The coefficient of determination R2 and intra-class correlation coefficient from generalized linear mixed-effects models revisited and expanded

The coefficient of determinationR2quantifies the proportion of varianceexplained by a statistical model and is an important summary statisticof biological interest. However, estimatingR2for generalized linear mixedmodels (GLMMs) remains challenging. We have previously introduced a ver-sion ofR2that we calledR2GLMMfor Poisson and binomial GLMMs, but notfor other distributional families. Similarly, we earlier discussed how to estimateintra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs.Inthis paper, we generalize our methodsto allothernon-Gaussian distributions,in particular to negative binomial and gamma distributions that are commonlyused formodellingbiological data. Whileexpanding ourapproach,we highlighttwo useful concepts for biologists, Jensen’s inequality and the delta method,both of which help us in understanding the properties of GLMMs. Jensen’sinequality has important implications for biologically meaningful interpretationof GLMMs, whereas the delta method allows a general derivation of varianceassociated with non-Gaussian distributions. We also discuss some special con-siderations for binomial GLMMs with binary or proportion data. We illustratethe implementation of our extension by worked examples from the field of ecol-ogy and evolution in theRenvironment. However, our method can be usedacross disciplines and regardless of statistical environments

Increased tolerance to humans among disturbed wildlife.

Human disturbance drives the decline of many species, both directly and indirectly. Nonetheless, some species do particularly well around humans. One mechanism that may explain coexistence is the degree to which a species tolerates human disturbance. Here we provide a comprehensive meta-analysis of birds, mammals and lizards to investigate species tolerance of human disturbance and explore the drivers of this tolerance in birds. We find that, overall, disturbed populations of the three major taxa are more tolerant of human disturbance than less disturbed populations. The best predictors of the direction and magnitude of bird tolerance of human disturbance are the type of disturbed area (urbanized birds are more tolerant than rural or suburban populations) and body mass (large birds are more tolerant than small birds). By identifying specific features associated with tolerance, these results guide evidence-based conservation strategies to predict and manage the impacts of increasing human disturbance on birds

partR2:partitioning R2 in generalized linear mixed models

The coefficient of determination R(2) quantifies the amount of variance explained by regression coefficients in a linear model. It can be seen as the fixed-effects complement to the repeatability R (intra-class correlation) for the variance explained by random effects and thus as a tool for variance decomposition. The R(2) of a model can be further partitioned into the variance explained by a particular predictor or a combination of predictors using semi-partial (part) R(2) and structure coefficients, but this is rarely done due to a lack of software implementing these statistics. Here, we introduce partR2, an R package that quantifies part R(2) for fixed effect predictors based on (generalized) linear mixed-effect model fits. The package iteratively removes predictors of interest from the model and monitors the change in the variance of the linear predictor. The difference to the full model gives a measure of the amount of variance explained uniquely by a particular predictor or a set of predictors. partR2 also estimates structure coefficients as the correlation between a predictor and fitted values, which provide an estimate of the total contribution of a fixed effect to the overall prediction, independent of other predictors. Structure coefficients can be converted to the total variance explained by a predictor, here called ‘inclusive’ R(2), as the square of the structure coefficients times total R(2). Furthermore, the package reports beta weights (standardized regression coefficients). Finally, partR2 implements parametric bootstrapping to quantify confidence intervals for each estimate. We illustrate the use of partR2 with real example datasets for Gaussian and binomial GLMMs and discuss interactions, which pose a specific challenge for partitioning the explained variance among predictors

General methods for evolutionary quantitative genetic inference from generalized mixed models

P.d.V. was supported by a doctoral studentship from the French Ministère de la Recherche et de l’Enseignement Supérieur. H.S. was supported by an Emmy Noether fellowship from the German Research Foundation (SCHI 1188/1-1). S.N. is supported by a Future Fellowship, Australia (FT130100268). M.M. is supported by a University Research Fellowship from the Royal Society (London). The collection of the Soay sheep data is supported by the National Trust for Scotland and QinetQ, with funding from the Natural Environment Research Council, the Royal Society, and the Leverhulme Trust.Methods for inference and interpretation of evolutionary quantitative genetic parameters, and for prediction of the response to selection, are best developed for traits with normal distributions. Many traits of evolutionary interest, including many life history and behavioural traits, have inherently non-normal distributions. The generalised linear mixed model (GLMM) framework has become a widely used tool for estimating quantitative genetic parameters for non-normal traits. However, whereas GLMMs provide inference on a statistically-convenient latent scale, it is often desirable to express quantitative genetic parameters on the scale upon which traits are measured. The parameters of fitted GLMMs, despite being on a latent scale, fully determine all quantities of potential interest on the scale on which traits are expressed. We provide expressions for deriving each of such quantities, including population means, phenotypic (co)variances, variance components including additive genetic (co)variances, and parameters such as heritability. We demonstrate that fixed effects have a strong impact on those parameters and show how to deal with this by averaging or integrating over fixed effects. The expressions require integration of quantities determined by the link function, over distributions of latent values. In general cases, the required integrals must be solved numerically, but efficient methods are available and we provide an implementation in an R package, QGGLMM. We show that known formulae for quantities such as heritability of traits with Binomial and Poisson distributions are special cases of our expressions. Additionally, we show how fitted GLMM can be incorporated into existing methods for predicting evolutionary trajectories. We demonstrate the accuracy of the resulting method for evolutionary prediction by simulation, and apply our approach to data from a wild pedigreed vertebrate population.Publisher PDFPeer reviewe

