Holger Schielzeth

Repeatability for Gaussian and non-Gaussian data: a practical guide for biologists

Repeatability (more precisely the common measure of repeatability, the intra‐class correlation coefficient, ICC) is an important index for quantifying the accuracy of measurements and the constancy of phenotypes. It is the proportion of phenotypic variation that can be attributed to between‐subject (or between‐group) variation. As a consequence, the non‐repeatable fraction of phenotypic variation is the sum of measurement error and phenotypic flexibility. There are several ways to estimate repeatability for Gaussian data, but there are no formal agreements on how repeatability should be calculated for non‐Gaussian data (e.g. binary, proportion and count data). In addition to point estimates, appropriate uncertainty estimates (standard errors and confidence intervals) and statistical significance for repeatability estimates are required regardless of the types of data. We review the methods for calculating repeatability and the associated statistics for Gaussian and non‐Gaussian data. For Gaussian data, we present three common approaches for estimating repeatability: correlation‐based, analysis of variance (ANOVA)‐based and linear mixed‐effects model (LMM)‐based methods, while for non‐Gaussian data, we focus on generalised linear mixed‐effects models (GLMM) that allow the estimation of repeatability on the original and on the underlying latent scale. We also address a number of methods for calculating standard errors, confidence intervals and statistical significance; the most accurate and recommended methods are parametric bootstrapping, randomisation tests and Bayesian approaches. We advocate the use of LMM‐ and GLMM‐based approaches mainly because of the ease with which confounding variables can be controlled for. Furthermore, we compare two types of repeatability (ordinary repeatability and extrapolated repeatability) in relation to narrow‐sense heritability. This review serves as a collection of guidelines and recommendations for biologists to calculate repeatability and heritability from both Gaussian and non‐Gaussian data.

Conclusions beyond support: overconfident estimates in mixed models

Mixed-effect models are frequently used to control for the nonindependence of data points, for example, when repeated measures from the same individuals are available. The aim of these models is often to estimate fixed effects and to test their significance. This is usually done by including random intercepts, that is, intercepts that are allowed to vary between individuals. The widespread belief is that this controls for all types of pseudoreplication within individuals. Here we show that this is not the case, if the aim is to estimate effects that vary within individuals and individuals differ in their response to these effects. In these cases, random intercept models give overconfident estimates leading to conclusions that are not supported by the data. By allowing individuals to differ in the slopes of their responses, it is possible to account for the nonindependence of data points that pseudoreplicate slope information. Such random slope models give appropriate standard errors and are easily implemented in standard statistical software. Because random slope models are not always used where they are essential, we suspect that many published findings have too narrow confidence intervals and a substantially inflated type I error rate. Besides reducing type I errors, random slope models have the potential to reduce residual variance by accounting for between-individual variation in slopes, which makes it easier to detect treatment effects that are applied between individuals, hence reducing type II errors as well.

Cryptic multiple hypotheses testing in linear models: overestimated effect sizes and the winner's curse

Fitting generalised linear models (GLMs) with more than one predictor has become the standard method of analysis in evolutionary and behavioural research. Often, GLMs are used for exploratory data analysis, where one starts with a complex full model including interaction terms and then simplifies by removing non-significant terms. While this approach can be useful, it is problematic if significant effects are interpreted as if they arose from a single a priori hypothesis test. This is because model selection involves cryptic multiple hypothesis testing, a fact that has only rarely been acknowledged or quantified. We show that the probability of finding at least one ‘significant’ effect is high, even if all null hypotheses are true (e.g. 40% when starting with four predictors and their two-way interactions). This probability is close to theoretical expectations when the sample size (N) is large relative to the number of predictors including interactions (k). In contrast, type I error rates strongly exceed even those expectations when model simplification is applied to models that are over-fitted before simplification (low N/k ratio). The increase in false-positive results arises primarily from an overestimation of effect sizes among significant predictors, leading to upward-biased effect sizes that often cannot be reproduced in follow-up studies (‘the winners curse’). Despite having their own problems, full model tests and P value adjustments can be used as a guide to how frequently type I errors arise by sampling variation alone. We favour the presentation of full models, since they best reflect the range of predictors investigated and ensure a balanced representation also of non-significant results.

