A comparison of the alr and ilr transformations for kernel density estimation of compositional data

In a seminal paper, Aitchison and Lauder (1985) introduced classical kernel densityestimation techniques in the context of compositional data analysis. Indeed, they gavetwo options for the choice of the kernel to be used in the kernel estimator. One ofthese kernels is based on the use the alr transformation on the simplex SD jointly withthe normal distribution on RD-1. However, these authors themselves recognized thatthis method has some deficiencies. A method for overcoming these dificulties based onrecent developments for compositional data analysis and multivariate kernel estimationtheory, combining the ilr transformation with the use of the normal density with a fullbandwidth matrix, was recently proposed in Martín-Fernández, Chacón and Mateu-Figueras (2006). Here we present an extensive simulation study that compares bothmethods in practice, thus exploring the finite-sample behaviour of both estimators

CODAMAT: a modern analogue techinque for compositional data

The quantitative estimation of Sea Surface Temperatures from fossils assemblages is afundamental issue in palaeoclimatic and paleooceanographic investigations. TheModern Analogue Technique, a widely adopted method based on direct comparison offossil assemblages with modern coretop samples, was revised with the aim ofconforming it to compositional data analysis. The new CODAMAT method wasdeveloped by adopting the Aitchison metric as distance measure. Modern coretopdatasets are characterised by a large amount of zeros. The zero replacement was carriedout by adopting a Bayesian approach to the zero replacement, based on a posteriorestimation of the parameter of the multinomial distribution. The number of modernanalogues from which reconstructing the SST was determined by means of a multipleapproach by considering the Proxies correlation matrix, Standardized Residual Sum ofSquares and Mean Squared Distance. This new CODAMAT method was applied to theplanktonic foraminiferal assemblages of a core recovered in the Tyrrhenian Sea.Kew words: Modern analogues, Aitchison distance, Proxies correlation matrix,Standardized Residual Sum of Squares

Extensive variation at MHC DRB in the New Zealand sea lion (Phocarctos hookeri) provides evidence for balancing selection.

Marine mammals are often reported to possess reduced variation of major histocompatibility complex (MHC) genes compared with their terrestrial counterparts. We evaluated diversity at two MHC class II B genes, DQB and DRB, in the New Zealand sea lion (Phocarctos hookeri, NZSL) a species that has suffered high mortality owing to bacterial epizootics, using Sanger sequencing and haplotype reconstruction, together with next-generation sequencing. Despite this species' prolonged history of small population size and highly restricted distribution, we demonstrate extensive diversity at MHC DRB with 26 alleles, whereas MHC DQB is dimorphic. We identify four DRB codons, predicted to be involved in antigen binding, that are evolving under adaptive evolution. Our data suggest diversity at DRB may be maintained by balancing selection, consistent with the role of this locus as an antigen-binding region and the species' recent history of mass mortality during a series of bacterial epizootics. Phylogenetic analyses of DQB and DRB sequences from pinnipeds and other carnivores revealed significant allelic diversity, but little phylogenetic depth or structure among pinniped alleles; thus, we could neither confirm nor refute the possibility of trans-species polymorphism in this group. The phylogenetic pattern observed however, suggests some significant evolutionary constraint on these loci in the recent past, with the pattern consistent with that expected following an epizootic event. These data may help further elucidate some of the genetic factors underlying the unusually high susceptibility to bacterial infection of the threatened NZSL, and help us to better understand the extent and pattern of MHC diversity in pinnipeds.

Multi-isotopic and compositional exploration of factors controlling nitrate pollution

