple attempts at replication. For decades, researchers working with birds have individually marked their study species with colored leg bands. For the zebra finch Taeniopygia guttata, a model organism in behavioral ecology, many studies over the past 35 years have reported effects of bands of certain colors on male or female attractiveness and further on behavior, physiology, life history, and fitness. Only eight of 39 publications presented exclusively null findings. Here, we analyze the results of eight experiments in which we quantified the fitness of a total of 730 color‐banded individuals from four captive populations (two domesticated and two recently wild derived). This sample size exceeds the combined sample size of all 23 publications that clearly support the “color‐band effect” hypothesis. We found that band color explains no variance in either male or female fitness. We also found no heterogeneity in color‐band effects, arguing against both context and population specificity. Analysis of unpublished data from three other laboratories strengthens the generality of our null finding. Finally, a meta‐analysis of previously published results is indicative of selective reporting and suggests that the effect size approaches zero when sample size is large. We argue that our field—and science in general—would benefit from more effective means to counter confirmation bias and publication bias.     

The effects of sex hormones on immune function: a meta‐analysis

The effects of sex hormones on immune function have received much attention, especially following the proposal of the immunocompetence handicap hypothesis. Many studies, both experimental and correlational, have been conducted to test the relationship between immune function and the sex hormones testosterone in males and oestrogen in females. However, the results are mixed. We conducted four cross‐species meta‐analyses to investigate the relationship between sex hormones and immune function: (i) the effect of testosterone manipulation on immune function in males, (ii) the correlation between circulating testosterone level and immune function in males, (iii) the effect of oestrogen manipulation on immune function in females, and (iv) the correlation between circulating oestrogen level and immune function in females. The results from the experimental studies showed that testosterone had a medium‐sized immunosuppressive effect on immune function. The effect of oestrogen, on the other hand, depended on the immune measure used. Oestrogen suppressed cell‐mediated immune function while reducing parasite loads. The overall correlation (meta‐analytic relationship) between circulating sex hormone level and immune function was not statistically significant for either testosterone or oestrogen despite the power of meta‐analysis. These results suggest that correlational studies have limited value for testing the effects of sex hormones on immune function. We found little evidence of publication bias in the four data sets using indirect tests. There was a weak and positive relationship between year of publication and effect size for experimental studies of testosterone that became non‐significant after we controlled for castration and immune measure, suggesting that the temporal trend was due to changes in these moderators over time. Graphical analyses suggest that the temporal trend was due to an increased use of cytokine measures across time. We found substantial heterogeneity in effect sizes, except in correlational studies of testosterone, even after we accounted for the relevant random and fixed factors. In conclusion, our results provide good evidence that testosterone suppresses immune function and that the effect of oestrogen varies depending on the immune measure used.     

Inference for binomial probability based on dependent Bernoulli random variables with applications to meta‐analysis and group level studies

We study bias arising as a result of nonlinear transformations of random variables in random or mixed effects models and its effect on inference in group‐level studies or in meta‐analysis. The findings are illustrated on the example of overdispersed binomial distributions, where we demonstrate considerable biases arising from standard log‐odds and arcsine transformations of the estimated probability , both for single‐group studies and in combining results from several groups or studies in meta‐analysis. Our simulations confirm that these biases are linear in ρ, for small values of ρ, the intracluster correlation coefficient. These biases do not depend on the sample sizes or the number of studies K in a meta‐analysis and result in abysmal coverage of the combined effect for large K. We also propose bias‐correction for the arcsine transformation. Our simulations demonstrate that this bias‐correction works well for small values of the intraclass correlation. The methods are applied to two examples of meta‐analyses of prevalence.     

Trim and fill: A simple funnel-plot-based method of testing and adjusting for publication bias in meta-analysis

We study recently developed nonparametric methods for estimating the number of missing studies that might exist in a meta-analysis and the effect that these studies might have had on its outcome. These are simple rank-based data augmentation techniques, which formalize the use of funnel plots. We show that they provide effective and relatively powerful tests for evaluating the existence of such publication bias. After adjusting for missing studies, we find that the point estimate of the overall effect size is approximately correct and coverage of the effect size confidence intervals is substantially improved, in many cases recovering the nominal confidence levels entirely. We illustrate the trim and fill method on existing meta-analyses of studies in clinical trials and psychometrics.     

