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

Méthodes pour l’étude de l’adaptation locale et application au contexte de l’adaptation aux conditions d’altitude chez la plante alpine Arabis alpina

Local adaptation is a micro-evolutionary phenomenon, which arises when populations of the same species are exposed to contrasted environmental conditions.If this environment exert some natural selection pressure, if an adaptive potential exists among the populations and if the gene flow is sufficiently mild, populations are expected to tend toward a local adaptive optimum.In this thesis, I study the methodological means of the study of local adaptation on the one hand, and I investigate this phenomenon along an elevation gradient in the alpine plant Arabis alpina on the other hand.In the first, methodological part, I show that the genome scan methods to detect selection using genetic markers might suffer strong false positive rates when confronted to complex but realistic datasets.I then introduce a statistical method to detect markers under selection, which, contrary to existing methods, make use of both the concept of genetic differentiation (or Fst) and environmental information.This method has been developed in order to reduce its global false positive rate.Finally, I present some perspectives regarding the relationships between the relatively old ``common garden'' experiment and the new developments in molecular biology and statistics.In the second, empirical part, I introduce an analysis of the demographic characteristics of A. alpina in six natural populations. Besides providing interesting biological information on this species (low life expectancy, strongly contrasted reproduction and survival...), these analyses show that growth increase and survival decrease with the decrease of average temperature (hence with altitude).Since these analyses do not allow us to rule out hypotheses such as drift and phenotypic plasticity, I show the results of a common garden experiment which enable us to smooth phenotypic plasticity and, when combined with molecular data, enable us to rule out the hypothesis of drift.The results show the existence of an adaptive phenotypic syndrome, in which plants are smaller, are more compact, grow slower and reproduce less in cold temperature environments.Using the molecular data, I draw a list of 40 locus which might be involved in this adaptive process.In the end, I discuss these empirical findings as a whole to place them in a more general context of alpine ecology. I sum up the main methodological challenges when studying local adaptation and offer some methodological perspectives.L'adaptation locale est un phénomène micro-évolutif qui peut survenir lorsque des populations d'une même espèce sont exposées à des conditions environnementales différentes.Si cet environnement exerce une pression sous forme de sélection naturelle, qu'il existe un potentiel adaptatif au sein des populations et que le flux de gènes est suffisamment modéré, les populations vont alors tendre vers un optimum adaptatif local.Dans cette thèse, je m'intéresse aux moyens méthodologiques de l'étude de l'adaptation locale d'une part, et à l'étude de ce phénomène le long d'un gradient d'altitude chez la plante alpine Arabis alpina d'autre part.Dans la première partie méthodologique, je montre que les méthodes de scan génomique pour détecter les marqueurs génétiques sous sélection peuvent souffrir de forts taux de faux positifs lorsqu'exposées à des jeux de données complexes, mais réalistes.Je présente ensuite une méthode statistique de détection de marqueurs génétiques sous sélection qui, contrairement aux méthodes existantes, utilisent à la fois la notion de différentiation génétique (ou Fst) et une information environnementale.Cette méthode a été développée de manière à limiter son taux de faux positifs de manière générale.J'offre enfin une perspective concernant les liens entre une expérience ancienne en biologie évolutive (l'expérience de jardin commun) et les nouveaux développements moléculaires et statistiques modernes.Dans la seconde partie empirique, je présente une analyse de la démographie d'A. alpina dans six populations naturelles. Outre qu'elle révèle des caractéristiques biologiques intéressantes sur cette espèce (faible espérance de vie, reproduction et survie très différentielle...), cette analyse montre que la croissance diminue et la survie augmente chez cette espèce avec la baisse de la température moyenne (donc avec l'altitude).Puisque ces analyses ne permettent pas d'exclure des hypothèses de dérive et de plasticité phénotype, je présente une analyse en jardin commun sur A. alpina qui permet de lisser les problèmes de plasticité phénotypique et qui, combinée à des analyses moléculaires, permettent d'exclure l'hypothèse de dérive.Les résultats montrent qu'il existe un syndrome phénotypique adaptatif lié à la température moyenne qui tend à des plantes plus petites, plus compactes, qui croissent et se reproduisent moins, dans les milieux froids.À l'aide des données moléculaires et de méthodes de scan génomique, je présente une liste de 40 locus qui peuvent être impliqués dans ce processus.Pour finir, je discute l'ensemble de ces résultats empiriques dans un contexte plus général d'écologie alpine. Je résume ensuite les principaux obstacles méthodologiques à l'étude de l'adaptation locale et je fourni quelques perspectives méthodologiques

