The additive genetic variance after bottlenecks is affected by the number of loci involved in epistatic interactions.

We investigated the role of the number of loci coding for a neutral trait on the release of additive variance for this trait after population bottlenecks. Different bottleneck sizes and durations were tested for various matrices of genotypic values, with initial conditions covering the allele frequency space. We used three different types of matrices. First, we extended Cheverud and Routman's model by defining matrices of "pure" epistasis for three and four independent loci; second, we used genotypic values drawn randomly from uniform, normal, and exponential distributions; and third we used two models of simple metabolic pathways leading to physiological epistasis. For all these matrices of genotypic values except the dominant metabolic pathway, we find that, as the number of loci increases from two to three and four, an increase in the release of additive variance is occurring. The amount of additive variance released for a given set of genotypic values is a function of the inbreeding coefficient, independently of the size and duration of the bottleneck. The level of inbreeding necessary to achieve maximum release in additive variance increases with the number of loci. We find that additive-by-additive epistasis is the type of epistasis most easily converted into additive variance. For a wide range of models, our results show that epistasis, rather than dominance, plays a significant role in the increase of additive variance following bottlenecks.

Genetics of cadmium hyperaccumulation variance in Thlaspi caerulescens natural populations from Switzerland

SUMMARY Heavy metal presence in the environment is a serious concern since some of them can be toxic to plants, animals and humans once accumulated along the food chain. Cadmium (Cd) is one of the most toxic heavy metal. It is naturally present in soils at various levels and its concentration can be increased by human activities. Several plants however have naturally developed strategies allowing them to grow on heavy metal enriched soils. One of them consists in the accumulation and sequestration of heavy metals in the above-ground biomass. Some plants present in addition an extreme strategy by which they accumulate a limited number of heavy metals in their shoots in amounts 100 times superior to those expected for a non-accumulating plant in the same conditions. Understanding the genetic basis of the hyperaccumulation trait - particularly for Cd - remains an important challenge which may lead to biotechnological applications in the soil phytoremediation. In this thesis, Thlaspi caerulescens J. & C. Presl (Brassicaceae) was used as a model plant to study the Cd hyperaccumulation trait, owing to its physiological and genetic characteristics. Twenty-four wild populations were sampled in different regions of Switzerland. They were characterized for environmental and soil parameters as well as intrinsic characteristics of plants (i.e. metal concentrations in shoots). They were as well genetically characterized by AFLPs, plastid DNA polymorphism and genes markers (CAPS and microsatellites) mainly developed in this thesis. Some of the investigated genes were putatively linked to the Cd hyperaccumulation trait. Since the study of the Cd hyperaccumulation in the field is important as it allows the identification of patterns of selection, the present work offered a methodology to define the Cd hyperaccumulation capacity of populations from different habitats permitting thus their comparison in the field. We showed that Cd, Zn, Fe and Cu accumulations were linked and that populations with higher Cd hyperaccumulation capacity had higher shoot and reproductive fitness. Using our genetic data, statistical methods (Beaumont & Nichols's procedure, partial Mantel tests) were applied to identify genomic signatures of natural selection related to the Cd hyperaccumulation capacity. A significant genetic difference between populations related to their Cd hyperaccumulation capacity was revealed based on somè specific markers (AFLP and candidate genes). Polymorphism at the gene encoding IRTl (Iron-transporter also participating to the transport of Zn) was suggested as explaining part of the variation in Cd hyperaccumulation capacity of populations supporting previous physiological investigations. RÉSUMÉ La présence de métaux lourds dans l'environnement est un phénomène préoccupant. En effet, certains métaux lourds - comme le cadmium (Cd) -sont toxiques pour les plantes, les animaux et enfin, accumulés le long de la chaîne alimentaire, pour les hommes. Le Cd est naturellement présent dans le sol et sa concentration peut être accrue par différentes activités humaines. Certaines plantes ont cependant développé des stratégies leur permettant de pousser sur des sols contaminés en métaux lourds. Parmi elles, certaines accumulent et séquestrent les métaux lourds dans leurs parties aériennes. D`autres présentent une stratégie encore plus extrême. Elles accumulent un nombre limité de métaux lourds en quantités 100 fois supérieures à celles attendues pour des espèces non-accumulatrices sous de mêmes conditions. La compréhension des bases génétiques de l'hyperaccumulation -particulièrement celle du Cd - représente un défi important avec des applications concrètes en biotechnologies, tout particulièrement dans le but appliqué de la phytoremediation des sols contaminés. Dans cette thèse, Thlaspi caerulescens J. & C. Presl (Brassicaceae) a été utilisé comme modèle pour l'étude de l'hyperaccumulation du Cd de par ses caractéristiques physiologiques et génétiques. Vingt-quatre populations naturelles ont été échantillonnées en Suisse et pour chacune d'elles les paramètres environnementaux, pédologique et les caractéristiques intrinsèques aux plantes (concentrations en métaux lourds) ont été déterminés. Les populations ont été caractérisées génétiquement par des AFLP, des marqueurs chloroplastiques et des marqueurs de gènes spécifiques, particulièrement ceux potentiellement liés à l'hyperaccumulation du Cd (CAPS et microsatellites). La plupart ont été développés au cours de cette thèse. L'étude de l'hyperaccumulation du Cd en conditions naturelles est importante car elle permet d'identifier la marque, éventuelle de sélection naturelle. Ce travail offre ainsi une méthodologie pour définir et comparer la capacité des populations à hyperaccumuler le Cd dans différents habitats. Nous avons montré que les accumulations du Cd, Zn, Fe et Cu sont liées et que les populations ayant une grande capacité d'hyperaccumuler le Cd ont également une meilleure fitness végétative et reproductive. Des méthodes statistiques (l'approche de Beaumont & Nichols, tests de Martel partiels) ont été utilisées sur les données génétiques pour identifier la signature génomique de la sélection naturelle liée à la capacité d'hyperaccumuler le Cd. Une différenciation génétique des populations liée à leur capacité d'hyperaccumuler le Cd a été mise en évidence sur certains marqueurs spécifiques. En accord avec les études physiologiques connues, le polymorphisme au gène codant IRT1 (un transporteur de Fe impliqué dans le transport du Zn) pourrait expliquer une partie de la variance de la capacité des populations à hyperaccumuler le Cd.