The recombination landscape of the zebra finch Taeniopygia guttata genome

Understanding the causes and consequences of variation in the rate of recombination is essential since this parameter is considered to affect levels of genetic variability, the efficacy of selection, and the design of association and linkage mapping studies. However, there is limited knowledge about the factors governing recombination rate variation. We genotyped 1920 single nucleotide polymorphisms in a multigeneration pedigree of more than 1000 zebra finches (Taeniopygia guttata) to develop a genetic linkage map, and then we used these map data together with the recently available draft genome sequence of the zebra finch to estimate recombination rates in 1 Mb intervals across the genome. The average zebra finch recombination rate (1.5 cM/Mb) is higher than in humans, but significantly lower than in chicken. The local rates of recombination in chicken and zebra finch were only weakly correlated, demonstrating evolutionary turnover of the recombination landscape in birds. The distribution of recombination events was heavily biased toward ends of chromosomes, with a stronger telomere effect than so far seen in any organism. In fact, the recombination rate was as low as 0.1 cM/Mb in intervals up to 100 Mb long in the middle of the larger chromosomes. We found a positive correlation between recombination rate and GC content, as well as GC-rich sequence motifs. Levels of linkage disequilibrium (LD) were significantly higher in regions of low recombination, showing that heterogeneity in recombination rates have left a footprint on the genomic landscape of LD in zebra finch populations.

Heterozygosity-fitness correlations in zebra finches: microsatellite markers can be better than their reputation

Numerous studies have reported associations between heterozygosity in microsatellite markers and fitness‐related traits (heterozygosity–fitness correlations, HFCs). However, it has often been questioned whether HFCs reflect general inbreeding depression, because a small panel of microsatellite markers does not reflect very well an individual’s inbreeding coefficient (F) as calculated from a pedigree. Here, we challenge this prevailing view. Because of chance events during Mendelian segregation, an individual’s realized proportion of the genome that is identical by descent (IBD) may substantially deviate from the pedigree‐based expectation (i.e. F). This Mendelian noise may result in a weak correlation between F and multi‐locus heterozygosity, but this does not imply that multi‐locus heterozygosity is a bad estimator of realized IBD. We examined correlations between 11 fitness‐related traits measured in up to 1192 captive zebra finches and three measures of inbreeding: (i) heterozygosity across 11 microsatellite markers, (ii) heterozygosity across 1359 single‐nucleotide polymorphism (SNP) markers and (iii) F, based on a 5th‐generation pedigree. All 11 phenotypic traits showed positive relationships with measures of heterozygosity, especially traits that are most closely related to fitness. Remarkably, the small panel of microsatellite markers produced equally strong HFCs as the large panel of SNP markers. Both marker‐based approaches produced stronger correlations with phenotypes than the pedigree‐based F, and this did not seem to result from the shortness of our pedigree. We argue that a small panel of microsatellites with high allelic richness may better reflect an individual’s realized IBD than previously appreciated, especially in species like the zebra finch, where much of the genome is inherited in large blocks that rarely experience cross‐over during meiosis.

Female extrapair mating behavior can evolve via indirect selection on males

In many species that form socially monogamous pair bonds, a considerable proportion of the offspring is sired by extrapair males. This observation has remained a puzzle for evolutionary biologists: although mating outside the pair bond can obviously increase the offspring production of males, the benefits of such behavior to females are less clear, yet females are known to actively solicit extrapair copulations. For more than two decades adaptionist explanations have dominated the discussions, yet remain controversial, and genetic constraint arguments have been dismissed without much consideration. An intriguing but still untested hypothesis states that extrapair mating behavior by females may be affected by the same genetic variants (alleles) as extrapair mating behavior by males, such that the female behavior could evolve through indirect selection on the male behavior. Here we show that in the socially monogamous zebra finch, individual differences in extrapair mating behavior have a hereditary component. Intriguingly, this genetic basis is shared between the sexes, as shown by a strong genetic correlation between male and female measurements of extrapair mating behavior. Hence, positive selection on males to sire extrapair young will lead to increased extrapair mating by females as a correlated evolutionary response. This behavior leads to a fundamentally different view of female extrapair mating: it may exist even if females obtain no net benefit from it, simply because the corresponding alleles were positively selected in the male ancestors.

Urbanization and its effects on personality traits : a result of microevolution or phenotypic plasticity?