Sexual selection and sperm quantity: meta‐analyses of strategic ejaculation

Multiple mating or group spawning leads to post‐copulatory sexual selection, which generally favours ejaculates that are more competitive under sperm competition. In four meta‐analyses we quantify the evidence that sperm competition (SC) favours greater sperm number using data from studies of strategic ejaculation. Differential investment into each ejaculate emerges at the individual level if males exhibit phenotypic plasticity in ejaculate properties in response to the likely risk and/or intensity of sperm competition after a given mating. Over the last twenty years, a series of theoretical models have been developed that predict how ejaculate size will be strategically adjusted in relation to: (a) the number of immediate rival males, with a distinction made between 0 versus 1 rival (‘risk’ of SC) and 1 versus several rivals (‘intensity’ of SC); (b) female mating status (virgin or previously mated); and (c) female phenotypic quality (e.g. female size or condition). Some well‐known studies have reported large adjustments in ejaculate size depending on the relevant social context and this has led to widespread acceptance of the claim that strategic sperm allocation occurs in response to each of these factors. It is necessary, however, to test each claim separately because it is easy to overlook studies with weak or negative findings. Compiling information on the variation in outcomes among species is potentially informative about the relevance of these assumptions in different taxa or mating systems. We found strong evidence that, on average, males transfer larger ejaculates to higher quality females. The effect of female mating status was less straightforward and depended on how ejaculate size was measured (i.e. use of proxy or direct measure). There is strong evidence that ejaculate size increased when males were exposed to a single rival, which is often described as a response to the risk of SC. There is, however, no evidence for the general prediction that ejaculate size decreases as the number of rivals increases from one to several males (i.e. in response to a higher intensity of SC which lowers the rate of return per sperm released). Our results highlight how meta‐analysis can reveal unintentional biases in narrative literature reviews. We note that several assumptions of theoretical models can alter an outcome's predicted direction in a given species (e.g. the effect of female mating status depends on whether there is first‐ or last‐male sperm priority). Many studies do not provide this background information and fail to make strong a priori predictions about the expected response of ejaculate size to manipulation of the mating context. Researchers should be explicit about which model they are testing to ensure that future meta‐analyses can better partition studies into different categories, or control for continuous moderator variables.     

Using conditional power of network meta‐analysis (NMA) to inform the design of future clinical trials

Clinical trials are typically designed with an aim to reach sufficient power to test a hypothesis about relative effectiveness of two or more interventions. Their role in informing evidence‐based decision‐making demands, however, that they are considered in the context of the existing evidence. Consequently, their planning can be informed by characteristics of relevant systematic reviews and meta‐analyses. In the presence of multiple competing interventions the evidence base has the form of a network of trials, which provides information not only about the required sample size but also about the interventions that should be compared in a future trial. In this paper we present a methodology to evaluate the impact of new studies, their information size, the comparisons involved, and the anticipated heterogeneity on the conditional power (CP) of the updated network meta‐analysis. The methods presented are an extension of the idea of CP initially suggested for a pairwise meta‐analysis and we show how to estimate the required sample size using various combinations of direct and indirect evidence in future trials. We apply the methods to two previously published networks and we show that CP for a treatment comparison is dependent on the magnitude of heterogeneity and the ratio of direct to indirect information in existing and future trials for that comparison. Our methodology can help investigators calculate the required sample size under different assumptions about heterogeneity and make decisions about the number and design of future studies (set of treatments compared).     

Publication Bias in Psychology: A Diagnosis Based on the Correlation between Effect Size and Sample Size

Background

The p value obtained from a significance test provides no information about the magnitude or importance of the underlying phenomenon. Therefore, additional reporting of effect size is often recommended. Effect sizes are theoretically independent from sample size. Yet this may not hold true empirically: non-independence could indicate publication bias.

Methods

We investigate whether effect size is independent from sample size in psychological research. We randomly sampled 1,000 psychological articles from all areas of psychological research. We extracted p values, effect sizes, and sample sizes of all empirical papers, and calculated the correlation between effect size and sample size, and investigated the distribution of p values.

Results

We found a negative correlation of r = −.45 [95% CI: −.53; −.35] between effect size and sample size. In addition, we found an inordinately high number of p values just passing the boundary of significance. Additional data showed that neither implicit nor explicit power analysis could account for this pattern of findings.

Conclusion

The negative correlation between effect size and samples size, and the biased distribution of p values indicate pervasive publication bias in the entire field of psychology.     

Stress and Adiposity: A Meta‐Analysis of Longitudinal Studies

Psychosocial stress has been strongly implicated in the biology of adiposity but epidemiological studies have produced inconsistent results. The aim of this analysis was to bring together results from published, longitudinal, prospective studies examining associations between psychosocial stress and objectively measured adiposity in a meta‐analysis. Searches were conducted on Medline, PsycINFO, Web of Science, and PubMed (to January 2009) and reference lists from relevant articles were examined. Prospective studies relating psychosocial stress (general life stress (including caregiver stress), work stress) to BMI, body fat, body weight, waist circumference, or waist‐to‐hip ratio were included. Analyses from 14 cohorts were collated and evaluated. There was no significant heterogeneity, no evidence of publication bias, and no association between study quality and outcomes. The majority of analyses found no significant relationship between stress and adiposity (69%), but among those with significant effects, more found positive than negative associations (25 vs. 6%). Combining results in a meta‐analysis showed that stress was associated with increasing adiposity (r = 0.014; confidence interval (CI) = 0.002–0.025, P < 0.05). Effects were stronger for men than women, in analyses with longer rather than shorter follow‐ups, and in better quality studies. We conclude that psychosocial stress is a risk factor for weight gain but effects are very small. Variability across studies indicates there are moderating variables to be elucidated.     