In Catalonia, according to the nitrate directive (91/676/EU), nine areas have been declared as vulnerable to nitrate pollution from agricultural sources (Decret 283/1998 and Decret 479/2004). Five of these areas have been studied coupling hydro chemical data with a multi-isotopic approach (Vitòria et al. 2005, Otero et al. 2007, Puig et al. 2007), in an ongoing research project looking for an integrated application of classical hydrochemistry data, with a comprehensive isotopic characterisation (δ15N and δ18O of dissolved nitrate, δ34S and δ18O of dissolved sulphate, δ13C of dissolved inorganic carbon, and δD and δ18O of water). Within this general frame, the contribution presented explores compositional ways of: (i) distinguish agrochemicals and manure N pollution, (ii) quantify natural attenuation of nitrate (denitrification), and identify possible controlling factors.To achieve this two-fold goal, the following techniques have been used. Separate biplots of each suite of data show that each studied region has a distinct δ34S and pH signatures, but they are homogeneous with regard to NO3- related variables. Also, the geochemical variables were projected onto the compositional directions associated with the possible denitrification reactions in each region. The resulting balances can be plot together with some isotopes, to assess their likelihood of occurrence

Studies in stoichiometry with compositional data

Geochemical data that is derived from the whole or partial analysis of various geologic materialsrepresent a composition of mineralogies or solute species. Minerals are composed of structuredrelationships between cations and anions which, through atomic and molecular forces, keep the elementsbound in specific configurations. The chemical compositions of minerals have specific relationships thatare governed by these molecular controls. In the case of olivine, there is a well-defined relationshipbetween Mn-Fe-Mg with Si. Balances between the principal elements defining olivine composition andother significant constituents in the composition (Al, Ti) have been defined, resulting in a near-linearrelationship between the logarithmic relative proportion of Si versus (MgMnFe) and Mg versus (MnFe),which is typically described but poorly illustrated in the simplex.The present contribution corresponds to ongoing research, which attempts to relate stoichiometry andgeochemical data using compositional geometry. We describe here the approach by which stoichiometricrelationships based on mineralogical constraints can be accounted for in the space of simplicialcoordinates using olivines as an example. Further examples for other mineral types (plagioclases andmore complex minerals such as clays) are needed. Issues that remain to be dealt with include thereduction of a bulk chemical composition of a rock comprised of several minerals from which appropriatebalances can be used to describe the composition in a realistic mineralogical framework. The overallobjective of our research is to answer the question: In the cases where the mineralogy is unknown, arethere suitable proxies that can be substituted?Kew words: Aitchison geometry, balances, mineral composition, oxides

Clustering compositional data trajectories

Our essay aims at studying suitable statistical methods for the clustering ofcompositional data in situations where observations are constituted by trajectories ofcompositional data, that is, by sequences of composition measurements along a domain.Observed trajectories are known as “functional data” and several methods have beenproposed for their analysis.In particular, methods for clustering functional data, known as Functional ClusterAnalysis (FCA), have been applied by practitioners and scientists in many fields. To ourknowledge, FCA techniques have not been extended to cope with the problem ofclustering compositional data trajectories. In order to extend FCA techniques to theanalysis of compositional data, FCA clustering techniques have to be adapted by using asuitable compositional algebra.The present work centres on the following question: given a sample of compositionaldata trajectories, how can we formulate a segmentation procedure giving homogeneousclasses? To address this problem we follow the steps described below.First of all we adapt the well-known spline smoothing techniques in order to cope withthe smoothing of compositional data trajectories. In fact, an observed curve can bethought of as the sum of a smooth part plus some noise due to measurement errors.Spline smoothing techniques are used to isolate the smooth part of the trajectory:clustering algorithms are then applied to these smooth curves.The second step consists in building suitable metrics for measuring the dissimilaritybetween trajectories: we propose a metric that accounts for difference in both shape andlevel, and a metric accounting for differences in shape only.A simulation study is performed in order to evaluate the proposed methodologies, usingboth hierarchical and partitional clustering algorithm. The quality of the obtained resultsis assessed by means of several indices

