Adjusting for publication bias in meta-analysis via inverse probability weighting using clinical trial registries

Publication bias is a major concern in conducting systematic reviews and meta-analyses. Various sensitivity analysis or bias-correction methods have been developed based on selection models, and they have some advantages over the widely used trim-and-fill bias-correction method. However, likelihood methods based on selection models may have difficulty in obtaining precise estimates and reasonable confidence intervals, or require a rather complicated sensitivity analysis process. Herein, we develop a simple publication bias adjustment method by utilizing the information on conducted but still unpublished trials from clinical trial registries. We introduce an estimating equation for parameter estimation in the selection function by regarding the publication bias issue as a missing data problem under the missing not at random assumption. With the estimated selection function, we introduce the inverse probability weighting (IPW) method to estimate the overall mean across studies. Furthermore, the IPW versions of heterogeneity measures such as the between-study variance and the I² measure are proposed. We propose methods to construct confidence intervals based on asymptotic normal approximation as well as on parametric bootstrap. Through numerical experiments, we observed that the estimators successfully eliminated bias, and the confidence intervals had empirical coverage probabilities close to the nominal level. On the other hand, the confidence interval based on asymptotic normal approximation is much wider in some scenarios than the bootstrap confidence interval. Therefore, the latter is recommended for practical use.     

p-Curve and p-Hacking in Observational Research

The p-curve, the distribution of statistically significant p-values of published studies, has been used to make inferences on the proportion of true effects and on the presence of p-hacking in the published literature. We analyze the p-curve for observational research in the presence of p-hacking. We show by means of simulations that even with minimal omitted-variable bias (e.g., unaccounted confounding) p-curves based on true effects and p-curves based on null-effects with p-hacking cannot be reliably distinguished. We also demonstrate this problem using as practical example the evaluation of the effect of malaria prevalence on economic growth between 1960 and 1996. These findings call recent studies into question that use the p-curve to infer that most published research findings are based on true effects in the medical literature and in a wide range of disciplines. p-values in observational research may need to be empirically calibrated to be interpretable with respect to the commonly used significance threshold of 0.05. Violations of randomization in experimental studies may also result in situations where the use of p-curves is similarly unreliable.     

Publication Bias in Recent Meta-Analyses

Introduction

Positive results have a greater chance of being published and outcomes that are statistically significant have a greater chance of being fully reported. One consequence of research underreporting is that it may influence the sample of studies that is available for a meta-analysis. Smaller studies are often characterized by larger effects in published meta-analyses, which can be possibly explained by publication bias. We investigated the association between the statistical significance of the results and the probability of being included in recent meta-analyses.

Methods

For meta-analyses of clinical trials, we defined the relative risk as the ratio of the probability of including statistically significant results favoring the treatment to the probability of including other results. For meta-analyses of other studies, we defined the relative risk as the ratio of the probability of including biologically plausible statistically significant results to the probability of including other results. We applied a Bayesian selection model for meta-analyses that included at least 30 studies and were published in four major general medical journals (BMJ, JAMA, Lancet, and PLOS Medicine) between 2008 and 2012.

Results

We identified 49 meta-analyses. The estimate of the relative risk was greater than one in 42 meta-analyses, greater than two in 16 meta-analyses, greater than three in eight meta-analyses, and greater than five in four meta-analyses. In 10 out of 28 meta-analyses of clinical trials, there was strong evidence that statistically significant results favoring the treatment were more likely to be included. In 4 out of 19 meta-analyses of observational studies, there was strong evidence that plausible statistically significant outcomes had a higher probability of being included.

Conclusions

Publication bias was present in a substantial proportion of large meta-analyses that were recently published in four major medical journals.     

Evaluation of the Kullback-Leibler Discrepancy for Model Selection in Open Population Capture-Recapture Models

The objective of this paper is to introduce the logical basis of AIC-based model selection to persons analyzing capture-recapture data and to explore the key theorettical aspect of AIC based model selection, for open-model capture-recapture, needed for AIC to perform well in this context. Almost all previous work on AIC assumes a Gaussian model; that assumption does not hold for capture-recapture models. Assuming the Cormack-Jolly-Seber model as the true model, we used numerical methods to evaluate the expectation of the log-likelihood relative to Akaike's target predictive log-likelihood. The use of this particular target criterion was motivated by the idea of using the Kullback-Leibler discrepancy for model selection, for which Akaike found the bias of the sample log-likelihood was asymptotically K, where K = the number of estimated (by MLE) parameters. In some sense, then, AIC is a bias-adjusted log-likelihood. For a set of 81 plausible cases, we evaluated this bias almost exactly. The ratio of this bias to the first order theory (bias of K) and to second order theory (K + a sample size adjustment) is essentially 1 for these 81 cases. Thus, AIC should be a suitable basis for model selection in open model capture-recapture.     

