Quantitative genetic modeling and inference in the presence of nonignorable missing data.

Natural selection is typically exerted at some specific life stages. If natural selection takes place before a trait can be measured, using conventional models can cause wrong inference about population parameters. When the missing data process relates to the trait of interest, a valid inference requires explicit modeling of the missing process. We propose a joint modeling approach, a shared parameter model, to account for nonrandom missing data. It consists of an animal model for the phenotypic data and a logistic model for the missing process, linked by the additive genetic effects. A Bayesian approach is taken and inference is made using integrated nested Laplace approximations. From a simulation study we find that wrongly assuming that missing data are missing at random can result in severely biased estimates of additive genetic variance. Using real data from a wild population of Swiss barn owls Tyto alba, our model indicates that the missing individuals would display large black spots; and we conclude that genes affecting this trait are already under selection before it is expressed. Our model is a tool to correctly estimate the magnitude of both natural selection and additive genetic variance.

Correlated evolution of mating strategy and inbreeding depression within and among populations of the hermaphroditic snail Physa acuta

Inbreeding depression is one of the main forces opposing the evolution of self-fertilization. Of central importance is the hypothesis that inbreeding depression and selfing coevolve antagonistically, generating either low selfing rate and high inbreeding depression or vice versa. However, there is limited evidence for this coevolution within species. We investigated this topic in the hermaphroditic snail Physa acuta. In this species, isolated individuals delay the onset of egg laying compared to individuals having access to mates. Longer delays (''waiting times'') indicate more intense selfing avoidance. We measured inbreeding depression and waiting time in a large quantitative-genetic experiment (281 outbred families derived from 26 natural populations). We observed large genetic variance for both traits and a strong positive genetic covariance between them, most of which resided within rather than among populations. It means that, within populations, individuals with higher mutation load avoided selfing more strongly on average. This genetic covariance may result from pleiotropy and/or linkage disequilibrium. Whatever its genetic architecture, the fact it emerges specifically when individuals are deprived of mates suggests it is not fortuitous and rather reflects the action of natural selection. We conclude that a diversity of mating strategies can arise within populations subjected to variation in inbreeding depression.

A quantitative genetic signature of senescence in a short-lived perennial plant.

The evolution of senescence (the physiological decline of organisms with age) poses an apparent paradox because it represents a failure of natural selection to increase the survival and reproductive performance of organisms. The paradox can be resolved if natural selection becomes less effective with age, because the death of postreproductive individuals should have diminished effects on Darwinian fitness [1, 2]. A substantial body of empirical work is consistent with this prediction for animals, which transmit their genes to progeny via an immortal germline. However, such evidence is still lacking in plants, which lack a germline and whose reproduction is diffuse and modular across the soma. Here, we provide experimental evidence for a genetic basis of senescence in the short-lived perennial plant Silene latifolia. Our pedigree-based analysis revealed a marked increase with age in the additive genetic variance of traits closely associated with fitness. This result thus extends to plants the quantitative genetic support for the evolutionary theory of senescence.

Meta-analysis of gene-level associations for rare variants based on single-variant statistics.

Meta-analysis of genome-wide association studies (GWASs) has led to the discoveries of many common variants associated with complex human diseases. There is a growing recognition that identifying "causal" rare variants also requires large-scale meta-analysis. The fact that association tests with rare variants are performed at the gene level rather than at the variant level poses unprecedented challenges in the meta-analysis. First, different studies may adopt different gene-level tests, so the results are not compatible. Second, gene-level tests require multivariate statistics (i.e., components of the test statistic and their covariance matrix), which are difficult to obtain. To overcome these challenges, we propose to perform gene-level tests for rare variants by combining the results of single-variant analysis (i.e., p values of association tests and effect estimates) from participating studies. This simple strategy is possible because of an insight that multivariate statistics can be recovered from single-variant statistics, together with the correlation matrix of the single-variant test statistics, which can be estimated from one of the participating studies or from a publicly available database. We show both theoretically and numerically that the proposed meta-analysis approach provides accurate control of the type I error and is as powerful as joint analysis of individual participant data. This approach accommodates any disease phenotype and any study design and produces all commonly used gene-level tests. An application to the GWAS summary results of the Genetic Investigation of ANthropometric Traits (GIANT) consortium reveals rare and low-frequency variants associated with human height. The relevant software is freely available.