Possible solution of some essential zero problems in compositional data analysis

One of the tantalising remaining problems in compositional data analysis lies in how to deal with data sets in which there are components which are essential zeros. By anessential zero we mean a component which is truly zero, not something recorded as zero simply because the experimental design or the measuring instrument has not been sufficiently sensitive to detect a trace of the part. Such essential zeros occur inmany compositional situations, such as household budget patterns, time budgets,palaeontological zonation studies, ecological abundance studies. Devices such as nonzero replacement and amalgamation are almost invariably ad hoc and unsuccessful insuch situations. From consideration of such examples it seems sensible to build up amodel in two stages, the first determining where the zeros will occur and the secondhow the unit available is distributed among the non-zero parts. In this paper we suggest two such models, an independent binomial conditional logistic normal model and a hierarchical dependent binomial conditional logistic normal model. The compositional data in such modelling consist of an incidence matrix and a conditional compositional matrix. Interesting statistical problems arise, such as the question of estimability of parameters, the nature of the computational process for the estimation of both the incidence and compositional parameters caused by the complexity of the subcompositional structure, the formation of meaningful hypotheses, and the devising of suitable testing methodology within a lattice of such essential zero-compositional hypotheses. The methodology is illustrated by application to both simulated and real compositional data

Undertreatment of acute pain (oligoanalgesia) and medical practice variation in prehospital analgesia of adult trauma patients: a 10 yr retrospective study.

BACKGROUND: Prehospital oligoanalgesia is prevalent among trauma victims, even when the emergency medical services team includes a physician. We investigated if not only patients' characteristics but physicians' practice variations contributed to prehospital oligoanalgesia. METHODS: Patient records of conscious adult trauma victims transported by our air rescue helicopter service over 10 yr were reviewed retrospectively. Oligoanalgesia was defined as a numeric rating scale (NRS) >3 at hospital admission. Multilevel logistic regression analysis was used to predict oligoanalgesia, accounting first for patient case-mix, and then physician-level clustering. The intraclass correlation was expressed as the median odds ratio (MOR). RESULTS: A total of 1202 patients and 77 physicians were included in the study. NRS at the scene was 6.9 (1.9). The prevalence of oligoanalgesia was 43%. Physicians had a median of 5.7 yr (inter-quartile range: 4.2-7.5) of post-graduate training and 27% were female. In our multilevel analysis, significant predictors of oligoanalgesia were: no analgesia [odds ratio (OR) 8.8], National Advisory Committee for Aeronautics V on site (OR 4.4), NRS on site (OR 1.5 per additional NRS unit >4), female physician (OR 2.0), and years of post-graduate experience [>4.0 to ≤5.0 (OR 1.3), >3.0 to ≤4.0 (OR 1.6), >2.0 to ≤3.0 (OR 2.6), and ≤2.0 yr (OR 16.7)]. The MOR was 2.6, and was statistically significant. CONCLUSIONS: Physicians' practice variations contributed to oligoanalgesia, a factor often overlooked in analyses of prehospital pain management. Further exploration of the sources of these variations may provide innovative targets for quality improvement programmes to achieve consistent pain relief for trauma victims.

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by asimplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able togenerate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow definingmonitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

Disentangling reasons for low Y chromosome variation in the greater white-toothed shrew (Crocidura russula).

Y chromosome variation is determined by several confounding factors including mutation rate, effective population size, demography, and selection. Disentangling these factors is essential to better understand the evolutionary properties of the Y chromosome. We analyzed genetic variation on the Y chromosome, X chromosome, and mtDNA of the greater white-toothed shrew, a species with low variance in male reproductive success and limited sex-biased dispersal, which enables us to control to some extent for life-history effects. We also compared ancestral (Moroccan) to derived (European) populations to investigate the role of demographic history in determining Y variation. Recent colonization of Europe by a small number of founders (combined with low mutation rates) is largely responsible for low diversity observed on the European Y and X chromosomes compared to mtDNA. After accounting for mutation rate, copy number, and demography, the Y chromosome still displays a deficit in variation relative to the X in both populations. This is possibly influenced by directional selection, but the slightly higher variance in male reproductive success is also likely to play a role, even though the difference is small compared to that in highly polygynous species. This study illustrates that demography and life-history effects should be scrutinized before inferring strong selective pressure as a reason for low diversity on the Y chromosome.

Between-year variation in population sex ratio increases with complexity of the breeding system in Hymenoptera.

