An objective anisotropic elastic plastic model and Algorithm applicable to bone mechanics

The implicit projection algorithm of isotropic plasticity is extended to an objective anisotropic elastic perfectly plastic model. The recursion formula developed to project the trial stress on the yield surface, is applicable to any non linear elastic law and any plastic yield function.A curvilinear transverse isotropic model based on a quadratic elastic potential and on Hill's quadratic yield criterion is then developed and implemented in a computer program for bone mechanics perspectives. The paper concludes with a numerical study of a schematic bone-prosthesis system to illustrate the potential of the model.

Gains from switching and evolutionary stability in multi-player matrix games.

In this paper we unify, simplify, and extend previous work on the evolutionary dynamics of symmetric N-player matrix games with two pure strategies. In such games, gains from switching strategies depend, in general, on how many other individuals in the group play a given strategy. As a consequence, the gain function determining the gradient of selection can be a polynomial of degree N-1. In order to deal with the intricacy of the resulting evolutionary dynamics, we make use of the theory of polynomials in Bernstein form. This theory implies a tight link between the sign pattern of the gains from switching on the one hand and the number and stability of the rest points of the replicator dynamics on the other hand. While this relationship is a general one, it is most informative if gains from switching have at most two sign changes, as is the case for most multi-player matrix games considered in the literature. We demonstrate that previous results for public goods games are easily recovered and extended using this observation. Further examples illustrate how focusing on the sign pattern of the gains from switching obviates the need for a more involved analysis.

Evolutionary and convergence stability for continuous phenotypes in finite populations derived from two-allele models.

The evolution of a quantitative phenotype is often envisioned as a trait substitution sequence where mutant alleles repeatedly replace resident ones. In infinite populations, the invasion fitness of a mutant in this two-allele representation of the evolutionary process is used to characterize features about long-term phenotypic evolution, such as singular points, convergence stability (established from first-order effects of selection), branching points, and evolutionary stability (established from second-order effects of selection). Here, we try to characterize long-term phenotypic evolution in finite populations from this two-allele representation of the evolutionary process. We construct a stochastic model describing evolutionary dynamics at non-rare mutant allele frequency. We then derive stability conditions based on stationary average mutant frequencies in the presence of vanishing mutation rates. We find that the second-order stability condition obtained from second-order effects of selection is identical to convergence stability. Thus, in two-allele systems in finite populations, convergence stability is enough to characterize long-term evolution under the trait substitution sequence assumption. We perform individual-based simulations to confirm our analytic results.

THE USE OF SIMULATIONS IN EVOLUTIONARY POPULATION GENETICS: APPLICATIONS ON HUMANS, OWLS AND VIRTUAL ORGANISMS

Summary (in English) Computer simulations provide a practical way to address scientific questions that would be otherwise intractable. In evolutionary biology, and in population genetics in particular, the investigation of evolutionary processes frequently involves the implementation of complex models, making simulations a particularly valuable tool in the area. In this thesis work, I explored three questions involving the geographical range expansion of populations, taking advantage of spatially explicit simulations coupled with approximate Bayesian computation. First, the neutral evolutionary history of the human spread around the world was investigated, leading to a surprisingly simple model: A straightforward diffusion process of migrations from east Africa throughout a world map with homogeneous landmasses replicated to very large extent the complex patterns observed in real human populations, suggesting a more continuous (as opposed to structured) view of the distribution of modern human genetic diversity, which may play a better role as a base model for further studies. Second, the postglacial evolution of the European barn owl, with the formation of a remarkable coat-color cline, was inspected with two rounds of simulations: (i) determine the demographic background history and (ii) test the probability of a phenotypic cline, like the one observed in the natural populations, to appear without natural selection. We verified that the modern barn owl population originated from a single Iberian refugium and that they formed their color cline, not due to neutral evolution, but with the necessary participation of selection. The third and last part of this thesis refers to a simulation-only study inspired by the barn owl case above. In this chapter, we showed that selection is, indeed, effective during range expansions and that it leaves a distinguished signature, which can then be used to detect and measure natural selection in range-expanding populations. Résumé (en français) Les simulations fournissent un moyen pratique pour répondre à des questions scientifiques qui seraient inabordable autrement. En génétique des populations, l'étude des processus évolutifs implique souvent la mise en oeuvre de modèles complexes, et les simulations sont un outil particulièrement précieux dans ce domaine. Dans cette thèse, j'ai exploré trois questions en utilisant des simulations spatialement explicites dans un cadre de calculs Bayésiens approximés (approximate Bayesian computation : ABC). Tout d'abord, l'histoire de la colonisation humaine mondiale et de l'évolution de parties neutres du génome a été étudiée grâce à un modèle étonnement simple. Un processus de diffusion des migrants de l'Afrique orientale à travers un monde avec des masses terrestres homogènes a reproduit, dans une très large mesure, les signatures génétiques complexes observées dans les populations humaines réelles. Un tel modèle continu (opposé à un modèle structuré en populations) pourrait être très utile comme modèle de base dans l'étude de génétique humaine à l'avenir. Deuxièmement, l'évolution postglaciaire d'un gradient de couleur chez l'Effraie des clocher (Tyto alba) Européenne, a été examiné avec deux séries de simulations pour : (i) déterminer l'histoire démographique de base et (ii) tester la probabilité qu'un gradient phénotypique, tel qu'observé dans les populations naturelles puisse apparaître sans sélection naturelle. Nous avons montré que la population actuelle des chouettes est sortie d'un unique refuge ibérique et que le gradient de couleur ne peux pas s'être formé de manière neutre (sans l'action de la sélection naturelle). La troisième partie de cette thèse se réfère à une étude par simulations inspirée par l'étude de l'Effraie. Dans ce dernier chapitre, nous avons montré que la sélection est, en effet, aussi efficace dans les cas d'expansion d'aire de distribution et qu'elle laisse une signature unique, qui peut être utilisée pour la détecter et estimer sa force.