Genomic signatures of inbreeding depression for a threatened Aotearoa New Zealand passerine

For small and isolated populations, the increased chance of mating between related individuals can result in a substantial reduction in individual and population fitness. Despite the increasing availability of genomic data to measure inbreeding accurately across the genome, inbreeding depression studies for threatened species are still scarce due to the difficulty of measuring fitness in the wild. Here, we investigate inbreeding and inbreeding depression for the extensively monitored Tiritiri Mātangi island population of a threatened Aotearoa New Zealand passerine, the hihi (Notiomystis cincta). First, using a custom 45 k single nucleotide polymorphism (SNP) array, we explore genomic inbreeding patterns by inferring homozygous segments across the genome. Although all individuals have similar levels of ancient inbreeding, highly inbred individuals are affected by recent inbreeding, which can probably be explained by bottleneck effects such as habitat loss after European arrival and their translocation to the island in the 1990s. Second, we investigate genomic inbreeding effects on fitness, measured as lifetime reproductive success, and its three components, juvenile survival, adult annual survival and annual reproductive success, in 363 hihi. We find that global inbreeding significantly affects juvenile survival but none of the remaining fitness traits. Finally, we employ a genome-wide association approach to test the locus-specific effects of inbreeding on fitness, and identify 13 SNPs significantly associated with lifetime reproductive success. Our findings suggest that inbreeding depression does impact hihi, but at different genomic scales for different traits, and that purging has therefore failed to remove all variants with deleterious effects from this population of conservation concern

Fixed-effect variance and the estimation of repeatabilities and heritabilities : issues and solutions

HS was supported by an Emmy Noether fellowship from the German Research Foundation (DFG; SCHI 1188/1-1). SN is supported by a Future Fellowship, Australia (FT130100268). MBM is supported by a University Research Fellowship from the Royal Society (London).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 individual 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 example 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.PostprintPeer reviewe

Can threatened species adapt in restored habitat? No expected evolutionary response in lay date for the New Zealand hihi

Many bird species have been observed shifting their laying date to earlier in the year in response to climate change. However, the vast majority of these studies were performed on non‐threatened species, less impacted by reduced genetic diversity (which is expected to limit evolutionary response) as a consequence of genetic bottlenecks, drift and population isolation. Here, we study the relationship between lay date and fitness, as well as its genetic basis, to understand the evolutionary constraints on phenology faced by threatened species using a recently reintroduced population of the endangered New Zealand passerine, the hihi (Notiomystis cincta). A large discrepancy between the optimal laying date and the mode of laying date creates a strong selection differential of −11.24. The impact of this discrepancy on fitness is principally mediated through survival of offspring from hatchling to fledgling. This discrepancy does not seem to arise from a difference in female quality or a trade‐off with lifetime breeding success. We find that start of breeding season depends on female age and average temperature prior to the breeding season. Laying date is not found to be significantly heritable. Overall, our research suggests that this discrepancy is a burden on hihi fitness, which will not be resolved through evolution or phenotypic plasticity. More generally, these results show that threatened species introduced to restored habitats might lack adaptive potential and plasticity to adjust their phenology to their new environment. This constraint is also likely to limit their ability to face future challenges, including climate change

Patterns of phenotypic plasticity and local adaptation in the wide elevation range of the alpine plant Arabis alpina

OEG was supported by the Marine Alliance for Science and Technology for Scotland (MASTS).1.  Local adaptation and phenotypic plasticity are two important characteristics of alpine plants to overcome the threats caused by global changes. Among alpine species, Arabis alpina is characterised by an unusually wide altitudinal amplitude, ranging from 800 to 3,100 m of elevation in the French Alps. Two non‐exclusive hypotheses can explain the presence of A. alpina across this broad ecological gradient: adaptive phenotypic plasticity or local adaptation, making this species especially useful to better understand these phenomena in alpine plant species. 2.  We carried out common garden experiments at two different elevations with maternal progenies from six sites that differed in altitude. We showed that (1) key phenotypic traits (morphotype, total fruit length, growth, height) display significant signs of local adaptation, (2) most traits studied are characterised by a high phenotypic plasticity between the two experimental gardens and (3) the two populations from the highest elevations lacked morphological plasticity compared to the other populations. 3.  By combining two genome scan approaches (detection of selection and association methods), we isolated a candidate gene (Sucrose‐Phosphate Synthase 1). This gene was associated with height and local average temperature in our studied populations, consistent with previous studies on this gene in Arabidopsis thaliana. 4.  Synthesis. Given the nature of the traits involved in the detected pattern of local adaptation and the relative lack of plasticity of the two most extreme populations, our findings are consistent with a scenario of a locally adaptive stress response syndrome in high elevation populations. Due to a reduced phenotypic plasticity, an overall low intra‐population genetic diversity of the adaptive traits and weak gene flow, populations of high altitude might have difficulties to cope with, e.g. a rise of temperature.PostprintPeer reviewe

