Ever-young sex chromosomes in European tree frogs.

Non-recombining sex chromosomes are expected to undergo evolutionary decay, ending up genetically degenerated, as has happened in birds and mammals. Why are then sex chromosomes so often homomorphic in cold-blooded vertebrates? One possible explanation is a high rate of turnover events, replacing master sex-determining genes by new ones on other chromosomes. An alternative is that X-Y similarity is maintained by occasional recombination events, occurring in sex-reversed XY females. Based on mitochondrial and nuclear gene sequences, we estimated the divergence times between European tree frogs (Hyla arborea, H. intermedia, and H. molleri) to the upper Miocene, about 5.4-7.1 million years ago. Sibship analyses of microsatellite polymorphisms revealed that all three species have the same pair of sex chromosomes, with complete absence of X-Y recombination in males. Despite this, sequences of sex-linked loci show no divergence between the X and Y chromosomes. In the phylogeny, the X and Y alleles cluster according to species, not in groups of gametologs. We conclude that sex-chromosome homomorphy in these tree frogs does not result from a recent turnover but is maintained over evolutionary timescales by occasional X-Y recombination. Seemingly young sex chromosomes may thus carry old-established sex-determining genes, a result at odds with the view that sex chromosomes necessarily decay until they are replaced. This raises intriguing perspectives regarding the evolutionary dynamics of sexually antagonistic genes and the mechanisms that control X-Y recombination.

High heritability of ambulatory blood pressure in families of East African descent.

We estimated the heritability of ambulatory systolic blood pressure (SBP), diastolic blood pressure (DBP), and pulse pressure (PP) in east African families with at least 2 hypertensive siblings and living in the Seychelles islands (Indian Ocean). The sample consisted of 314 individuals (147 men and 167 women), both normotensive and hypertensive, from 76 pedigrees (mean+/-SD of 4.1+/-2.8 persons per pedigree). After a 2-week off-treatment period, daytime and nighttime ambulatory blood pressure (BP) was monitored. Office BP was measured with a standard mercury sphygmomanometer. We estimated by maximum likelihood the age- and sex-adjusted heritabilities from the additive polygenic component of the variance of the traits allowing for the presence of other familial correlations. We also adjusted for ascertainment (ie, for the fact that 2 siblings had to be hypertensive) and examined the effect of adjusting for body mass index, 24-hour urinary excretion of sodium and potassium, plasma renin activity, and plasma aldosterone concentration. Heritability estimates (+/-SE) for ambulatory SBP, DBP, and PP were, respectively, 0.37+/-0.12/0.24+/-0.12/0.54+/-0.12 for daytime and 0.34+/-0.13/ 0.37+/-0.15/0.47+/-0.12 for nighttime measurements (P<0.05 for all estimates). Heritability estimates for office SBP, DBP, and PP were, respectively, 0.20+/-0.11, 0.05+/-0.09, and 0.37+/-0.12. Heritability estimates for SBP varied markedly according to whether participants were treated for hypertension at baseline. The present data show that ambulatory BP and PP have a high heritability in families of African descent. They also demonstrate that antihypertensive treatment and the number of BP measurements have a major influence on the heritability estimates.

Cryptic diversity among Western Palearctic tree frogs: postglacial range expansion, range limits, and secondary contacts of three European tree frog lineages (Hyla arborea group).

We characterize divergence times, intraspecific diversity and distributions for recently recognized lineages within the Hyla arborea species group, based on mitochondrial and nuclear sequences from 160 localities spanning its whole distribution. Lineages of H. arborea, H. orientalis, H. molleri have at least Pliocene age, supporting species level divergence. The genetically uniform Iberian H. molleri, although largely isolated by the Pyrenees, is parapatric to H. arborea, with evidence for successful hybridization in a small Aquitanian corridor (southwestern France), where the distribution also overlaps with H. meridionalis. The genetically uniform H. arborea, spread from Crete to Brittany, exhibits molecular signatures of a postglacial range expansion. It meets different mtDNA clades of H. orientalis in NE-Greece, along the Carpathians, and in Poland along the Vistula River (there including hybridization). The East-European H. orientalis is strongly structured genetically. Five geographic mitochondrial clades are recognized, with a molecular signature of postglacial range expansions for the clade that reached the most northern latitudes. Hybridization with H. savignyi is suggested in southwestern Turkey. Thus, cryptic diversity in these Pliocene Hyla lineages covers three extremes: a genetically poor, quasi-Iberian endemic (H. molleri), a more uniform species distributed from the Balkans to Western Europe (H. arborea), and a well-structured Asia Minor-Eastern European species (H. orientalis).