Assessing the effect of elevated carbon dioxide on soil carbon: a comparison of four meta-analyses

Soil is the largest reservoir of organic carbon (C) in the terrestrial biosphere and soil C has a relatively long mean residence time. Rising atmospheric carbon dioxide (CO₂) concentrations generally increase plant growth and C input to soil, suggesting that soil might help mitigate atmospheric CO₂ rise and global warming. But to what extent mitigation will occur is unclear. The large size of the soil C pool not only makes it a potential buffer against rising atmospheric CO₂, but also makes it difficult to measure changes amid the existing background. Meta‐analysis is one tool that can overcome the limited power of single studies. Four recent meta‐analyses addressed this issue but reached somewhat different conclusions about the effect of elevated CO₂ on soil C accumulation, especially regarding the role of nitrogen (N) inputs. Here, we assess the extent of differences between these conclusions and propose a new analysis of the data. The four meta‐analyses included different studies, derived different effect size estimates from common studies, used different weighting functions and metrics of effect size, and used different approaches to address nonindependence of effect sizes. Although all factors influenced the mean effect size estimates and subsequent inferences, the approach to independence had the largest influence. We recommend that meta‐analysts critically assess and report choices about effect size metrics and weighting functions, and criteria for study selection and independence. Such decisions need to be justified carefully because they affect the basis for inference. Our new analysis, with a combined data set, confirms that the effect of elevated CO₂ on net soil C accumulation increases with the addition of N fertilizers. Although the effect at low N inputs was not significant, statistical power to detect biogeochemically important effect sizes at low N is limited, even with meta‐analysis, suggesting the continued need for long‐term experiments.     

The association between Barrett's esophagus and Helicobacter pylori infection: a meta-analysis

Objective: The effect of Helicobacter pylori on Barrett’s esophagus is poorly understood. We conducted a meta‐analysis to summarize the existing literature examining the effect that H. pylori has on Barrett’s esophagus. Design: We performed a comprehensive search to identify studies pertaining to the association between H. pylori and Barrett’s esophagus. We conducted meta‐regression analyses to identify sources of variation in the effect of H. pylori on Barrett’s esophagus. Results: Our analysis included a total of 49 studies that examined the effect of H. pylori on Barrett’s esophagus and seven studies that examined the effect of cag A positivity on Barrett’s esophagus. Overall, H. pylori, and even more so cag A, tended to be protective for Barrett’s esophagus in most studies; however, there was obvious heterogeneity across studies. The effect of H. pylori on Barrett’s esophagus varied by geographic location and in the presence of selection and information biases. Only four studies were found without obvious selection and information bias, and these showed a protective effect of H. pylori on Barrett’s esophagus (Relative risk = 0.46 [95% CI: 0.35, 0.60]). Conclusions: Estimates for the effect of H. pylori on Barrett’s esophagus were heterogeneous across studies. We identified selection and information bias as potential sources of this heterogeneity. Few studies without obvious selection and information bias have been conducted to examine the effect of H. pylori on Barrett’s esophagus, but in these, H. pylori infection is associated with a reduced risk of Barrett’s esophagus.     

A quantitative review of MHC‐based mating preference: the role of diversity and dissimilarity

Sexual selection hypotheses stipulate that the major histocompatibility complex genes (MHC) constitute a key molecular underpinning for mate choice in vertebrates. The last four decades saw growing empirical literature on the role of MHC diversity and dissimilarity in mate choice for a wide range of vertebrate animals, but with mixed support for its significance in natural populations. Using formal phylogenetic meta‐analysis and meta‐regression techniques, we quantitatively review the existing literature on MHC‐dependent mating preferences in nonhuman vertebrates with a focus on the role of MHC diversity and dissimilarity. Overall, we found small, statistically nonsignificant, average effect sizes for both diversity‐ and dissimilarity‐based mate choice (r = 0.113 and 0.064, respectively). Importantly, however, meta‐regression models revealed statistically significant support regarding female choice for diversity, and choice for dissimilarity (regardless of choosy sex) only when dissimilarity is characterized across multiple loci. Little difference was found among vertebrate taxa; however, the lack of statistical power meant statistically significant effects were limited to some taxa. We found little sign of publication bias; thus, our results are likely to be robust. In light of our quantitative assessment, methodological improvements and fruitful future avenues of research are highlighted.