Complete metamorphosis and microbiota turnover in insects

The insects constitute the majority of animal diversity. Most insects are holometabolous: during complete metamorphosis their bodies are radically reorganized. This reorganization poses a significant challenge to the gut microbiota, as the gut is replaced during pupation, a process that does not occur in hemimetabolous insects. In holometabolous hosts, it offers the opportunity to decouple the gut microbiota between the larval and adult life stages resulting in high beta diversity whilst limiting alpha diversity. Here, we studied 18 different herbivorous insect species from five orders of holometabolous and three orders of hemimetabolous insects. Comparing larval and adult specimens, we find a much higher beta-diversity and hence microbiota turnover in holometabolous insects compared to hemimetabolous insects. Alpha diversity did not differ between holo- and hemimetabolous insects nor between developmental stages within these groups. Our results support the idea that pupation offers the opportunity to change the gut microbiota and hence might facilitate ecological niche shifts. This possible effect of niche shift facilitation could explain a selective advantage of the evolution of complete metamorphosis, which is a defining trait of the most speciose insect taxon, the holometabola

Non-genetic inheritance of environmental exposures : a protocol for a map of systematic reviews with bibliometric analysis

Abstract Background Over the last few decades, we increasingly see examples of parental environmental experiences influencing offspring health and fitness. More recently, it has become clear that some non-genetic effects can be conferred across multiple generations. This topic has attracted research from a diversity of disciplines such as toxicology, biomedical sciences, and ecology, due to its importance for environmental and health issues, as well as ecological and evolutionary processes, with implications for environmental policies. The rapid accumulation of primary research has enabled researchers to perform systematic reviews (SRs), including meta-analyses, to investigate the generality of and sources of variation in non-genetic effects. However, different disciplines ask different questions and SRs can vary substantially in scope, quality, and terminology usage. This diversity in SRs makes it difficult to assess broad patterns of non-genetic effects across disciplines as well as determine common areas of interest and gaps in the literature. To clarify research patterns within the SR literature on non-genetic inheritance, we plan to create a map of systematic reviews as well as conduct bibliometric mapping (referred to as ‘research weaving’). We will address four key questions: first, what are the broad research patterns unifying the SR literature on non-genetic inheritance across disciplines? Second, are there discipline-specific research patterns, including terminology use, between disciplines? Third, how are authors of the SR literature connected? Fourth, what is the reliability of the SR literature? Methods We will systematically collect reviews within the SR ‘family’ that examine non-genetic inheritance arising from parental and ancestral environment by searching databases for journal articles and grey literature, as well as conducting backwards and forwards searching. Search hits will be double screened using ‘decision trees’ that represent the inclusion criteria. All relevant data elements on the review’s topic, as well as a critical appraisal of the review’s approach and reporting, will be extracted into Excel flat sheets. Bibliometric data will be directly extracted from Scopus. We will then query all relevant data elements to address our objectives and present outcomes in easily interpretable tables and figures, accompanied by a narrative description of results

Quantifying crop pollinator dependence and its heterogeneity using multi-level meta-analysis

1. Biotic pollination can benefit crop production, but its effects are highly variable. To maximise benefits from this ecosystem service, we need a greater understanding of the factors that cause variation so that ecological intensification can be more effectively applied. 2. We focus on understanding the benefits of pollination to faba bean (Vicia faba). We use a literature review followed by multi-level meta-analysis to estimate overall benefits of pollination to faba bean yield and to quantify variation (heterogeneity) in these benefits associated with different contextual factors (e.g. plant genotype, growing environment). 3. Our overall estimate of pollination benefit to faba bean yield, expressed as the percentage yield reduction without pollination, is 32.9% (confidence interval 21 to 43%). Based on the prediction intervals, which include the heterogeneity in pollination benefit, there is an 80% chance that pollination will increase yield of a faba bean crop. 4. Half of all heterogeneity in pollination dependence was due to differences between plant genotypes. The number of beans per plant showed similar pollination dependence to yield mass per plant, while pod number and number of beans per pod underestimated yield benefits. There was weak evidence to suggest pollination benefits vary between pollinator species, with honeybees showing a smaller yield increase. 5. Differences in the experimental method used to assess pollination benefit did not significantly affect the estimate, including the growing environment, measurement scale, or whether the effects of experimental pollinator enclosures were controlled. This suggests that simplified experimental studies comparing yield of open-pollinated and enclosed plants can provide reliable insights into pollination benefits across a large range of plant genotypes and landscapes. 6. Synthesis and application: We found high variability in pollination benefits both between and within publications in our meta-analysis. Plant genotype, how yield was measured, and pollinator species affected the level of pollination benefit. Despite variability in pollination benefits due to various contextual factors (both inside and outside of grower control), there is a high likelihood that biotic pollination will increase faba bean yield. Our findings support ecological intensification and specifically the management of pollinators to maximise pollination benefits to faba bean production