Adaptive divergence of ancient gene duplicates in the avian MHC class II beta.

Gene duplication and neofunctionalization are known to be 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 crucial to the vertebrate immune system. In birds, two MHC class II β (MHCIIβ) exon 3 lineages have been recently characterized, and two hypotheses for the evolutionary history of MHCIIβ lineages were proposed. These lineages could have arisen either by 1) an ancient duplication and subsequent divergence of one paralog or by 2) recent parallel duplications followed by functional convergence. Here, we compiled a data set consisting of 63 MHCIIβ exon 3 sequences from six avian orders to distinguish between these hypotheses and to understand the role of selection in the divergent evolution of the two avian MHCIIβ lineages. Based on phylogenetic reconstructions and simulations, we show that a unique duplication event preceding the major avian radiations gave rise to two ancestral MHCIIβ lineages that were each likely lost once later during avian evolution. Maximum likelihood estimation shows that following the ancestral duplication, positive selection drove a radical shift from basic to acidic amino acid composition of a protein domain facing the α-chain in the MHCII α β-heterodimer. Structural analyses of the MHCII α β-heterodimer highlight that three of these residues are potentially involved in direct interactions with the α-chain, suggesting that the shift following duplication may have been accompanied by coevolution of the interacting α- and β-chains. These results provide new insights into the long-term evolutionary relationships among avian MHC genes and open interesting perspectives for comparative and population genomic studies of avian MHC evolution.

Forensic identification of urine samples: a comparison between nuclear and mitochondrial DNA markers.

Urine samples from 20 male volunteers of European Caucasian origin were stored at 4 degrees C over a 4-month period in order to compare the identification potential of nuclear DNA (nDNA) and mitochondrial DNA (mtDNA) markers. The amount of nDNA recovered from urines dramatically declined over time. Consequently, nDNA likelihood ratios (LRs) greater than 1,000 were obtained for 100, 70 and 55% of the urines analysed after 6, 60 and 120 days, respectively. For the mtDNA, HVI and HVII sequences were obtained for all samples tested, whatever the period considered. Nevertheless, the highest mtDNA LR of 435 was relatively low compared to its nDNA equivalent. Indeed, LRs obtained with only three nDNA loci could easily exceed this value and are quite easier to obtain. Overall, the joint use of nDNA and mtDNA markers enabled the 20 urine samples to be identified, even after the 4-month period.

Use of forensic investigations in anti-doping.

The fight against doping is mainly focused on direct detection, using analytical methods for the detection of doping agents in biological samples. However, the World Anti-Doping Code also defines doping as possession, administration or attempted administration of prohibited substances or methods, trafficking or attempted trafficking in any prohibited substance or methods. As these issues correspond to criminal investigation, a forensic approach can help assessing potential violation of these rules. In the context of a rowing competition, genetic analyses were conducted on biological samples collected in infusion apparatus, bags and tubing in order to obtain DNA profiles. As no database of athletes' DNA profiles was available, the use of information from the location detection as well as contextual information were key to determine a population of suspected athletes and to obtain reference DNA profiles for comparison. Analysis of samples from infusion systems provided 8 different DNA profiles. The comparison between these profiles and 8 reference profiles from suspected athletes could not be distinguished. This case-study is one of the first where a forensic approach was applied for anti-doping purposes. Based on this investigation, the International Rowing Federation authorities decided to ban not only the incriminated athletes, but also the coaches and officials for 2 years.

The role of migration and domestic transmission in the spread of HIV-1 non-B subtypes in Switzerland.