Using journal impact factors to correct for the publication bias of medical studies

Publication bias of the results of medical studies can invalidate evidence-based medicine. The existing methodology for modeling this essentially relies upon the symmetry of the funnel plot. We present a new method of modeling publication bias that uses this information plus the impact factors of the publishing journals. A simple model of the publication process enables the estimation of bias-corrected intervention effects. The procedure is illustrated using a meta-analysis of the effectiveness of single-dose oral aspirin for acute pain, and results are also obtained for five other meta-analyses. The method enables the fitting of a wide range of models and is considered more flexible than other ways of compensating for publication bias. The model also provides the basis of a statistical test for the existence of publication bias. Use of the new methodology to supplement existing methods is recommended, in the context of a sensitivity analysis.     

Synonymous substitution-rate constants in Escherichia coli and Salmonella typhimurium and their relationship to gene expression and selection pressure

Based on the differences in synonymous codon use between E. coli and S. typhimurium, the synonymous substitution rates can be estimated. In contrast to previous studies on the substitution rates in these two organisms, we use a kinetic model that explicitly takes the selection bias into account. The selection pressure on synonymous codons for a particular amino acid can be calculated from the observed codon bias. This offers a unique opportunity to study systematically the relationship between substitution-rate constants and selection pressure. The results indicate that the codon bias in these organisms is determined by a mutation-selection balance rather than by stabilizing selection. A best fit to the data implies that the mutation rate constant increases about threefold in genes at low expression levels relative to those that are highly expressed.Correspondence to: O.G. Berg     

CRY1 circadian gene variant interacts with carbohydrate intake for insulin resistance in two independent populations: Mediterranean and North American

Dysregulation in the circadian system induced by variants of clock genes has been associated with type 2 diabetes. Evidence for the role of cryptochromes, core components of the system, in regulating glucose homeostasis is not supported by CRY1 candidate gene association studies for diabetes and insulin resistance in human, suggesting possible dietary influences. The purpose of this study was to test for interactions between a CRY1 polymorphism, rs2287161, and carbohydrate intake on insulin resistance in two independent populations: a Mediterranean (n?=?728) and an European origin North American population (n?=?820). Linear regression interaction models were performed in two populations to test for gene–diet interactions on fasting insulin and glucose and two insulin-related traits, homeostasis model assessment of insulin resistance (HOMA-IR) and quantitative insulin sensitivity check index (QUICKI). In addition, fixed effects meta-analyses for these interactions were performed. Cohort-specific interaction analyses showed significant interactions between the CRY1 variant and dietary carbohydrates for insulin resistance in both populations (p?<?0.05). Findings from the meta-analyses of carbohydrate–single nucleotide polymorphism interactions indicated that an increase in carbohydrate intake (% of energy intake) was associated with a significant increase in HOMA-IR (p?=?0.011), fasting insulin (p?=?0.007) and a decrease in QUICKI (p?=?0.028), only among individuals homozygous for the minor C allele. This novel finding supports the link between the circadian system and glucose metabolism and suggests the importance this CRY1 locus in developing personalized nutrition programs aimed at reducing insulin resistance and diabetes risk.     

Evidence for complex selection on four‐fold degenerate sites in Drosophila melanogaster