While adaptive adjustment of sex ratio in the function of colony kin structure and food availability commonly occurs in social Hymenoptera, long-term studies have revealed substantial unexplained between-year variation in sex ratio at the population level. In order to identify factors that contribute to increased between-year variation in population sex ratio, we conducted a comparative analysis across 47 Hymenoptera species differing in their breeding system. We found that between-year variation in population sex ratio steadily increased as one moved from solitary species, to primitively eusocial species, to single-queen eusocial species, to multiple-queen eusocial species. Specifically, between-year variation in population sex ratio was low (6.6% of total possible variation) in solitary species, which is consistent with the view that in solitary species, sex ratio can vary only in response to fluctuations in ecological factors such as food availability. In contrast, we found significantly higher (19.5%) between-year variation in population sex ratio in multiple-queen eusocial species, which supports the view that in these species, sex ratio can also fluctuate in response to temporal changes in social factors such as queen number and queen-worker control over sex ratio, as well as factors influencing caste determination. The simultaneous adjustment of sex ratio in response to temporal fluctuations in ecological and social factors seems to preclude the existence of a single sex ratio optimum. The absence of such an optimum may reflect an additional cost associated with the evolution of complex breeding systems in Hymenoptera societies.

Investigating the genetic variation underlying episodicity in major depressive disorder: Suggestive evidence for a bipolar contribution.

BACKGROUND: Highly recurrent major depressive disorder (MDD) has reportedly increased risk of shifting to bipolar disorder; high recurrence frequency has, therefore, featured as evidence of 'soft bipolarity'. We aimed to investigate the genetic underpinnings of total depressive episode count in recurrent MDD. METHODS: Our primary sample included 1966 MDD cases with negative family history of bipolar disorder from the RADIANT studies. Total episode count was adjusted for gender, age, MDD duration, study and center before being tested for association with genotype in two separate genome-wide analyses (GWAS), in the full set and in a subset of 1364 cases with positive family history of MDD (FH+). We also calculated polygenic scores from the Psychiatric Genomics Consortium MDD and bipolar disorder studies. RESULTS: Episodicity (especially intermediate episode counts) was an independent index of MDD familial aggregation, replicating previous reports. The GWAS produced no genome-wide significant findings. The strongest signals were detected in the full set at MAGI1 (p=5.1×10(-7)), previously associated with bipolar disorder, and in the FH+ subset at STIM1 (p=3.9×10(-6) after imputation), a calcium channel signaling gene. However, these findings failed to replicate in an independent Munich cohort. In the full set polygenic profile analyses, MDD polygenes predicted episodicity better than bipolar polygenes; however, in the FH+ subset, both polygenic scores performed similarly. LIMITATIONS: Episode count was self-reported and, therefore, subject to recall bias. CONCLUSIONS: Our findings lend preliminary support to the hypothesis that highly recurrent MDD with FH+ is part of a 'soft bipolar spectrum' but await replication in larger cohorts.

Can we continue to neglect genomic variation in introgression rates when inferring the history of speciation? A case study in a Mytilus hybrid zone.

The use of molecular data to reconstruct the history of divergence and gene flow between populations of closely related taxa represents a challenging problem. It has been proposed that the long-standing debate about the geography of speciation can be resolved by comparing the likelihoods of a model of isolation with migration and a model of secondary contact. However, data are commonly only fit to a model of isolation with migration and rarely tested against the secondary contact alternative. Furthermore, most demographic inference methods have neglected variation in introgression rates and assume that the gene flow parameter (Nm) is similar among loci. Here, we show that neglecting this source of variation can give misleading results. We analysed DNA sequences sampled from populations of the marine mussels, Mytilus edulis and M. galloprovincialis, across a well-studied mosaic hybrid zone in Europe and evaluated various scenarios of speciation, with or without variation in introgression rates, using an Approximate Bayesian Computation (ABC) approach. Models with heterogeneous gene flow across loci always outperformed models assuming equal migration rates irrespective of the history of gene flow being considered. By incorporating this heterogeneity, the best-supported scenario was a long period of allopatric isolation during the first three-quarters of the time since divergence followed by secondary contact and introgression during the last quarter. By contrast, constraining migration to be homogeneous failed to discriminate among any of the different models of gene flow tested. Our simulations thus provide statistical support for the secondary contact scenario in the European Mytilus hybrid zone that the standard coalescent approach failed to confirm. Our results demonstrate that genomic variation in introgression rates can have profound impacts on the biological conclusions drawn from inference methods and needs to be incorporated in future studies.