BACKGROUND: By analyzing human immunodeficiency virus type 1 (HIV-1) pol sequences from the Swiss HIV Cohort Study (SHCS), we explored whether the prevalence of non-B subtypes reflects domestic transmission or migration patterns. METHODS: Swiss non-B sequences and sequences collected abroad were pooled to construct maximum likelihood trees, which were analyzed for Swiss-specific subepidemics, (subtrees including ≥80% Swiss sequences, bootstrap >70%; macroscale analysis) or evidence for domestic transmission (sequence pairs with genetic distance <1.5%, bootstrap ≥98%; microscale analysis). RESULTS: Of 8287 SHCS participants, 1732 (21%) were infected with non-B subtypes, of which A (n = 328), C (n = 272), CRF01_AE (n = 258), and CRF02_AG (n = 285) were studied further. The macroscale analysis revealed that 21% (A), 16% (C), 24% (CRF01_AE), and 28% (CRF02_AG) belonged to Swiss-specific subepidemics. The microscale analysis identified 26 possible transmission pairs: 3 (12%) including only homosexual Swiss men of white ethnicity; 3 (12%) including homosexual white men from Switzerland and partners from foreign countries; and 10 (38%) involving heterosexual white Swiss men and females of different nationality and predominantly nonwhite ethnicity. CONCLUSIONS: Of all non-B infections diagnosed in Switzerland, <25% could be prevented by domestic interventions. Awareness should be raised among immigrants and Swiss individuals with partners from high prevalence countries to contain the spread of non-B subtypes.

Time-lapse and probabilistic inversion strategies for plane-wave electromagnetic data.