Common garden experiments in the genomic era : new perspectives and opportunities

PdV was supported by a doctoral studentship from the French Ministère de la Recherche et de l’Enseignement Supérieur. OEG was supported by the Marine Alliance for Science and Technology for Scotland (MASTS)The study of local adaptation is rendered difficult by many evolutionary confounding phenomena (e.g. genetic drift and demographic history). When complex traits are involved in local adaptation, phenomena such as phenotypic plasticity further hamper evolutionary biologists to study the complex relationships between phenotype, genotype and environment. In this perspective paper, we suggest that the common garden experiment, specifically designed to deal with phenotypic plasticity has a clear role to play in the study of local adaptation, even (if not specifically) in the genomic era. After a quick review of some high-throughput genotyping protocols relevant in the context of a common garden, we explore how to improve common garden analyses with dense marker panel data and recent statistical methods. We then show how combining approaches from population genomics and genome-wide association studies with the settings of a common garden can yield to a very efficient, thorough and integrative study of local adaptation. Especially, evidence from genomic (e.g. genome scan) and phenotypic origins constitute independent insights into the possibility of local adaptation scenarios, and genome-wide association studies in the context of a common garden experiment allow to decipher the genetic bases of adaptive traits.PostprintPeer reviewe

Many Options, Few Solutions: Over 60 My Snakes Converged on a Few Optimal Venom Formulations

Gene expression changes contribute to complex trait variations in both individuals and populations. However, the evolution of gene expression underlying complex traits over macroevolutionary timescales remains poorly understood. Snake venoms are proteinaceous cocktails where the expression of each toxin can be quantified and mapped to a distinct genomic locus and traced for millions of years. Using a phylogenetic generalized linear mixed model, we analyzed expression data of toxin genes from 52 snake species spanning the 3 venomous snake families and estimated phylogenetic covariance, which acts as a measure of evolutionary constraint. We find that evolution of toxin combinations is not constrained. However, although all combinations are in principle possible, the actual dimensionality of phylomorphic space is low, with envenomation strategies focused around only four major toxin families: metalloproteases, three-finger toxins, serine proteases, and phospholipases A2. Although most extant snakes prioritize either a single or a combination of major toxin families, they are repeatedly recruited and lost. We find that over macroevolutionary timescales, the venom phenotypes were not shaped by phylogenetic constraints, which include important microevolutionary constraints such as epistasis and pleiotropy, but more likely by ecological filtering that permits a small number of optimal solutions. As a result, phenotypic optima were repeatedly attained by distantly related species. These results indicate that venoms evolve by selection on biochemistry of prey envenomation, which permit diversity through parallelism, and impose strong limits, since only a few of the theoretically possible strategies seem to work well and are observed in extant snakes

A bayesian test for Hardy-Weinberg equilibrium of bi-allelic X-chromosomal markers

The X chromosome is a relatively large chromosome, harboring a lot of genetic information. Much of the statistical analysis of X-chromosomal information is complicated by the fact that males only have one copy. Recently, frequentist statistical tests for Hardy–Weinberg equilibrium have been proposed specifically for dealing with markers on the X chromosome. Bayesian test procedures for Hardy–Weinberg equilibrium for the autosomes have been described, but Bayesian work on the X chromosome in this context is lacking. This paper gives the first Bayesian approach for testing Hardy–Weinberg equilibrium with biallelic markers at the X chromosome. Marginal and joint posterior distributions for the inbreeding coefficient in females and the male to female allele frequency ratio are computed, and used for statistical inference. The paper gives a detailed account of the proposed Bayesian test, and illustrates it with data from the 1000 Genomes project. In that implementation, a novel approach to tackle multiple testing from a Bayesian perspective through posterior predictive checks is used.Peer ReviewedPostprint (author's final draft