Additive genetic effects on embryo viability in a whitefish (Salmonidae) influenced by the water mould Saprolegnia ferax

Animals and plants are associated with symbiotic microbes whose roles range from mutualism to commensalism to parasitism. These roles may not only be taxon-specific but also dependent on environmental conditions and host factors. To experimentally test these possibilities, we drew a random sample of adult whitefish from a natural population, bred them in vitro in a full-factorial design in order to separate additive genetic from maternal environmental effects on offspring, and tested the performance of the resulting embryos under different environmental conditions. Enhancing the growth of symbiotic microbes with supplemental nutrients released cryptic additive genetic variance for viability in the fish host. These effects vanished with the concurrent addition of the water mould Saprolegnia ferax. Our findings demonstrate that the heritability of host fitness is environment-specific and critically depends on the interaction between symbiotic microbes.

Genetic differentiation in Silene dioica metapopulations: estimation of spatiotemporal effects in a successional plant species

Silene dioica is a diploid, dioecious, perennial, insect-pollinated herb and part of the deciduous phase of primary succession in Skeppsvik Archipelago, Gulf of Bothnia, Sweden. These islands are composed of material deposited and left underwater by melting ice at the end of the last ice age. A rapid and relatively constant rate of land uplift of 0.9 cm per year continually creates new islands available for colonization by plants. Because the higher deposits appear first, islands differ in age. Because it is possible to estimate the ages of islands and populations of plant species belonging to early stages of succession, the genetic dynamics occurring within an age-structured metapopulation can be investigated in this archipelago. Fifty-two island populations of S. dioica of known ages, sizes, and distances from each other were studied through electrophoretic data. A number of factors increase the degree of genetic differentiation among these island populations relative to an island model at equilibrium. Newly founded populations were more differentiated than those of intermediate age, which suggests that colonization dynamics increase genetic variance among populations. The very old populations, which decrease in size as they approach extinction, were more differentiated than intermediate-aged populations. Isolation by distance occurs in this system. Colonizers are likely to come from more than one source, and the migrant pool model best explains colonization events in the archipelago. Degree of environmental exposure also affects population differentiation.

Impact of incorrect assumptions on the covariance structure of random effects and/or residuals in nonlinear mixed models for repeated measures data

In this paper we analyse, using Monte Carlo simulation, the possible consequences of incorrect assumptions on the true structure of the random effects covariance matrix and the true correlation pattern of residuals, over the performance of an estimation method for nonlinear mixed models. The procedure under study is the well known linearization method due to Lindstrom and Bates (1990), implemented in the nlme library of S-Plus and R. Its performance is studied in terms of bias, mean square error (MSE), and true coverage of the associated asymptotic confidence intervals. Ignoring other criteria like the convenience of avoiding over parameterised models, it seems worst to erroneously assume some structure than do not assume any structure when this would be adequate.

Scale-specific sex-biased dispersal in the Valais shrew unveiled by genetic variation on the Y chromosome, autosomes, and mitochondrial DNA.

We investigated sex specificities in the evolutionary processes shaping Y chromosome, autosomes, and mitochondrial DNA patterns of genetic structure in the Valais shrew (Sorex antinorii), a mountain dwelling species with a hierarchical distribution. Both hierarchical analyses of variance and isolation-by-distance analyses revealed patterns of population structure that were not consistent across maternal, paternal, and biparentally inherited markers. Differentiation on a Y microsatellite was lower than expected from the comparison with autosomal microsatellites and mtDNA, and it was mostly due to genetic variance among populations within valleys, whereas the opposite was observed on other markers. In addition, there was no pattern of isolation by distance for the Y, whereas there was strong isolation by distance on mtDNA and autosomes. We use a hierarchical island model of coancestry dynamics to discuss the relative roles of the microevolutionary forces that may induce such patterns. We conclude that sex-biased dispersal is the most important driver of the observed genetic structure, but with an intriguing twist: it seems that dispersal is strongly male biased at large spatial scale, whereas it is mildly biased in favor of females at local scale. These results add to recent reports of scale-specific sex-biased dispersal patterns, and emphasize the usefulness of the Y chromosome in conjunction with mtDNA and autosomes to infer sex specificities.