L'utilisation efficace des systèmes géothermaux, la séquestration du CO2 pour limiter le changement climatique et la prévention de l'intrusion d'eau salée dans les aquifères costaux ne sont que quelques exemples qui démontrent notre besoin en technologies nouvelles pour suivre l'évolution des processus souterrains à partir de la surface. Un défi majeur est d'assurer la caractérisation et l'optimisation des performances de ces technologies à différentes échelles spatiales et temporelles. Les méthodes électromagnétiques (EM) d'ondes planes sont sensibles à la conductivité électrique du sous-sol et, par conséquent, à la conductivité électrique des fluides saturant la roche, à la présence de fractures connectées, à la température et aux matériaux géologiques. Ces méthodes sont régies par des équations valides sur de larges gammes de fréquences, permettant détudier de manières analogues des processus allant de quelques mètres sous la surface jusqu'à plusieurs kilomètres de profondeur. Néanmoins, ces méthodes sont soumises à une perte de résolution avec la profondeur à cause des propriétés diffusives du champ électromagnétique. Pour cette raison, l'estimation des modèles du sous-sol par ces méthodes doit prendre en compte des informations a priori afin de contraindre les modèles autant que possible et de permettre la quantification des incertitudes de ces modèles de façon appropriée. Dans la présente thèse, je développe des approches permettant la caractérisation statique et dynamique du sous-sol à l'aide d'ondes EM planes. Dans une première partie, je présente une approche déterministe permettant de réaliser des inversions répétées dans le temps (time-lapse) de données d'ondes EM planes en deux dimensions. Cette stratégie est basée sur l'incorporation dans l'algorithme d'informations a priori en fonction des changements du modèle de conductivité électrique attendus. Ceci est réalisé en intégrant une régularisation stochastique et des contraintes flexibles par rapport à la gamme des changements attendus en utilisant les multiplicateurs de Lagrange. J'utilise des normes différentes de la norme l2 pour contraindre la structure du modèle et obtenir des transitions abruptes entre les régions du model qui subissent des changements dans le temps et celles qui n'en subissent pas. Aussi, j'incorpore une stratégie afin d'éliminer les erreurs systématiques de données time-lapse. Ce travail a mis en évidence l'amélioration de la caractérisation des changements temporels par rapport aux approches classiques qui réalisent des inversions indépendantes à chaque pas de temps et comparent les modèles. Dans la seconde partie de cette thèse, j'adopte un formalisme bayésien et je teste la possibilité de quantifier les incertitudes sur les paramètres du modèle dans l'inversion d'ondes EM planes. Pour ce faire, je présente une stratégie d'inversion probabiliste basée sur des pixels à deux dimensions pour des inversions de données d'ondes EM planes et de tomographies de résistivité électrique (ERT) séparées et jointes. Je compare les incertitudes des paramètres du modèle en considérant différents types d'information a priori sur la structure du modèle et différentes fonctions de vraisemblance pour décrire les erreurs sur les données. Les résultats indiquent que la régularisation du modèle est nécessaire lorsqu'on a à faire à un large nombre de paramètres car cela permet d'accélérer la convergence des chaînes et d'obtenir des modèles plus réalistes. Cependent, ces contraintes mènent à des incertitudes d'estimations plus faibles, ce qui implique des distributions a posteriori qui ne contiennent pas le vrai modèledans les régions ou` la méthode présente une sensibilité limitée. Cette situation peut être améliorée en combinant des méthodes d'ondes EM planes avec d'autres méthodes complémentaires telles que l'ERT. De plus, je montre que le poids de régularisation des paramètres et l'écart-type des erreurs sur les données peuvent être retrouvés par une inversion probabiliste. Finalement, j'évalue la possibilité de caractériser une distribution tridimensionnelle d'un panache de traceur salin injecté dans le sous-sol en réalisant une inversion probabiliste time-lapse tridimensionnelle d'ondes EM planes. Etant donné que les inversions probabilistes sont très coûteuses en temps de calcul lorsque l'espace des paramètres présente une grande dimension, je propose une stratégie de réduction du modèle ou` les coefficients de décomposition des moments de Legendre du panache de traceur injecté ainsi que sa position sont estimés. Pour ce faire, un modèle de résistivité de base est nécessaire. Il peut être obtenu avant l'expérience time-lapse. Un test synthétique montre que la méthodologie marche bien quand le modèle de résistivité de base est caractérisé correctement. Cette méthodologie est aussi appliquée à un test de trac¸age par injection d'une solution saline et d'acides réalisé dans un système géothermal en Australie, puis comparée à une inversion time-lapse tridimensionnelle réalisée selon une approche déterministe. L'inversion probabiliste permet de mieux contraindre le panache du traceur salin gr^ace à la grande quantité d'informations a priori incluse dans l'algorithme. Néanmoins, les changements de conductivités nécessaires pour expliquer les changements observés dans les données sont plus grands que ce qu'expliquent notre connaissance actuelle des phénomenès physiques. Ce problème peut être lié à la qualité limitée du modèle de résistivité de base utilisé, indiquant ainsi que des efforts plus grands devront être fournis dans le futur pour obtenir des modèles de base de bonne qualité avant de réaliser des expériences dynamiques. Les études décrites dans cette thèse montrent que les méthodes d'ondes EM planes sont très utiles pour caractériser et suivre les variations temporelles du sous-sol sur de larges échelles. Les présentes approches améliorent l'évaluation des modèles obtenus, autant en termes d'incorporation d'informations a priori, qu'en termes de quantification d'incertitudes a posteriori. De plus, les stratégies développées peuvent être appliquées à d'autres méthodes géophysiques, et offrent une grande flexibilité pour l'incorporation d'informations additionnelles lorsqu'elles sont disponibles. -- The efficient use of geothermal systems, the sequestration of CO2 to mitigate climate change, and the prevention of seawater intrusion in coastal aquifers are only some examples that demonstrate the need for novel technologies to monitor subsurface processes from the surface. A main challenge is to assure optimal performance of such technologies at different temporal and spatial scales. Plane-wave electromagnetic (EM) methods are sensitive to subsurface electrical conductivity and consequently to fluid conductivity, fracture connectivity, temperature, and rock mineralogy. These methods have governing equations that are the same over a large range of frequencies, thus allowing to study in an analogous manner processes on scales ranging from few meters close to the surface down to several hundreds of kilometers depth. Unfortunately, they suffer from a significant resolution loss with depth due to the diffusive nature of the electromagnetic fields. Therefore, estimations of subsurface models that use these methods should incorporate a priori information to better constrain the models, and provide appropriate measures of model uncertainty. During my thesis, I have developed approaches to improve the static and dynamic characterization of the subsurface with plane-wave EM methods. In the first part of this thesis, I present a two-dimensional deterministic approach to perform time-lapse inversion of plane-wave EM data. The strategy is based on the incorporation of prior information into the inversion algorithm regarding the expected temporal changes in electrical conductivity. This is done by incorporating a flexible stochastic regularization and constraints regarding the expected ranges of the changes by using Lagrange multipliers. I use non-l2 norms to penalize the model update in order to obtain sharp transitions between regions that experience temporal changes and regions that do not. I also incorporate a time-lapse differencing strategy to remove systematic errors in the time-lapse inversion. This work presents improvements in the characterization of temporal changes with respect to the classical approach of performing separate inversions and computing differences between the models. In the second part of this thesis, I adopt a Bayesian framework and use Markov chain Monte Carlo (MCMC) simulations to quantify model parameter uncertainty in plane-wave EM inversion. For this purpose, I present a two-dimensional pixel-based probabilistic inversion strategy for separate and joint inversions of plane-wave EM and electrical resistivity tomography (ERT) data. I compare the uncertainties of the model parameters when considering different types of prior information on the model structure and different likelihood functions to describe the data errors. The results indicate that model regularization is necessary when dealing with a large number of model parameters because it helps to accelerate the convergence of the chains and leads to more realistic models. These constraints also lead to smaller uncertainty estimates, which imply posterior distributions that do not include the true underlying model in regions where the method has limited sensitivity. This situation can be improved by combining planewave EM methods with complimentary geophysical methods such as ERT. In addition, I show that an appropriate regularization weight and the standard deviation of the data errors can be retrieved by the MCMC inversion. Finally, I evaluate the possibility of characterizing the three-dimensional distribution of an injected water plume by performing three-dimensional time-lapse MCMC inversion of planewave EM data. Since MCMC inversion involves a significant computational burden in high parameter dimensions, I propose a model reduction strategy where the coefficients of a Legendre moment decomposition of the injected water plume and its location are estimated. For this purpose, a base resistivity model is needed which is obtained prior to the time-lapse experiment. A synthetic test shows that the methodology works well when the base resistivity model is correctly characterized. The methodology is also applied to an injection experiment performed in a geothermal system in Australia, and compared to a three-dimensional time-lapse inversion performed within a deterministic framework. The MCMC inversion better constrains the water plumes due to the larger amount of prior information that is included in the algorithm. The conductivity changes needed to explain the time-lapse data are much larger than what is physically possible based on present day understandings. This issue may be related to the base resistivity model used, therefore indicating that more efforts should be given to obtain high-quality base models prior to dynamic experiments. The studies described herein give clear evidence that plane-wave EM methods are useful to characterize and monitor the subsurface at a wide range of scales. The presented approaches contribute to an improved appraisal of the obtained models, both in terms of the incorporation of prior information in the algorithms and the posterior uncertainty quantification. In addition, the developed strategies can be applied to other geophysical methods, and offer great flexibility to incorporate additional information when available.