We considered genome‐wide four‐fold degenerate sites from an African Drosophila melanogaster population and compared them to short introns. To include divergence and to polarize the data, we used its close relatives Drosophila simulans, Drosophila sechellia, Drosophila erecta and Drosophila yakuba as outgroups. In D. melanogaster, the GC content at four‐fold degenerate sites is higher than in short introns; compared to its relatives, more AT than GC is fixed. The former has been explained by codon usage bias (CUB) favouring GC; the latter by decreased intensity of directional selection or by increased mutation bias towards AT. With a biallelic equilibrium model, evidence for directional selection comes mostly from the GC‐rich ancestral base composition. Together with a slight mutation bias, it leads to an asymmetry of the unpolarized allele frequency spectrum, from which directional selection is inferred. Using a quasi‐equilibrium model and polarized spectra, however, only purifying and no directional selection is detected. Furthermore, polarized spectra are proportional to those of the presumably unselected short introns. As we have no evidence for a decrease in effective population size, relaxed CUB must be due to a reduction in the selection coefficient. Going beyond the biallelic model and considering all four bases, signs of directional selection are stronger. In contrast to short introns, complementary bases show strand specificity and allele frequency spectra depend on mutation directions. Hence, the traditional biallelic model to describe the evolution of four‐fold degenerate sites should be replaced by more complex models assuming only quasi‐equilibrium and accounting for all four bases.     

Information-Theoretic Model Selection and Model Averaging for Closed-Population Capture-Recapture Studies

Specification of an appropriate model is critical to valid statistical inference. Given the “true model” for the data is unknown, the goal of model selection is to select a plausible approximating model that balances model bias and sampling variance. Model selection based on information criteria such as AIC or its variant AIC_c, or criteria like CAIC, has proven useful in a variety of contexts including the analysis of open-population capture-recapture data. These criteria have not been intensively evaluated for closed-population capture-recapture models, which are integer parameter models used to estimate population size (N), and there is concern that they will not perform well. To address this concern, we evaluated AIC, AIC_c, and CAIC model selection for closed-population capture-recapture models by empirically assessing the quality of inference for the population size parameter N. We found that AIC-, AIC_c-, and CAIC-selected models had smaller relative mean squared errors than randomly selected models, but that confidence interval coverage on N was poor unless unconditional variance estimates (which incorporate model uncertainty) were used to compute confidence intervals. Overall, AIC and AIC_c outperformed CAIC, and are preferred to CAIC for selection among the closed-population capture-recapture models we investigated. A model averaging approach to estimation, using AIC, AIC_c, or CAIC to estimate weights, was also investigated and proved superior to estimation using AIC-, AIC_c-, or CAIC-selected models. Our results suggested that, for model averaging, AIC or AIC_c should be favored over CAIC for estimating weights.     

The file-drawer problem revisited: a general weighted method for calculating fail-safe numbers in meta-analysis

Quantitative literature reviews such as meta-analysis are becoming common in evolutionary biology but may be strongly affected by publication biases. Using fail-safe numbers is a quick way to estimate whether publication bias is likely to be a problem for a specific study. However, previously suggested fail-safe calculations are unweighted and are not based on the framework in which most meta-analyses are performed. A general, weighted fail-safe calculation, grounded in the meta-analysis framework, applicable to both fixed- and random-effects models, is proposed. Recent meta-analyses published in Evolution are used for illustration.     

Sensory bias as an explanation for the evolution of mate preferences

The sensory bias model of sexual selection posits that female mating preferences are by-products of natural selection on sensory systems. Although sensory bias was proposed 20 years ago, its critical assumptions remain untested. This paradox arises because sensory bias has been used to explain two different phenomena. First, it has been used as a hypothesis about signal design, that is, that males evolve traits that stimulate female sensory systems. Second, sensory bias has been used as a hypothesis for the evolution of female preference itself, that is, to explain why females exhibit particular preferences. We focus on this second facet. First, we clarify the unique features of sensory bias relative to the alternative models by considering each in the same quantitative genetic framework. The key assumptions of sensory bias are that natural selection is the predominant evolutionary mechanism that affects preference and that sexual selection on preferences is quantitatively negligible. We describe four studies that would test these assumptions and review what we can and cannot infer about sensory bias from existing studies. We suggest that the importance of sensory bias as an explanation for the evolution of female preferences remains to be determined.     