Spanning tests in return and stochastic discount factor mean-variance frontiers: A unifying approach

We propose new spanning tests that assess if the initial and additional assets share theeconomically meaningful cost and mean representing portfolios. We prove their asymptoticequivalence to existing tests under local alternatives. We also show that unlike two-step oriterated procedures, single-step methods such as continuously updated GMM yield numericallyidentical overidentifyng restrictions tests, so there is arguably a single spanning test.To prove these results, we extend optimal GMM inference to deal with singularities in thelong run second moment matrix of the influence functions. Finally, we test for spanningusing size and book-to-market sorted US stock portfolios.

Breeding system and genetic variance in the monogamous, semi-social shrew, Crocidura russula

The population-genetic consequences of monogamy and male philopatry (a rare breeding system in mammals) were investigated using microsatellite markers in the semisocial and anthropophilic shrew Crocidura russula. A hierarchical sampling design over a 16-km geographical transect revealed a large genetic diversity (h = 0.813) with significant differentiation among subpopulations (F-ST = 5-6%), which suggests an exchange of 4.4 migrants per generation. Demic effective-size estimates were very high, due both to this limited gene inflow and to the inner structure of subpopulations. These were made of 13-20 smaller units (breeding groups), comprising an estimate of four breeding pairs each. Members of the same breeding groups displayed significant coancestries (F-LS = 9-10%), which was essentially due to strong male kinship: syntopic males were on average related at the half-sib level. Female dispersal among breeding groups was not complete (similar to 39%), and insufficient to prevent inbreeding. From our results, the breeding strategy of C. russula seems less efficient than classical mammalian systems (polygyny and male dispersal) in disentangling coancestry from inbreeding, but more so in retaining genetic variance.

Variance reduction methods for simulation of densities on Wiener space

We develop a general error analysis framework for the Monte Carlo simulationof densities for functionals in Wiener space. We also study variancereduction methods with the help of Malliavin derivatives. For this, wegive some general heuristic principles which are applied to diffusionprocesses. A comparison with kernel density estimates is made.

Duality in mean-variance frontiers with conditioning information

Portfolio and stochastic discount factor (SDF) frontiers are usually regarded as dual objects, and researchers sometimes use one to answer questions about the other. However, the introduction of conditioning information and active portfolio strategies alters this relationship. For instance, the unconditional portfolio frontier in Hansen and Richard (1987) is not dual to the unconditional SDF frontier in Gallant, Hansen and Tauchen (1990). We characterise the dual objects to those frontiers, and relate them to the frontiers generated with managed portfolios, which are commonly used in empirical work. We also study the implications of a safe asset and other special cases.

Sample size and statistical power in the hierarchical analysis of variance: applications in morphometry of the nervous system.

Analysis of variance is commonly used in morphometry in order to ascertain differences in parameters between several populations. Failure to detect significant differences between populations (type II error) may be due to suboptimal sampling and lead to erroneous conclusions; the concept of statistical power allows one to avoid such failures by means of an adequate sampling. Several examples are given in the morphometry of the nervous system, showing the use of the power of a hierarchical analysis of variance test for the choice of appropriate sample and subsample sizes. In the first case chosen, neuronal densities in the human visual cortex, we find the number of observations to be of little effect. For dendritic spine densities in the visual cortex of mice and humans, the effect is somewhat larger. A substantial effect is shown in our last example, dendritic segmental lengths in monkey lateral geniculate nucleus. It is in the nature of the hierarchical model that sample size is always more important than subsample size. The relative weight to be attributed to subsample size thus depends on the relative magnitude of the between observations variance compared to the between individuals variance.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