Characterization and distribution of Pogonomyrmex harvester ant lineages with genetic caste determination.

Genetic caste determination has been described in two populations of Pogonomyrmex harvester ants, each comprising a pair of interbreeding lineages. Queens mate with males of their own and of the alternate lineage and produce two types of diploid offspring, those fertilized by males of the queens' lineage which develop into queens and those fertilized by males of the other lineage which develop into workers. Each of the lineages has been shown to be itself of hybrid origin between the species Pogonomyrmex barbatus and Pogonomyrmex rugosus, which both have typical, environmentally determined caste differentiation. In a large scale genetic survey across 35 sites in Arizona, New Mexico and Texas, we found that genetic caste determination associated with pairs of interbreeding lineages occurred frequently (in 26 out of the 35 sites). Overall, we identified eight lineages with genetic caste determination that always co-occurred in the same complementary lineage pairs. Three of the four lineage pairs appear to have a common origin while their relationship with the fourth remains unclear. The level of genetic differentiation among these eight lineages was significantly higher than the differentiation between P. rugosus and P. barbatus, which questions the appropriate taxonomic status of these genetic lineages. In addition to being genetically isolated from one another, all lineages with genetic caste determination were genetically distinct from P. rugosus and P. barbatus, even when colonies of interbreeding lineages co-occurred with colonies of either putative parent at the same site. Such nearly complete reproductive isolation between the lineages and the species with environmental caste determination might prevent the genetic caste determination system to be swept away by gene flow.

One billion years of bZIP transcription factor evolution: conservation and change in dimerization and DNA-binding site specificity.

The genomic era has revealed that the large repertoire of observed animal phenotypes is dependent on changes in the expression patterns of a finite number of genes, which are mediated by a plethora of transcription factors (TFs) with distinct specificities. The dimerization of TFs can also increase the complexity of a genetic regulatory network manifold, by combining a small number of monomers into dimers with distinct functions. Therefore, studying the evolution of these dimerizing TFs is vital for understanding how complexity increased during animal evolution. We focus on the second largest family of dimerizing TFs, the basic-region leucine zipper (bZIP), and infer when it expanded and how bZIP DNA-binding and dimerization functions evolved during the major phases of animal evolution. Specifically, we classify the metazoan bZIPs into 19 families and confirm the ancient nature of at least 13 of these families, predating the split of the cnidaria. We observe fixation of a core dimerization network in the last common ancestor of protostomes-deuterostomes. This was followed by an expansion of the number of proteins in the network, but no major dimerization changes in interaction partners, during the emergence of vertebrates. In conclusion, the bZIPs are an excellent model with which to understand how DNA binding and protein interactions of TFs evolved during animal evolution.