Are All Global Positioning System Collars Created Equal? Correcting Habitat-Induced Bias Using Three Brands in the Central Canadian Rockies

Abstract: Global positioning system (GPS) collars are changing the face of wildlife research, yet they still possess biases such as habitat-induced fix-rate bias, which is a serious concern for habitat selection studies. We studied GPS bias in the Central Canadian Rockies, a critical area for wildlife conservation, to provide a statistical approach to correct GPS habitat bias for habitat selection studies using GPS collars. To model GPS habitat bias we deployed 11 different collars from 3 brands of GPS collars (Advanced Telemetry Systems [ATS], Asanti, MN; LOTEK Engineering Ltd., Newmarket, ON, Canada; and Televilt, Lindesberg, Sweden) in a random-stratified design at 86 sites across habitat and topographic conditions. We modeled the probability of obtaining a successful location, P_FIX, as a function of habitat, topography, and collar brand using mixed-effects logistic regression in an information theoretic approach. For LOTEK collars, we also investigated the effect of 8 and 12 GPS channels on fix rate. The ATS collars had the highest overall fix rates (97.4%), followed by LOTEK 12 channel (94.5%), LOTEK 8 channel (85.6%), and Televilt (82.3%). Sufficient model selection uncertainty existed to warrant model averaging for logistic regression P_FIX models. Collar brand influenced fix rate in all P_FIX models: fix rates for ATS and LOTEK 12 channel were not statistically different, whereas LOTEK 8 channel receivers had intermediate fix rates, and Televilt had the lowest. Fix rate was reduced in aspen stands, closed coniferous stands, and sites in narrow mountainous valleys but was higher on upper mountain slopes. Slight discrepancies between fix rates from field trials and observed species fix rates (wolf [Canis lupus] and elk [Cervus elaphus]) suggest uncorrected behavioral or movement-induced bias similar to other recent studies. Regardless, the strong habitat-induced bias in GPS fix rates confirms that in our study area habitat effects are critical, especially for poorer performance brands. Based on previous studies of effects of the amount of bias on inferences, our results suggest correction for GPS bias should be mandatory for Televilt collars in the Canadian Rockies, optional for LOTEK (dependent on the no. of channels), and unnecessary for ATS. Thus, our GPS bias model will be useful to researchers using GPS collars on a variety of species throughout the Rocky Mountain cordillera.     

Towards compendia of negative genetic association studies: an example for Alzheimer disease

Most genetic sequence variants that contribute to variability in complex human traits will have small effects that are not readily detectable with population samples typically used in genetic association studies. A potentially valuable tool in the gene discovery process is meta-analysis of the accumulated published data, but in order to be valid these require a sample of studies representative of the true genetic effect and thus hypothetically should include some positive and an abundance of negative reports. A survey of the literature on association studies for Alzheimer disease (AD) from January 2004–April 2005, identified 138 studies, 86 of which reported positive findings other than for apolipoprotein E (APOE), strongly indicative of publication bias. We report here an analysis of 62 genetic markers, tested for association with AD risk as well as for possible effects upon quantitative indices of AD severity (mini-mental state examination scores, age-at-onset, and cerebrospinal fluid (CSF) β-amyloid (Aβ) and CSF tau proteins). Within this set, only modest signals were present that, with the exception of APOE are easily lost when corrections for multiple hypotheses are applied. In isolation, results are thus broadly negative. Genes studied encompass both novel candidates as well as several recently claimed to be associated with AD (e.g. urokinase plasminogen activator (PLAU) and acetyl-coenzyme A acetyltransferase 1 (ACAT1)). By reporting these data we hope to encourage the publication of gene compendia to guide further studies and aid future meta-analyses aimed at resolving the involvement of genes in complex human traits.     

Evolutionary Patterns of Codon Usage in the Chloroplast Gene rbcL

In this study we reconstruct the evolution of codon usage bias in the chloroplast gene rbcL using a phylogeny of 92 green-plant taxa. We employ a measure of codon usage bias that accounts for chloroplast genomic nucleotide content, as an attempt to limit plausible explanations for patterns of codon bias evolution to selection- or drift-based processes. This measure uses maximum likelihood-ratio tests to compare the performance of two models, one in which a single codon is overrepresented and one in which two codons are overrepresented. The measure allowed us to analyze both the extent of bias in each lineage and the evolution of codon choice across the phylogeny. Despite predictions based primarily on the low G+C content of the chloroplast and the high functional importance of rbcL, we found large differences in the extent of bias, suggesting differential molecular selection that is clade specific. The seed plants and simple leafy liverworts each independently derived a low level of bias in rbcL, perhaps indicating relaxed selectional constraint on molecular changes in the gene. Overrepresentation of a single codon was typically plesiomorphic, and transitions to overrepresentation of two codons occurred commonly across the phylogeny, possibly indicating biochemical selection. The total codon bias in each taxon, when regressed against the total bias of each amino acid, suggested that twofold amino acids play a strong role in inflating the level of codon usage bias in rbcL, despite the fact that twofolds compose a minority of residues in this gene. Those amino acids that contributed most to the total codon usage bias of each taxon are known through amino acid knockout and replacement to be of high functional importance. This suggests that codon usage bias may be constrained by particular amino acids and, thus, may serve as a good predictor of what residues are most important for protein fitness. Present address (Joshua T. Herbeck): JBP Center for Comparative Molecular Biology and Evolution, Marine Biological Laboratory, Woods Hole, MA 02543, USA     