Evolutionary ecology of learning: insights from fruit flies

Ecologically and evolutionarily oriented research on learning has traditionally been carried out on vertebrates and bees. While less sophisticated than those animals, fruit flies (Drosophila) are capable of several forms of learning, and have an advantage of a short generation time, which makes them an ideal system for experimental evolution studies. This review summarizes the insights into evolutionary questions about learning gained in the last decade from evolutionary experiments on Drosophila. These experiments demonstrate that Drosophila have the genetic potential to evolve substantially improved learning performance in ecologically relevant learning tasks. In at least one set of selected populations the improved learning generalized to another task than that used to impose selection, involving a different behavior, different stimuli, and a different sensory channel for the aversive reinforcement. This improvement in learning ability was associated with reduction in other fitness-related traits, such as larval competitive ability and lifespan, pointing out to evolutionary trade-offs of improved learning. These trade-offs were confirmed by other evolutionary experiments where reduction in learning performance was observed as a correlated response to selection for tolerance to larval nutritional stress or for delayed aging. Such trade-offs could be one reason why fruit flies have not fully used up their evolutionary potential for learning ability. Finally, another evolutionary experiment with Drosophila provided the first direct evidence for the long-standing ideas that learning can under some circumstances accelerate and in other slow down genetically-based evolutionary change. These results demonstrate the usefulness of fruit flies as a model system to address evolutionary questions about learning.

Nest-box design for the study of diurnal raptors and owls is still an overlooked point in ecological, evolutionary and conservation studies: a review

The use of artificial nest-boxes has led to significant progress in bird conservation and in our understanding of the functional and evolutionary ecology of free-ranging birds that exploit cavities for roosting and reproduction. Nest-boxes and their improved accessibility have made it easier to perform comparative and experimental field investigations. However, concerns about the generality and applicability of scientific studies involving birds breeding in nest-boxes have been raised because the occupants of boxes may differ from conspecifics occupying other nest sites. Here we review the existing evidence demonstrating the importance of nest-box design to individual life-history traits in three falcon (Falconiformes) and seven owl (Strigiformes) species, as well as the extent to which publications on these birds describe the characteristics of exploited artificial nest-boxes in their 'methods' sections. More than 60% of recent publications did not provide any details on nest-box design (e.g. size, shape, material), despite several calls >15 years ago to increase the reporting of such information. We exemplify and discuss how variation in nest-box characteristics can affect or confound conclusions from nest-box studies and conclude that it is of overall importance to present details of nest-box characteristics in scientific publications.