Testing the effects of genetic crossing distance on embryo survival within a metapopulation of brown trout (Salmo trutta)

Predicting progeny performance from parental genetic divergence can potentially enhance the efficiency of supportive breeding programmes and facilitate risk assessment. Yet, experimental testing of the effects of breeding distance on offspring performance remains rare, especially in wild populations of vertebrates. Recent studies have demonstrated that embryos of salmonid fish are sensitive indicators of additive genetic variance for viability traits. We therefore used gametes of wild brown trout (Salmo trutta) from five genetically distinct populations of a river catchment in Switzerland, and used a full factorial design to produce over 2,000 embryos in 100 different crosses with varying genetic distances (FST range 0.005-0.035). Customized egg capsules allowed recording the survival of individual embryos until hatching under natural field conditions. Our breeding design enabled us to evaluate the role of the environment, of genetic and nongenetic parental contributions, and of interactions between these factors, on embryo viability. We found that embryo survival was strongly affected by maternal environmental (i.e. non-genetic) effects and by the microenvironment, i.e. by the location within the gravel. However, embryo survival was not predicted by population divergence, parental allelic dissimilarity, or heterozygosity, neither in the field nor under laboratory conditions. Our findings suggest that the genetic effects of inter-population hybridization within a genetically differentiated meta-population can be minor in comparison to environmental effects.

Second-order parameter estimation

This work provides a general framework for the design of second-order blind estimators without adopting anyapproximation about the observation statistics or the a prioridistribution of the parameters. The proposed solution is obtainedminimizing the estimator variance subject to some constraints onthe estimator bias. The resulting optimal estimator is found todepend on the observation fourth-order moments that can be calculatedanalytically from the known signal model. Unfortunately,in most cases, the performance of this estimator is severely limitedby the residual bias inherent to nonlinear estimation problems.To overcome this limitation, the second-order minimum varianceunbiased estimator is deduced from the general solution by assumingaccurate prior information on the vector of parameters.This small-error approximation is adopted to design iterativeestimators or trackers. It is shown that the associated varianceconstitutes the lower bound for the variance of any unbiasedestimator based on the sample covariance matrix.The paper formulation is then applied to track the angle-of-arrival(AoA) of multiple digitally-modulated sources by means ofa uniform linear array. The optimal second-order tracker is comparedwith the classical maximum likelihood (ML) blind methodsthat are shown to be quadratic in the observed data as well. Simulationshave confirmed that the discrete nature of the transmittedsymbols can be exploited to improve considerably the discriminationof near sources in medium-to-high SNR scenarios.

Genetic interactions involving major genes at the dwarf locus in egg-type chickens

Three egg-type stocks segregating dwarf (dw) and bantam (dwB) genes in female progeny were produced from the same 18 heterozygous (dwB/dw) sires used to inseminate dams of three different genotypes: normal (dw+), dwarf (dw) and bantam (dwB) dams. The heritability of 8-week body weight estimated from full-sibs of the same phenotype of progeny was 0.40, and that estimated from paternal half-sibs of the same phenotype (dwarf or bantam), and from the same genotype of dam was 0.38. Therefore, maternal and non-additive effects within genotypic classes of dam made little contribution to the genetic variance for 8-week body weight among their progeny. The interaction of sires (S) with genotypes (dw+, dw and dwB) of dam (G) was significant at the 5% level. This indicates that the rankings of the sires within each one of the three genotypes of dam were not the same, probably due to non-additive genetic variation among genotypes of dams. The evidence indicated that in general the genes from individual sires combined differently with each type of dam (G). Those genes which combined well with the genes from normal (dw+) dams combined poorly with both the genes from the dwarf (dw) and the genes from the bantam (dwB) dams. The interaction of sires (S) with phenotypes (dwarf and bantam) of progeny (P) was significant at the 10% level. The results indicated a probable gene x genotype interaction for 8-week weight between genes at the dwarf locus (dw and dwB) and the background genotype (single and/or polygenes). The correlation among paternal half-sibs was influenced more by the S x G than by the S x P interaction, but the effects tended to be cumulative

