Problems of allometric scaling analysis: examples from mammalian reproductive biology.

Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2) objective recognition of divergent subsets in the data (allometric grades); (3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution, greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation (rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of 'independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.

Analysis of susceptibility to human immunodeficiency virus 1 (HIV-1) by comparative genetics

Summary [résumé français voir ci-dessous] From the beginning of the 20th century the world population has been confronted with the human immune deficiency virus 1 (HIV-1). This virus has the particularity to mutate fast, and could thus evade and adapt to the human host. Our closest evolutionary related organisms, the non-human primates, are less susceptible to HIV-1. In a broader sense, primates are differentially susceptible to various retrovirus. Species specificity may be due to genetic differences among primates. In the present study we applied evolutionary and comparative genetic techniques to characterize the evolutionary pattern of host cellular determinants of HIV-1 pathogenesis. The study of the evolution of genes coding for proteins participating to the restriction or pathogenesis of HIV-1 may help understanding the genetic basis of modern human susceptibility to infection. To perform comparative genetics analysis, we constituted a collection of primate DNA and RNA to allow generation of de novo sequence of gene orthologs. More recently, release to the public domain of two new primate complete genomes (bornean orang-utan and common marmoset) in addition of the three previously available genomes (human, chimpanzee and Rhesus monkey) help scaling up the evolutionary and comparative genome analysis. Sequence analysis used phylogenetic and statistical methods for detecting molecular adaptation. We identified different selective pressures acting on host proteins involved in HIV-1 pathogenesis. Proteins with HIV-1 restriction properties in non-human primates were under strong positive selection, in particular in regions of interaction with viral proteins. These regions carried key residues for the antiviral activity. Proteins of the innate immunity presented an evolutionary pattern of conservation (purifying selection) but with signals of relaxed constrain if we compared them to the average profile of purifying selection of the primate genomes. Large scale analysis resulted in patterns of evolutionary pressures according to molecular function, biological process and cellular distribution. The data generated by various analyses served to guide the ancestral reconstruction of TRIM5a a potent antiviral host factor. The resurrected TRIM5a from the common ancestor of Old world monkeys was effective against HIV-1 and the recent resurrected hominoid variants were more effective against other retrovirus. Thus, as the result of trade-offs in the ability to restrict different retrovirus, human might have been exposed to HIV-1 at a time when TRIM5a lacked the appropriate specific restriction activity. The application of evolutionary and comparative genetic tools should be considered for the systematical assessment of host proteins relevant in viral pathogenesis, and to guide biological and functional studies. Résumé La population mondiale est confrontée depuis le début du vingtième siècle au virus de l'immunodéficience humaine 1 (VIH-1). Ce virus a un taux de mutation particulièrement élevé, il peut donc s'évader et s'adapter très efficacement à son hôte. Les organismes évolutivement le plus proches de l'homme les primates nonhumains sont moins susceptibles au VIH-1. De façon générale, les primates répondent différemment aux rétrovirus. Cette spécificité entre espèces doit résider dans les différences génétiques entre primates. Dans cette étude nous avons appliqué des techniques d'évolution et de génétique comparative pour caractériser le modèle évolutif des déterminants cellulaires impliqués dans la pathogenèse du VIH- 1. L'étude de l'évolution des gènes, codant pour des protéines impliquées dans la restriction ou la pathogenèse du VIH-1, aidera à la compréhension des bases génétiques ayant récemment rendu l'homme susceptible. Pour les analyses de génétique comparative, nous avons constitué une collection d'ADN et d'ARN de primates dans le but d'obtenir des nouvelles séquences de gènes orthologues. Récemment deux nouveaux génomes complets ont été publiés (l'orang-outan du Bornéo et Marmoset commun) en plus des trois génomes déjà disponibles (humain, chimpanzé, macaque rhésus). Ceci a permis d'améliorer considérablement l'étendue de l'analyse. Pour détecter l'adaptation moléculaire nous avons analysé les séquences à l'aide de méthodes phylogénétiques et statistiques. Nous avons identifié différentes pressions de sélection agissant sur les protéines impliquées dans la pathogenèse du VIH-1. Des protéines avec des propriétés de restriction du VIH-1 dans les primates non-humains présentent un taux particulièrement haut de remplacement d'acides aminés (sélection positive). En particulier dans les régions d'interaction avec les protéines virales. Ces régions incluent des acides aminés clé pour l'activité de restriction. Les protéines appartenant à l'immunité inné présentent un modèle d'évolution de conservation (sélection purifiante) mais avec des traces de "relaxation" comparé au profil général de sélection purifiante du génome des primates. Une analyse à grande échelle a permis de classifier les modèles de pression évolutive selon leur fonction moléculaire, processus biologique et distribution cellulaire. Les données générées par les différentes analyses ont permis la reconstruction ancestrale de TRIM5a, un puissant facteur antiretroviral. Le TRIM5a ressuscité, correspondant à l'ancêtre commun entre les grands singes et les groupe des catarrhiniens, est efficace contre le VIH-1 moderne. Les TRIM5a ressuscités plus récents, correspondant aux ancêtres des grands singes, sont plus efficaces contre d'autres rétrovirus. Ainsi, trouver un compromis dans la capacité de restreindre différents rétrovirus, l'homme aurait été exposé au VIH-1 à une période où TRIM5a manquait d'activité de restriction spécifique contre celui-ci. L'application de techniques d'évolution et de génétique comparative devraient être considérées pour l'évaluation systématique de protéines impliquées dans la pathogenèse virale, ainsi que pour guider des études biologiques et fonctionnelles