Publication bias in ecology and evolution: an empirical assessment using the 'trim and fill' method

Recent reviews of specific topics, such as the relationship between male attractiveness to females and fluctuating asymmetry or attractiveness and the expression of secondary sexual characters, suggest that publication bias might be a problem in ecology and evolution. In these cases, there is a significant negative correlation between the sample size of published studies and the magnitude or strength of the research findings (formally the ‘effect size’). If all studies that are conducted are equally likely to be published, irrespective of their findings, there should not be a directional relationship between effect size and sample size; only a decrease in the variance in effect size as sample size increases due to a reduction in sampling error. One interpretation of these reports of negative correlations is that studies with small sample sizes and weaker findings (smaller effect sizes) are less likely to be published. If the biological literature is systematically biased this could undermine the attempts of reviewers to summarise actual biology relationships by inflating estimates of average effect sizes. But how common is this problem? And does it really effect the general conclusions of literature reviews? Here, we examine data sets of effect sizes extracted from 40 peer‐reviewed, published meta‐analyses. We estimate how many studies are missing using the newly developed ‘trim and fill’ method. This method uses asymmetry in plots of effect size against sample size (‘funnel plots’) to detect ‘missing’ studies. For random‐effect models of meta‐analysis 38% (15/40) of data sets had a significant number of ‘missing’ studies. After correcting for potential publication bias, 21% (8/38) of weighted mean effects were no longer significantly greater than zero, and 15% (5/34) were no longer statistically robust when we used random‐effects models in a weighted meta‐analysis. The mean correlation between sample size and the magnitude of standardised effect size was also significantly negative (r_s=‐0.20, P < 0‐0001). Individual correlations were significantly negative (P < 0.10) in 35% (14/40) of cases. Publication bias may therefore effect the main conclusions of at least 15–21% of meta‐analyses. We suggest that future literature reviews assess the robustness of their main conclusions by correcting for potential publication bias using the ‘trim and fill’ method.     

Additional Psychometric Evidence and Construct Validity for a Revised Preferences Scale of Morningness

The Preferences Scale of morningness was originally conceived as a two‐factor, 11‐item model. More recently, a two‐factor, six‐item model has been developed and supported in two independent samples. These competing models were examined using structural equation modeling in a mixed student and working sample (n=120). The results supported the two factor, six‐item model (χ²(8, N=120)=10.84, p>0.05) as best fitting the sample data. The two factors explained 59% of the variance and Cronbach's alpha was 0.71. Significant differences (p<0.01) in self‐reported driving ability between morning and evening types were obtained by time‐of‐day, providing some evidence of construct validity. Morning types rated their performance as better in the morning hours and evening types rated their performance as better at night. We then examined whether self‐rated performance is subject to some degree of bias. For both morning and evening types, there was a tendency for those scoring high on self‐deception to rate their driving ability as better, but these differences were not significant. Overall, these findings suggest that self‐ratings are suitable for use in determining construct validity. Recommendations for future studies are made.     

Goodness‐of‐fit tests for disorder detection in NGS experiments

Next‐generation sequencing (NGS) experiments are often performed in biomedical research nowadays, leading to methodological challenges related to the high‐dimensional and complex nature of the recorded data. In this work we review some of the issues that arise in disorder detection from NGS experiments, that is, when the focus is the detection of deletion and duplication disorders for homozygosity and heterozygosity in DNA sequencing. A statistical model to cope with guanine/cytosine bias and phasing and prephasing phenomena at base level is proposed, and a goodness‐of‐fit procedure for disorder detection is derived. The method combines the proper evaluation of local p‐values (one for each DNA base) with suitable corrections for multiple comparisons and the discrete nature of the p‐values. A global test for the detection of disorders in the whole DNA region is proposed too. The performance of the introduced procedures is investigated through simulations. A real data illustration is provided.     