Effects of common origin and common rearing environment on variance in ectoparasite load and phenotype of nestling Alpine swifts

Knowledge of the quantitative genetics of resistance to parasitism is key to appraise host evolutionary responses to parasite selection. Here, we studied effects of common origin (i.e. genetic and pre-hatching parental effects) and common rearing environment (i.e. post-hatching parental effects and other environment effects) on variance in ectoparasite load in nestling Alpine swifts (Apus melba). This colonial bird is intensely parasitized by blood sucking louse-flies that impair nestling development and survival. By cross-fostering half of the hatchlings between pairs of nests, we show strong significant effect of common rearing environment on variance (90.7% in 2002 and 90.9% in 2003) in the number of louse-flies per nestling and no significant effect of common origin on variance in the number of louse-flies per nestling. In contrast, significant effects of common origin were found for all the nestling morphological traits (i.e. body mass, wing length, tail length, fork length and sternum length) under investigation. Hence, our study suggests that genetic and pre-hatching parental effects play little role in the distribution of parasites among nestling Alpine swifts, and thus that nestlings have only limited scope for evolutionary responses against parasites. Our results highlight the need to take into consideration environmental factors, including the evolution of post-hatching parental effects such as nest sanitation, in our understanding of host-parasite relationships.

The mean-variance model from the inverse of the variance-covariance matrix

En este artículo, a partir de la inversa de la matriz de varianzas y covarianzas se obtiene el modelo Esperanza-Varianza de Markowitz siguiendo un camino más corto y matemáticamente riguroso. También se obtiene la ecuación de equilibrio del CAPM de Sharpe.

The evolution and consequences of sex-specific reproductive variance.

Natural selection favors alleles that increase the number of offspring produced by their carriers. But in a world that is inherently uncertain within generations, selection also favors alleles that reduce the variance in the number of offspring produced. If previous studies have established this principle, they have largely ignored fundamental aspects of sexual reproduction and therefore how selection on sex-specific reproductive variance operates. To study the evolution and consequences of sex-specific reproductive variance, we present a population-genetic model of phenotypic evolution in a dioecious population that incorporates previously neglected components of reproductive variance. First, we derive the probability of fixation for mutations that affect male and/or female reproductive phenotypes under sex-specific selection. We find that even in the simplest scenarios, the direction of selection is altered when reproductive variance is taken into account. In particular, previously unaccounted for covariances between the reproductive outputs of different individuals are expected to play a significant role in determining the direction of selection. Then, the probability of fixation is used to develop a stochastic model of joint male and female phenotypic evolution. We find that sex-specific reproductive variance can be responsible for changes in the course of long-term evolution. Finally, the model is applied to an example of parental-care evolution. Overall, our model allows for the evolutionary analysis of social traits in finite and dioecious populations, where interactions can occur within and between sexes under a realistic scenario of reproduction.

Natural selection on fecundity variance in subdivided populations: kin selection meets bet hedging.

In a series of seminal articles in 1974, 1975, and 1977, J. H. Gillespie challenged the notion that the "fittest" individuals are those that produce on average the highest number of offspring. He showed that in small populations, the variance in fecundity can determine fitness as much as mean fecundity. One likely reason why Gillespie's concept of within-generation bet hedging has been largely ignored is the general consensus that natural populations are of large size. As a consequence, essentially no work has investigated the role of the fecundity variance on the evolutionary stable state of life-history strategies. While typically large, natural populations also tend to be subdivided in local demes connected by migration. Here, we integrate Gillespie's measure of selection for within-generation bet hedging into the inclusive fitness and game theoretic measure of selection for structured populations. The resulting framework demonstrates that selection against high variance in offspring number is a potent force in large, but structured populations. More generally, the results highlight that variance in offspring number will directly affect various life-history strategies, especially those involving kin interaction. The selective pressures on three key traits are directly investigated here, namely within-generation bet hedging, helping behaviors, and the evolutionary stable dispersal rate. The evolutionary dynamics of all three traits are markedly affected by variance in offspring number, although to a different extent and under different demographic conditions.

Analysis of experiments in square lattice with emphasis on variance components. i. Individual analysis

This paper focused on four alternatives of analysis of experiments in square lattice as far as the estimation of variance components and some genetic parameters are concerned: 1) intra-block analysis with adjusted treatment and blocks within unadjusted repetitions; 2) lattice analysis as complete randomized blocks; 3) intrablock analysis with unadjusted treatment and blocks within adjusted repetitions; 4) lattice analysis as complete randomized blocks, by utilizing the adjusted means of treatments, obtained from the analysis with recovery of interblock information, having as mean square of the error the mean effective variance of this same analysis with recovery of inter-block information. For the four alternatives of analysis, the estimators and estimates were obtained for the variance components and heritability coefficients. The classification of material was also studied. The present study suggests that for each experiment and depending of the objectives of the analysis, one should observe which alternative of analysis is preferable, mainly in cases where a negative estimate is obtained for the variance component due to effects of blocks within adjusted repetitions.