New insights into the long-term evolutionary history of the avian MHC

SummaryGene duplication and neofunctidnalization are important processes in the evolution of phenotypic complexity. They account for important evolutionary novelties that confer ecological adaptation, such as the major histocompatibility complex (MHC), a multigene family with a central role in vertebrates' adaptive immune system. Multigene families, which evolved in large part through duplication, represent promising systems to study the still strongly depbated relative roles of neutral and adaptive processes in the evolution of phenotypic complexity. Detailed knowledge on ecological function and a well-characterized evolutionary history place the mammals' MHC amongst ideal study systems. However mammalian MHCs usually encompass several million base pairs and hold a large number of functional and non-functional duplicate genes, which makes their study complex. Avian MHCs on the other hand are usually way more compact, but the reconstruction of. their evolutionary history has proven notoriously difficult. However, no focused attempt has been undertaken so far to study the avian MHC evolutionary history in a broad phylogenetic context and using adequate gene regions.In the present PhD, we were able to make important contributions to the understanding of the long-term evolution of the avian MHC class II Β (MHCI1B). First, we isolated and characterized MHCIIB genes in barn owl (Tyto alba?, Strigiformes, Tytonidae), a species from an avian lineage in which MHC has not been studied so far. Our results revealed that with only two functional MHCIIB genes the MHC organization of barn owl may be similar to the 'minimal essential' MHC of chicken (Gallus gallus), indicating that simple MHC organization may be ancestral to birds. Taking advantage of the sequence information from barn owl, we studied the evolution of MHCIIB genes in 13 additional species of 'typical' owls (Strigiformes, Strigidae). Phylogenetic analyses revealed that according to their function, in owls the peptide-binding region (PBR) encoding exon 2 and the non-PBR encoding exon 3 evolve by different patterns. Exon 2 exhibited an evolutionary history of positive selection and recombination, while exon 3 traced duplication history and revealed two paralogs evolving divergently from each other in owls, and in a shorebird, the great snipe {Gallinago media). The results from exon 3 were the first ever from birds to demonstrate gene orthology in species that diverged tens of millions of years ago, and strongly questioned whether the taxa studied before provided an adequate picture of avian MHC evolution. In a follow-up study, we aimed at explaining a striking pattern revealed by phylogenetic trees analyzing the owl sequences along with MHCIIB sequences from other birds: One owl paralog (termed DAB1) grouped with sequences of passerines and falcons, while the other (DAB2) grouped with wildfowl, penguins and birds of prey. This could be explained by either a duplication event preceding the evolution of these bird orders, or by convergent evolution of similar sequences in a number of orders. With extensive phylogenetic analyses we were able to show, that indeed a duplication event preceeded the major avian radiation -100 my ago, and that following this duplication, the paralogs evolved under positive selection. Furthermore, we showed that the divergently evolving amino acid residues in the MHCIIB-encoded β-chain potentially interact with the MHCI I α-chain, and that molecular coevolution of the interacting residues may have been involved in the divergent evolution of the MHCIIB paralogs.The findings of this PhD are of particular interest to the understanding of the evolutionary history of the avian MHC and, by providing essential information on long-term gene history in the avian MHC, open promising perspectives for advances in the understanding of the evolution of multigene families in general, and for avian MHC organization in particular. Amongst others I discuss the importance of including protein structure in the phylogenetic study of multigene families, and the roles of ecological versus molecular selection pressures. I conclude by providing a population genomic perspective on avian MHC, which may serve as a basis for future research to investigate the relative roles of neutral processes involving effective population size effects and of adaptation in the evolution of avian MHC diversity and organization.RésuméLa duplication de gènes et leur néo-fonctionnalisation sont des processus importants dans l'évolution de la complexité phénotypique. Ils sont impliqués dans l'apparition d'importantes nouveautés évolutives favorisant l'adaptation écologique, comme c'est le cas pour le complexe majeur d'histocompatibilité eaux sont généralement plus compacts, mais la reconstruction de leur histoire évolutive s'est révélée difficile. Aucune analyse spécifique n'a cependant été entreprise jusqu'à présent pour étudier l'histoire évolutive du CMH aviaire dans un large contexte phylogénétique et en utilisant des régions géniques adéquates.Ce travail de thèse a contribué à la compréhension de l'évolution à long-terme du CMH aviaire classe II Β (CMH II Β). Nous avons isolé et caractérisé les gènes CMH I IB de la chouette effraie (Tyto alba; Strigiformes, Tytonidae), une espèce appartenant à une lignée aviaire dont le CMH n'avait pas été étudié jusqu'ici. Avec uniquement deux gènes CMHIIB fonctionnels, l'organisation CMH de la chouette effraie semble être comparable à celle "minimale" du poulet (Gallus gallus), ce qui suggère qu'une organisation simple du CMH pourrait être ancestrale chez les oiseaux. En se basant sur l'information obtenue pour cette espèce, nous avons ensuite étudié l'évolution des gènes CMHIIB chez 13 espèces de chouettes "typiques" (Strigiformes, Strigidae). Les analyses phylogénétiques ont révélé que chez les chouettes, selon leur fonction, l'exon 2 codant pour la 'peptide-binding region' (PBR) et l'exon 3 ne codant pas pour la région PBR évoluent de manière distincte. L'exon 2 montre une histoire évolutive de sélection positive et recombinaison, tandis que l'exon 3 retrace l'histoire de duplication et révèle deux paralogues évoluant de façon divergente chez les chouettes, ainsi que chez un limicole, la bécassine double (Gallinago media). Les résultats découlant de l'analyse de l'exon 3 ont montré pour la première fois chez les oiseaux une orthologie de gènes chez des espèces ayant divergé il y a des dizaines de millions d'années. Dans une deuxième étude, nous avons voulu expliquer le pattern surprenant révélé par les arbres phylogénétiques lorsque les séquences CMHIIB des chouettes sont analysées avec les séquences d'autres oiseaux: un paralogue de chouette (appelé DABI) forme un groupe avec les séquences de passereaux et faucons, tandis que l'autre (DAB2) se regroupe avec les gallo-ansériformes, les manchots et les rapaces diurnes. Ceci pourrait être expliqué soit par une duplication qui a précédé l'évolution de ces ordres aviaires soit par évolution convergente dans un certain nombre d'ordres. Grâce à des analyses phylogénétiques approfondies, nous avons pu montrer qu'un événement de duplication a effectivement précédé la radiation aviaire principale d'il y a environ 100 millions d'années, et qu'après cette duplication les paralogues ont évolué sous sélection positive. De plus, les résidus d'acides aminés évoluant de façon divergente dans la chaîne β codée par le CMHIIB interagissent potentiellement avec la chaîne α codée par le CMHII, et que la coévolution moléculaire de ces résidus pourrait être à la base de l'évolution divergente des paralogues CMHIIB.Dans cette thèse sont discutés entre autres l'importance d'inclure la structure des protéines dans l'étude phylogénétique des familles multigéniques, ainsi que les rôles respectifs des pressions sélectives écologique et moléculaire. La conclusion comporte une perspective sur la génomique des populations du CMH aviaire, qui pourrait servir de base pour de futures recherches sur les rôles relatifs joués par Îes processus neutres comprenant les effets de la taille efficace des populations et l'adaptation dans l'évolution de la diversité et l'organisation du MHC aviaire.