GPS analysis of human locomotion: further evidence for long-range correlations in stride-to-stride fluctuations of gait parameters.

During free walking, gait is automatically adjusted to provide optimal mechanical output and minimal energy expenditure; gait parameters, such as cadence, fluctuate from one stride to the next around average values. It was described that this fluctuation exhibited long-range correlations and fractal-like patterns. In addition, it was suggested that these long-range correlations disappeared if the participant followed the beep of metronome to regulate his or her pace. Until now, these fractal fluctuations were only observed for stride interval, because no technique existed to adequately analyze an extended time of free walking. The aim of the present study was to measure walking speed (WS), step frequency (SF) and step length (SL) with high accuracy (<1 cm) satellite positioning method (global positioning system or GPS) in order to detect long-range correlations in the stride-to-stride fluctuations. Eight participants walked 30 min under free and constrained (metronome) conditions. Under free walking conditions, DFA (detrended fluctuation analysis) and surrogate data tests showed that the fluctuation of WS, SL and SF exhibited a fractal pattern (i.e., scaling exponent alpha: 0.5 < alpha < 1) in a large majority of participants (7/8). Under constrained conditions (metronome), SF fluctuations became significantly anti-correlated (alpha < 0.5) in all participants. However, the scaling exponent of SL and WS was not modified. We conclude that, when the walking pace is controlled by an auditory signal, the feedback loop between the planned movement (at supraspinal level) and the sensory inputs induces a continual shifting of SF around the mean (persistent anti-correlation), but with no effect on the fluctuation dynamics of the other parameters (SL, WS).

On the Schoenberg transformations in data analysis: theory and illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A distance-based discriminant algorithm and a robust multidimensional centroid estimate illustrate the theory, closely connected to the Gaussian kernels of Machine Learning.

Emergence of Swiss metropole and scaling properties of urban clusters

Defining the limits of an urban agglomeration is essential both for fundamental and applied studies in quantitative and theoretical geography. A simple and consistent way for defining such urban clusters is important for performing different statistical analysis and comparisons. Traditionally, agglomerations are defined using a rather qualitative approach based on various statistical measures. This definition varies generally from one country to another, and the data taken into account are different. In this paper, we explore the use of the City Clustering Algorithm (CCA) for the agglomeration definition in Switzerland. This algorithm provides a systemic and easy way to define an urban area based only on population data. The CCA allows the specification of the spatial resolution for defining the urban clusters. The results from different resolutions are compared and analysed, and the effect of filtering the data investigated. Different scales and parameters allow highlighting different phenomena. The study of Zipf's law using the visual rank-size rule shows that it is valid only for some specific urban clusters, inside a narrow range of the spatial resolution of the CCA. The scale where emergence of one main cluster occurs can also be found in the analysis using Zipf's law. The study of the urban clusters at different scales using the lacunarity measure - a complementary measure to the fractal dimension - allows to highlight the change of scale at a given range.