Choix de portefeuille de grande taille et mesures de risque pour preneurs de décision pessimistes

Cette thèse de doctorat consiste en trois chapitres qui traitent des sujets de choix de portefeuilles de grande taille, et de mesure de risque. Le premier chapitre traite du problème d’erreur d’estimation dans les portefeuilles de grande taille, et utilise le cadre d'analyse moyenne-variance. Le second chapitre explore l'importance du risque de devise pour les portefeuilles d'actifs domestiques, et étudie les liens entre la stabilité des poids de portefeuille de grande taille et le risque de devise. Pour finir, sous l'hypothèse que le preneur de décision est pessimiste, le troisième chapitre dérive la prime de risque, une mesure du pessimisme, et propose une méthodologie pour estimer les mesures dérivées. Le premier chapitre améliore le choix optimal de portefeuille dans le cadre du principe moyenne-variance de Markowitz (1952). Ceci est motivé par les résultats très décevants obtenus, lorsque la moyenne et la variance sont remplacées par leurs estimations empiriques. Ce problème est amplifié lorsque le nombre d’actifs est grand et que la matrice de covariance empirique est singulière ou presque singulière. Dans ce chapitre, nous examinons quatre techniques de régularisation pour stabiliser l’inverse de la matrice de covariance: le ridge, spectral cut-off, Landweber-Fridman et LARS Lasso. Ces méthodes font chacune intervenir un paramètre d’ajustement, qui doit être sélectionné. La contribution principale de cette partie, est de dériver une méthode basée uniquement sur les données pour sélectionner le paramètre de régularisation de manière optimale, i.e. pour minimiser la perte espérée d’utilité. Précisément, un critère de validation croisée qui prend une même forme pour les quatre méthodes de régularisation est dérivé. Les règles régularisées obtenues sont alors comparées à la règle utilisant directement les données et à la stratégie naïve 1/N, selon leur perte espérée d’utilité et leur ratio de Sharpe. Ces performances sont mesurée dans l’échantillon (in-sample) et hors-échantillon (out-of-sample) en considérant différentes tailles d’échantillon et nombre d’actifs. Des simulations et de l’illustration empirique menées, il ressort principalement que la régularisation de la matrice de covariance améliore de manière significative la règle de Markowitz basée sur les données, et donne de meilleurs résultats que le portefeuille naïf, surtout dans les cas le problème d’erreur d’estimation est très sévère. Dans le second chapitre, nous investiguons dans quelle mesure, les portefeuilles optimaux et stables d'actifs domestiques, peuvent réduire ou éliminer le risque de devise. Pour cela nous utilisons des rendements mensuelles de 48 industries américaines, au cours de la période 1976-2008. Pour résoudre les problèmes d'instabilité inhérents aux portefeuilles de grandes tailles, nous adoptons la méthode de régularisation spectral cut-off. Ceci aboutit à une famille de portefeuilles optimaux et stables, en permettant aux investisseurs de choisir différents pourcentages des composantes principales (ou dégrées de stabilité). Nos tests empiriques sont basés sur un modèle International d'évaluation d'actifs financiers (IAPM). Dans ce modèle, le risque de devise est décomposé en deux facteurs représentant les devises des pays industrialisés d'une part, et celles des pays émergents d'autres part. Nos résultats indiquent que le risque de devise est primé et varie à travers le temps pour les portefeuilles stables de risque minimum. De plus ces stratégies conduisent à une réduction significative de l'exposition au risque de change, tandis que la contribution de la prime risque de change reste en moyenne inchangée. Les poids de portefeuille optimaux sont une alternative aux poids de capitalisation boursière. Par conséquent ce chapitre complète la littérature selon laquelle la prime de risque est importante au niveau de l'industrie et au niveau national dans la plupart des pays. Dans le dernier chapitre, nous dérivons une mesure de la prime de risque pour des préférences dépendent du rang et proposons une mesure du degré de pessimisme, étant donné une fonction de distorsion. Les mesures introduites généralisent la mesure de prime de risque dérivée dans le cadre de la théorie de l'utilité espérée, qui est fréquemment violée aussi bien dans des situations expérimentales que dans des situations réelles. Dans la grande famille des préférences considérées, une attention particulière est accordée à la CVaR (valeur à risque conditionnelle). Cette dernière mesure de risque est de plus en plus utilisée pour la construction de portefeuilles et est préconisée pour compléter la VaR (valeur à risque) utilisée depuis 1996 par le comité de Bâle. De plus, nous fournissons le cadre statistique nécessaire pour faire de l’inférence sur les mesures proposées. Pour finir, les propriétés des estimateurs proposés sont évaluées à travers une étude Monte-Carlo, et une illustration empirique en utilisant les rendements journaliers du marché boursier américain sur de la période 2000-2011.