Taxonomic status and origin of the shrews (Soricidae) from the Canary islands inferred from a mtDNA comparison with the European Crocidura species.

European island shrews are either relicts of the endemic Pleistocene fauna, e.g.,. Crocidura zimmermanni, or were introduced from continental source populations. In order to clarify the taxonomic status and the origin of the two shrew species from the Canary islands, a 981bp fragment of cytochrome b gene was investigated in all European Crocidura species and compared with the Canary shrew (Crocidura canariensis) and the Osorio shrew (Crocidura osorio). The first shares its karyotype with the Sicilian shrew Crocidura sicula (2N=36), the second with the Greater white-toothed shrew Crocidura russula (2N=42), suggesting possible sister species relationships. Results confirm the monophyly of taxa sharing the same karyotype. Genetic distances between C. sicula and C. canariensis suggest a separation since 5 Myr. The first was probably isolated from the North African ancestor after the Messinian desiccation; the second arrived on the Canary islands by natural jump dispersal. Within the 2N=42 cluster, a first split separated an Eastern line (Tunisia) from a western line (Morocco/Europe) of C. russula. C. osorio clusters together with C. russula from Spain, indicating conspecificy. This suggests a recent introduction from Spain by human.

Improvement of cardiovascular risk prediction: time to review current knowledge, debates, and fundamentals on how to assess test characteristics.

Cardiovascular risk assessment might be improved with the addition of emerging, new tests derived from atherosclerosis imaging, laboratory tests or functional tests. This article reviews relative risk, odds ratios, receiver-operating curves, posttest risk calculations based on likelihood ratios, the net reclassification improvement and integrated discrimination. This serves to determine whether a new test has an added clinical value on top of conventional risk testing and how this can be verified statistically. Two clinically meaningful examples serve to illustrate novel approaches. This work serves as a review and basic work for the development of new guidelines on cardiovascular risk prediction, taking into account emerging tests, to be proposed by members of the 'Taskforce on Vascular Risk Prediction' under the auspices of the Working Group 'Swiss Atherosclerosis' of the Swiss Society of Cardiology in the future.

Reliable selfing rate estimates from imperfect population genetic data.

Genotypic frequencies at codominant marker loci in population samples convey information on mating systems. A classical way to extract this information is to measure heterozygote deficiencies (FIS) and obtain the selfing rate s from FIS = s/(2 - s), assuming inbreeding equilibrium. A major drawback is that heterozygote deficiencies are often present without selfing, owing largely to technical artefacts such as null alleles or partial dominance. We show here that, in the absence of gametic disequilibrium, the multilocus structure can be used to derive estimates of s independent of FIS and free of technical biases. Their statistical power and precision are comparable to those of FIS, although they are sensitive to certain types of gametic disequilibria, a bias shared with progeny-array methods but not FIS. We analyse four real data sets spanning a range of mating systems. In two examples, we obtain s = 0 despite positive FIS, strongly suggesting that the latter are artefactual. In the remaining examples, all estimates are consistent. All the computations have been implemented in a open-access and user-friendly software called rmes (robust multilocus estimate of selfing) available at http://ftp.cefe.cnrs.fr, and can be used on any multilocus data. Being able to extract the reliable information from imperfect data, our method opens the way to make use of the ever-growing number of published population genetic studies, in addition to the more demanding progeny-array approaches, to investigate selfing rates.

Bayes linear spaces

Linear spaces consisting of σ-finite probability measures and infinite measures (improper priors and likelihood functions) are defined. The commutative group operation, called perturbation, is the updating given by Bayes theorem; the inverse operation is the Radon-Nikodym derivative. Bayes spaces of measures are sets of classes of proportional measures. In this framework, basic notions of mathematical statistics get a simple algebraic interpretation. For example, exponential families appear as affine subspaces with their sufficient statistics as a basis. Bayesian statistics, in particular some well-known properties of conjugated priors and likelihood functions, are revisited and slightly extended