Natural genetic variation of root system architecture from Arabidopsis to Brachypodium: towards adaptive value.

Root system architecture is a trait that displays considerable plasticity because of its sensitivity to environmental stimuli. Nevertheless, to a significant degree it is genetically constrained as suggested by surveys of its natural genetic variation. A few regulators of root system architecture have been isolated as quantitative trait loci through the natural variation approach in the dicotyledon model, Arabidopsis. This provides proof of principle that allelic variation for root system architecture traits exists, is genetically tractable, and might be exploited for crop breeding. Beyond Arabidopsis, Brachypodium could serve as both a credible and experimentally accessible model for root system architecture variation in monocotyledons, as suggested by first glimpses of the different root morphologies of Brachypodium accessions. Whether a direct knowledge transfer gained from molecular model system studies will work in practice remains unclear however, because of a lack of comprehensive understanding of root system physiology in the native context. For instance, apart from a few notable exceptions, the adaptive value of genetic variation in root system modulators is unknown. Future studies should thus aim at comprehensive characterization of the role of genetic players in root system architecture variation by taking into account the native environmental conditions, in particular soil characteristics.

Impact of social structure variation on population genetics, social conflicts and life histories in ants

Summary The evolution of social structures and breeding systems in animals is a complex process that combines ecological, genetical and social factors. This thesis sheds light on important changes in population genetics, life-history and social behavior that are associated with variation in social structure in ants. The socially polymorphic ant Formica selysi was chosen as the model organism because single- and multiple-queen colonies occur in close proximity within a single large population. The shift from single- to multiple-queen colonies is generally associated with profound changes in dispersal behavior and mode of colony founding. In chapter 1, we examine the genetic consequences of variation in social structure at both the colony and population levels. A detailed microsatellite analysis reveals that both colony types have similar mating systems, with few or no queen turnover. Furthermore, the complete lack of genetic differentiation observed between single- and multiple-queen colonies provides no support to the hypothesis that change in queen number leads to restricted gene flow between social forms. Besides changes in the genetic composition of the colony, the variation in the number of queens per colony is associated with changes in a network of behavioral and life-history traits that have been described as forming a "polygyny syndrome". In chapter 2, we demonstrate that multiple-queen colonies profoundly differ from single-queen ones in terms of size, nest density and lifespan of colonies, in weight of queens produced, as well as in allocation to reproductive individuals relative to workers. These multifaceted changes in life-history traits can provide various fitness benefits to members of multiple-queen colonies. Increasing the number of queens in a colony usually results in a decreased level of aggression towards non-nestmates. The phenotype matching hypothesis predicts that, compared to single-queen colonies, multiple-queen colonies have more diverse genetically-derived cues used for recognition, resulting in a lower ability to discriminate non-nestmates. In sharp contrast to this hypothesis, we show in chapter 3 that single- and multiple-queen colonies exhibit on average similar levels of aggression. Moreover, stronger aggression is recorded between colonies of different social structure than between colonies of the same social structure. Several hypotheses propose that the evolution of multiple-queen colonies is at least partly due to benefits resulting from an increase in colony genetic diversity. The task-efficiency hypothesis holds that genetic variation improves task performance due to a more complete or more sensitive expression of the genetically-based division of labor. In .chapter 4, we evaluate if higher colony genetic diversity increases worker size polymorphism and thus may improve division of labor. We show that despite the fact that worker size has a heritable component, higher levels of genetic diversity do not result in more polymorphic workers. The smaller size and lower polymorphism levels of workers of multiple-queen colonies compared to single-queen ones further indicate that an