The challenge of modeling niches and distributions for data‐poor species: a comprehensive approach to model complexity

Models of species ecological niches and geographic distributions now represent a widely used tool in ecology, evolution, and biogeography. However, the very common situation of species with few available occurrence localities presents major challenges for such modeling techniques, in particular regarding model complexity and evaluation. Here, we summarize the state of the field regarding these issues and provide a worked example using the technique Maxent for a small mammal endemic to Madagascar (the nesomyine rodent Eliurus majori). Two relevant model‐selection approaches exist in the literature (information criteria, specifically AICc; and performance predicting withheld data, via a jackknife), but AICc is not strictly applicable to machine‐learning algorithms like Maxent. We compare models chosen under each selection approach with those corresponding to Maxent default settings, both with and without spatial filtering of occurrence records to reduce the effects of sampling bias. Both selection approaches chose simpler models than those made using default settings. Furthermore, the approaches converged on a similar answer when sampling bias was taken into account, but differed markedly with the unfiltered occurrence data. Specifically, for that dataset, the models selected by AICc had substantially fewer parameters than those identified by performance on withheld data. Based on our knowledge of the study species, models chosen under both AICc and withheld‐data‐selection showed higher ecological plausibility when combined with spatial filtering. The results for this species intimate that AICc may consistently select models with fewer parameters and be more robust to sampling bias. To test these hypotheses and reach general conclusions, comprehensive research should be undertaken with a wide variety of real and simulated species. Meanwhile, we recommend that researchers assess the critical yet underappreciated issue of model complexity both via information criteria and performance on withheld data, comparing the results between the two approaches and taking into account ecological plausibility.     

Text-analysis reveals taxonomic and geographic disparities in animal pollination literature

Ecological systematic reviews and meta-analyses have significantly increased our understanding of global biodiversity decline. However, for some ecological groups, incomplete and biased datasets have hindered our ability to construct robust, predictive models. One such group consists of the animal pollinators. Approximately 88% of wild plant species are thought to be pollinated by animals, with an estimated annual value of $230–410 billion dollars. Here we apply text-analysis to quantify the taxonomic and geographical distribution of the animal pollinator literature, both temporally and spatially. We show that the publication of pollinator literature increased rapidly in the 1980s and 1990s. Taxonomically, we show that the distribution of pollinator literature is concentrated in the honey bees (Apis) and bumble bees (Bombus), and geographically in North America and Europe. At least 25% of pollination-related abstracts mention a species of honey bee and at least 20% a species of bumble bee, and approximately 46% of abstracts are focussed on either North America (32%) or Europe (14%). Although these results indicate strong taxonomic and geographic biases in the pollinator literature, a large number of studies outside North America and Europe do exist. We then discuss how text-analysis could be used to shorten the literature search for ecological systematic reviews and meta-analyses, and to address more applied questions related to pollinator biodiversity, such as the identification of likely interacting plant–pollinator pairs and the number of pollinating species.     

Artificial selection on ant female caste ratio uncovers a link between female‐biased sex ratios and infection by Wolbachia endosymbionts

Social insect sex and caste ratios are well‐studied targets of evolutionary conflicts, but the heritable factors affecting these traits remain unknown. To elucidate these factors, we carried out a short‐term artificial selection study on female caste ratio in the ant Monomorium pharaonis. Across three generations of bidirectional selection, we observed no response for caste ratio, but sex ratios rapidly became more female‐biased in the two replicate high selection lines and less female‐biased in the two replicate low selection lines. We hypothesized that this rapid divergence for sex ratio was caused by changes in the frequency of infection by the heritable bacterial endosymbiont Wolbachia, because the initial breeding stock varied for Wolbachia infection, and Wolbachia is known to cause female‐biased sex ratios in other insects. Consistent with this hypothesis, the proportions of Wolbachia‐infected colonies in the selection lines changed rapidly, mirroring the sex ratio changes. Moreover, the estimated effect of Wolbachia on sex ratio (~13% female bias) was similar in colonies before and during artificial selection, indicating that this Wolbachia effect is likely independent of the effects of artificial selection on other heritable factors. Our study provides evidence for the first case of endosymbiont sex ratio manipulation in a social insect.