Human-altered environmental conditions affect many species at the global scale. An extreme form of anthropogenic alteration is the existence and rapid increase of urban areas. A key question, then, is how species cope with urbanization. It has been suggested that rural and urban conspecifics show differences in behaviour and personality. However, (i) a generalization of this phenomenon has never been made; and (ii) it is still unclear whether differences in personality traits between rural and urban conspecifics are the result of phenotypic plasticity or of intrinsic differences. In a literature review, we show that behavioural differences between rural and urban conspecifics are common and taxonomically widespread among animals, suggesting a significant ecological impact of urbanization on animal behaviour. In order to gain insight into the mechanisms leading to behavioural differences in urban individuals, we hand-raised and kept European blackbirds (Turdus merula) from a rural and a nearby urban area under common-garden conditions. Using these birds, we investigated individual variation in two behavioural responses to the presence of novel objects: approach to an object in a familiar area (here defined as neophilia), and avoidance of an object in a familiar foraging context (defined as neophobia). Neophilic and neophobic behaviours were mildly correlated and repeatable even across a time period of one year, indicating stable individual behavioural strategies. Blackbirds from the urban population were more neophobic and seasonally less neophilic than blackbirds from the nearby rural area. These intrinsic differences in personality traits are likely the result of microevolutionary changes, although we cannot fully exclude early developmental influences.

rptR: repeatability estimation and variance decomposition by generalized linear mixed-effects models

Summary Intra-class correlations (ICC) and repeatabilities (R) are fundamental statistics for quantifying the reproducibility of measurements and for understanding the structure of biological variation. Linear mixed effects models offer a versatile framework for estimating ICC and R. However, while point estimation and significance testing by likelihood ratio tests is straightforward, the quantification of uncertainty is not as easily achieved. A further complication arises when the analysis is conducted on data with non-Gaussian distributions because the separation of the mean and the variance is less clear-cut for non-Gaussian than for Gaussian models. Nonetheless, there are solutions to approximate repeatability for the most widely used families of generalized linear mixed models (GLMMs). Here, we introduce the R package rptR for the estimation of ICC and R for Gaussian, binomial and Poisson-distributed data. Uncertainty in estimators is quantified by parametric bootstrapping and significance testing is implemented by likelihood ratio tests and through permutation of residuals. The package allows control for fixed effects and thus the estimation of adjusted repeatabilities (that remove fixed effect variance from the estimate) and enhanced agreement repeatabilities (that add fixed effect variance to the denominator). Furthermore, repeatability can be estimated from random-slope models. The package features convenient summary and plotting functions. Besides repeatabilities, the package also allows the quantification of coefficients of determination R2 as well as of raw variance components. We present an example analysis to demonstrate the core features and discuss some of the limitations of rptR.

Compensatory investment in zebra finches: females lay larger eggs when paired to sexually unattractive males

The classical version of the differential allocation hypothesis states that, when females reproduce over their lifetime with partners that differ in their genetic quality, they should invest more in reproduction with high-quality males. However, in species with lifetime monogamy, such as the zebra finch, partner quality will typically remain the same. In this case, the compensatory investment (CI) hypothesis predicts higher investment for low-quality males, because low genetic quality offspring are more dependent on maternal resources. Here, we show that female zebra finches invested more resources, both in terms of egg volume and yolk carotenoid content, when paired to a low genetic quality male, as judged from his previous ability to obtain extra-pair paternity in aviary colonies. We also found that females deposited slightly larger amounts of testosterone into eggs when paired to a low parental quality male, as judging from his previous success in rearing offspring. This is, to our knowledge, the first experimental support for the CI hypothesis in a species with lifetime monogamy. We stress that in more promiscuous species, the benefits of classical differential allocation may partly be neutralized by the supposed benefits of CI.

Molecular evolution of genes in avian genomes

BackgroundObtaining a draft genome sequence of the zebra finch (Taeniopygia guttata), the second bird genome to be sequenced, provides the necessary resource for whole-genome comparative analysis of gene sequence evolution in a non-mammalian vertebrate lineage. To analyze basic molecular evolutionary processes during avian evolution, and to contrast these with the situation in mammals, we aligned the protein-coding sequences of 8,384 1:1 orthologs of chicken, zebra finch, a lizard and three mammalian species.ResultsWe found clear differences in the substitution rate at fourfold degenerate sites, being lowest in the ancestral bird lineage, intermediate in the chicken lineage and highest in the zebra finch lineage, possibly reflecting differences in generation time. We identified positively selected and/or rapidly evolving genes in avian lineages and found an over-representation of several functional classes, including anion transporter activity, calcium ion binding, cell adhesion and microtubule cytoskeleton.ConclusionsFocusing specifically on genes of neurological interest and genes differentially expressed in the unique vocal control nuclei of the songbird brain, we find a number of positively selected genes, including synaptic receptors. We found no evidence that selection for beneficial alleles is more efficient in regions of high recombination; in fact, there was a weak yet significant negative correlation between ω and recombination rate, which is in the direction predicted by the Hill-Robertson effect if slightly deleterious mutations contribute to protein evolution. These findings set the stage for studies of functional genetics of avian genes.