increase in colony genetic diversity does not increase worker size polymorphism but might improve colony homeostasis. In chapter 5, we provide clear evidence for an ongoing conflict between queens and workers on sex allocation, as predicted by kin selection theory. Our data show that queens of F. selysi strongly influence colony sex allocation by biasing the sex ratio of their eggs. However, there is also evidence that workers eliminated some male brood, resulting in a population sex-investment ratio that is between the queens' and workers' equilibria. Résumé L'évolution des structures sociales et systèmes d'accouplement chez les animaux est un processus complexe combinant à la fois des facteurs écologiques, génétiques et sociaux. Cette thèse met en lumière des changements importants dans la génétique des populations, les traits d'histoire de vie et les comportements sociaux qui sont associés à des variations de structure sociale chez les fourmis. Durant ce travail, nous avons étudié une population de Formica selysi composée à la fois de colonies à une reine et de colonies à plusieurs reines. La transition de colonie à une reine à colonie à plusieurs reines est généralement associée à des changements profonds dans le comportement de dispersion ainsi que le mode de fondation des sociétés. Dans le chapitre 1, nous examinons les conséquences génétiques de la variation de structure sociale tant au niveau de la colonie qu'au niveau de la population. Une analyse détaillée à l'aide de marqueurs microsatellites nous révèle que les deux types de colonies ont des systèmes d'accouplements similaires avec peu ou pas de renouvellement de reines. L'absence totale de différenciation génétique entre les colonies à une et à plusieurs reines n'apporte aucun support à l'hypothèse selon laquelle un changement dans le nombre de reines conduit à un flux de gènes restreint entre les deux formes sociales. A côté de changements dans la composition génétique de la colonie, la variation du nombre de reines dans une colonie est associée à une multitude de changements comportementaux et de traits d'histoire de vie qui ont été décrits comme formant un "syndrome polygyne". Dans le chapitre 2, nous démontrons que les colonies à plusieurs reines diffèrent profondément des colonies à une reine en terme de taille, densité de nids, longévité des colonies, poids des nouvelles reines produites ainsi que dans l'allocation entre les individus reproducteurs et les ouvrières. Ces changements multiples dans les traits d'histoire de vie peuvent apporter des bénéfices variés en terme de fitness aux colonies à plusieurs reines. L'augmentation du nombre de reines dans une colonie est généralement associée à une baisse du degré d'agressivité envers les fourmis étrangères au nid. L'hypothèse "phénotype matching" prédit que les colonies à plusieurs reines ont une plus grande diversité dans les facteurs d'origine génétique utilisés pour la reconnaissance, résultant en une capacité diminuée à discriminer une fourmi étrangère au nid. Contrairement à cette hypothèse, nous montrons dans le chapitre 3 que les colonies à une et à plusieurs reines ont des niveaux d'agressivité similaires. De plus, une agressivité accrue est observée entre colonies de structures sociales différentes comparée à des colonies de même structure sociale. Plusieurs hypothèses ont proposé que l'évolution de colonies ä plusieurs reines soit en partie due aux bénéfices résultant d'une augmentation de la diversité génétique dans la colonie. L'hypothèse "task efficiency" prédit que la diversité génétique améliore l'efficacité à effectuer certaines tâches grâce à une expression plus complète et plus souple d'une division du travail génétiquement déterminée. Nous évaluons dans le chapitre 4 si un accroissement de la diversité génétique augmente le polymorphisme de taille des ouvrières, d'où peut ainsi découler une meilleure division du travail. Nous montrons qu'en dépit du fait que la taille des ouvrières soit un caractère héritable, une forte diversité génétique ne se traduit pas par un plus fort polymorphisme chez les ouvrières. Les ouvrières de colonies à plusieurs reines sont plus petites et moins polymorphes que celles des colonies à une seule reine. Dans le chapitre 5, nous démontrons l'existence d'un conflit ouvert entre reines et ouvrières à propos de l'allocation dans les sexes, comme le prédit la théorie de la sélection de parentèle. Nos données révèlent que les reines de F. selysi influencent fortement l'allocation dans les sexes en biaisant la sexe ratio des oeufs. Cependant, certains indices indiquent que les ouvrières éliminent une partie du couvain mâle, ce qui a pour effet d'avoir un investissement dans les sexes au niveau de la population intermédiaire entre les intérêts des reines et des ouvrières.