ORCID Profile
0000-0002-9124-2261
Current Organisation
Friedrich Schiller University Jena
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Publisher: Cold Spring Harbor Laboratory
Date: 04-07-2017
DOI: 10.1101/159210
Abstract: Linear mixed effects models are frequently used for estimating quantitative genetic parameters, including the heritability, of traits of interest. Heritability is an important metric, because it acts as a filter that determines how efficiently phenotypic selection translates into evolutionary change. As a quantity of biological interest, it is important that the denominator, the phenotypic variance, actually reflects the amount of phenotypic variance in the relevant ecological stetting. The current practice of quantifying heritability from mixed effects models frequently deprives the heritability of variance explained by fixed effects (often leading to upward-bias) and it has been suggested to omit fixed effects when estimating heritabilities. We advocate an alternative option of fitting complex models incorporating all relevant effects, while including the variance explained by fixed effects into the estimation of heritabilities. The approach is easily implemented (an ex le is provided) and allows corrections for the estimation of heritability, such as the exclusion of variance arising from experimental design effects while still including all biologically relevant sources of variation. We explore the complications arising depending on the nature of the covariates included as fixed effects (e.g. biological or experimental origin, characteristics of biological covariates). Furthermore, we discuss fixed effects in non-linear and generalized linear models when fixed effects. In these cases, the variance parameters depend on the location of the intercept and hence on the scaling of the fixed effects. Integration over the biologically relevant range of fixed effects offers a preferred solution in those situations.
Publisher: Wiley
Date: 05-11-2015
Publisher: Wiley
Date: 15-10-2013
Publisher: Elsevier BV
Date: 09-2012
Publisher: Oxford University Press (OUP)
Date: 2009
Publisher: Wiley
Date: 03-12-2013
Publisher: Oxford University Press (OUP)
Date: 11-2016
DOI: 10.1534/GENETICS.115.186536
Abstract: 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 behavioral traits, have inherently nonnormal distributions. The generalized linear mixed model (GLMM) framework has become a widely used tool for estimating quantitative genetic parameters for nonnormal 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 formulas 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: Wiley
Date: 12-11-2020
Publisher: Wiley
Date: 16-07-2020
Publisher: Wiley
Date: 30-05-2017
Publisher: Elsevier
Date: 2019
Publisher: Wiley
Date: 07-09-2023
Publisher: Wiley
Date: 17-10-2016
Publisher: Wiley
Date: 21-06-2010
Publisher: Wiley
Date: 06-02-2017
DOI: 10.1111/MEC.14009
Abstract: Identifying causal genetic variants underlying heritable phenotypic variation is a long-standing goal in evolutionary genetics. We previously identified several quantitative trait loci (QTL) for five morphological traits in a captive population of zebra finches (Taeniopygia guttata) by whole-genome linkage mapping. We here follow up on these studies with the aim to narrow down on the quantitative trait variants (QTN) in one wild and three captive populations. First, we performed an association study using 672 single nucleotide polymorphisms (SNPs) within candidate genes located in the previously identified QTL regions in a s le of 939 wild-caught zebra finches. Then, we validated the most promising SNP-phenotype associations (n = 25 SNPs) in 5228 birds from four populations. Genotype-phenotype associations were generally weak in the wild population, where linkage disequilibrium (LD) spans only short genomic distances. In contrast, in captive populations, where LD blocks are large, apparent SNP effects on morphological traits (i.e. associations) were highly repeatable with independent data from the same population. Most of those SNPs also showed significant associations with the same trait in other captive populations, but the direction and magnitude of these effects varied among populations. This suggests that the tested SNPs are not the causal QTN but rather physically linked to them, and that LD between SNPs and causal variants differs between populations due to founder effects. While the identification of QTN remains challenging in nonmodel organisms, we illustrate that it is indeed possible to confirm the location and magnitude of QTL in a population with stable linkage between markers and causal variants.
Publisher: Wiley
Date: 24-04-2022
Abstract: In iduals differ in average phenotypes and in sensitivity to environmental variation. Such context sensitivity can be modelled as random slope variation. Random slope variation implies that the proportion of between‐in idual variation varies across the range of a covariate (environment/context/time/age) and has thus been called ‘conditional’ repeatability. We propose to put conditional repeatabilities in perspective of the total phenotypic variance and suggest a way of standardization using the random slope coefficient of determination . Furthermore, we illustrate that the marginalized repeatability averaged across an environmental gradient offers a biologically relevant description of between‐in idual variation. We provide simple equations for calculating key descriptors of conditional repeatabilities, clarify the difference between random intercept variation and average between‐in idual variation and make recommendations for comprehensive reporting. While we introduce the concept with in idual variation in mind, the framework is equally applicable to other type of between‐group/cluster variation that varies across some (environmental) gradient.