Aspectes metodològics i aplicacions de la modelització del temps de supervivència multivariant mitjançant models mixtes

Els estudis de supervivència s'interessen pel temps que passa des de l'inici de l'estudi (diagnòstic de la malaltia, inici del tractament,...) fins que es produeix l'esdeveniment d'interès (mort, curació, millora,...). No obstant això, moltes vegades aquest esdeveniment s'observa més d'una vegada en un mateix individu durant el període de seguiment (dades de supervivència multivariant). En aquest cas, és necessari utilitzar una metodologia diferent a la utilitzada en l'anàlisi de supervivència estàndard. El principal problema que l'estudi d'aquest tipus de dades comporta és que les observacions poden no ser independents. Fins ara, aquest problema s'ha solucionat de dues maneres diferents en funció de la variable dependent. Si aquesta variable segueix una distribució de la família exponencial s'utilitzen els models lineals generalitzats mixtes (GLMM); i si aquesta variable és el temps, variable amb una distribució de probabilitat no pertanyent a aquesta família, s'utilitza l'anàlisi de supervivència multivariant. El que es pretén en aquesta tesis és unificar aquests dos enfocs, és a dir, utilitzar una variable dependent que sigui el temps amb agrupacions d'individus o d'observacions, a partir d'un GLMM, amb la finalitat d'introduir nous mètodes pel tractament d'aquest tipus de dades.

A new set of orthogonal patterns in weather and climate: Optimally interpolated patterns.

A new spectral-based approach is presented to find orthogonal patterns from gridded weather/climate data. The method is based on optimizing the interpolation error variance. The optimally interpolated patterns (OIP) are then given by the eigenvectors of the interpolation error covariance matrix, obtained using the cross-spectral matrix. The formulation of the approach is presented, and the application to low-dimension stochastic toy models and to various reanalyses datasets is performed. In particular, it is found that the lowest-frequency patterns correspond to largest eigenvalues, that is, variances, of the interpolation error matrix. The approach has been applied to the Northern Hemispheric (NH) and tropical sea level pressure (SLP) and to the Indian Ocean sea surface temperature (SST). Two main OIP patterns are found for the NH SLP representing respectively the North Atlantic Oscillation and the North Pacific pattern. The leading tropical SLP OIP represents the Southern Oscillation. For the Indian Ocean SST, the leading OIP pattern shows a tripole-like structure having one sign over the eastern and north- and southwestern parts and an opposite sign in the remaining parts of the basin. The pattern is also found to have a high lagged correlation with the Niño-3 index with 6-months lag.

Identification of nonlinear systems using generalized kernel models

Nonlinear system identification is considered using a generalized kernel regression model. Unlike the standard kernel model, which employs a fixed common variance for all the kernel regressors, each kernel regressor in the generalized kernel model has an individually tuned diagonal covariance matrix that is determined by maximizing the correlation between the training data and the regressor using a repeated guided random search based on boosting optimization. An efficient construction algorithm based on orthogonal forward regression with leave-one-out (LOO) test statistic and local regularization (LR) is then used to select a parsimonious generalized kernel regression model from the resulting full regression matrix. The proposed modeling algorithm is fully automatic and the user is not required to specify any criterion to terminate the construction procedure. Experimental results involving two real data sets demonstrate the effectiveness of the proposed nonlinear system identification approach.