Evolutionary biology: genetics and bisexuality.

A population-genetic model indicates that if there is a gene responsible for homosexual behaviour it can readily spread in populations. The model also predicts widespread bisexuality in humans.

Evolutionary implications of a high selfing rate in the freshwater snail Lymnaea truncatula.

Self-compatible hermaphroditic organisms that mix self-fertilization and outcrossing are of great interest for investigating the evolution of mating systems. We investigate the evolution of selfing in Lymnaea truncatula, a self-compatible hermaphroditic freshwater snail. We first analyze the consequences of selfing in terms of genetic variability within and among populations and then investigate how these consequences along with the species ecology (harshness of the habitat and parasitism) might govern the evolution of selfing. Snails from 13 localities (classified as temporary or permanent depending on their water availability) were sampled in western Switzerland and genotyped for seven microsatellite loci. F(IS) (estimated on adults) and progeny array analyses (on hatchlings) provided similar selfing rate estimates of 80%. Populations presented a low polymorphism and were highly differentiated (F(ST) = 0.58). Although the reproductive assurance hypothesis would predict higher selfing rate in temporary populations, no difference in selfing level was observed between temporary and permanent populations. However, allelic richness and gene diversity declined in temporary habitats, presumably reflecting drift. Infection levels varied but were not simply related to either estimated population selfing rate or to differences in heterozygosity. These findings and the similar selfing rates estimated for hatchlings and adults suggest that within-population inbreeding depression is low in L. truncatula.

An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).