Publisher: Wiley
Date: 05-10-2020
DOI: 10.1111/BRV.12655
Publisher: Wiley
Date: 15-02-2018
DOI: 10.1111/JEB.13232
Abstract: Linear mixed-effects models are frequently used for estimating quantitative genetic parameters, including the heritability, as well as the repeatability, of traits. Heritability acts as a filter that determines how efficiently phenotypic selection translates into evolutionary change, whereas repeatability informs us about the in idual consistency of phenotypic traits. As quantities of biological interest, it is important that the denominator, the phenotypic variance in both cases, reflects the amount of phenotypic variance in the relevant ecological setting. The current practice of quantifying heritabilities and repeatabilities from mixed-effects models frequently deprives their denominator of variance explained by fixed effects (often leading to upward bias of heritabilities and repeatabilities), and it has been suggested to omit fixed effects when estimating heritabilities in particular. We advocate an alternative option of fitting models incorporating all relevant effects, while including the variance explained by fixed effects into the estimation of the phenotypic variance. The approach is easily implemented and allows optimizing the estimation of phenotypic variance, for ex le by the exclusion of variance arising from experimental design effects while still including all biologically relevant sources of variation. We address the estimation and interpretation of heritabilities in situations in which potential covariates are themselves heritable traits of the organism. Furthermore, we discuss complications that arise in generalized and nonlinear mixed models with fixed effects. In these cases, the variance parameters on the data scale depend on the location of the intercept and hence on the scaling of the fixed effects. Integration over the biologically relevant range of fixed effects offers a preferred solution in those situations.
Publisher: Cold Spring Harbor Laboratory
Date: 21-12-2016
DOI: 10.1101/095851
Abstract: The coefficient of determination R 2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called R 2 GLMM for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients ICC using Poisson and binomial GLMMs. In this article, we expand our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen’s inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen’s inequality has important implications for biologically meaningful interpretation of GLMMs, while the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked ex les from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments.
Publisher: California Digital Library (CDL)
Date: 18-03-2020
Publisher: The Royal Society
Date: 09-2017
Abstract: The coefficient of determination R 2 quantifies the proportion of variance explained by a statistical model and is an important summary statistic of biological interest. However, estimating R 2 for generalized linear mixed models (GLMMs) remains challenging. We have previously introduced a version of R 2 that we called for Poisson and binomial GLMMs, but not for other distributional families. Similarly, we earlier discussed how to estimate intra-class correlation coefficients (ICCs) using Poisson and binomial GLMMs. In this paper, we generalize our methods to all other non-Gaussian distributions, in particular to negative binomial and gamma distributions that are commonly used for modelling biological data. While expanding our approach, we highlight two useful concepts for biologists, Jensen's inequality and the delta method, both of which help us in understanding the properties of GLMMs. Jensen's inequality has important implications for biologically meaningful interpretation of GLMMs, whereas the delta method allows a general derivation of variance associated with non-Gaussian distributions. We also discuss some special considerations for binomial GLMMs with binary or proportion data. We illustrate the implementation of our extension by worked ex les from the field of ecology and evolution in the R environment. However, our method can be used across disciplines and regardless of statistical environments.
Publisher: Wiley
Date: 31-10-2021
Abstract: Plant damage by invertebrate herbivores and pathogens influences the dynamics of grassland ecosystems, but anthropogenic changes in nitrogen and phosphorus availability can modify these relationships. Using a globally distributed experiment, we describe leaf damage on 153 plant taxa from 27 grasslands worldwide, under ambient conditions and with experimentally elevated nitrogen and phosphorus. Invertebrate damage significantly increased with nitrogen addition, especially in grasses and non‐leguminous forbs. Pathogen damage increased with nitrogen in grasses and legumes but not forbs. Effects of phosphorus were generally weaker. Damage was higher in grasslands with more precipitation, but climatic conditions did not change effects of nutrients on leaf damage. On average, invertebrate damage was relatively higher on legumes and pathogen damage was relatively higher on grasses. Community‐weighted mean damage reflected these functional group patterns, with no effects of N on community‐weighted pathogen damage (due to opposing responses of grasses and forbs) but stronger effects of N on community‐weighted invertebrate damage (due to consistent responses of grasses and forbs). Synthesis . As human‐induced inputs of nitrogen and phosphorus continue to increase, understanding their impacts on invertebrate and pathogen damage becomes increasingly important. Our results demonstrate that eutrophication frequently increases plant damage and that damage increases with precipitation across a wide array of grasslands. Invertebrate and pathogen damage in grasslands is likely to increase in the future, with potential consequences for plant, invertebrate and pathogen communities, as well as the transfer of energy and nutrients across trophic levels.
No related grants have been discovered for Holger Schielzeth.