Motivation: Distribution analysis is one of the most basic forms of statistical analysis. Thanks to improved analytical methods, accurate and extensive quantitative measurements can now be made of the mRNA, protein, and metabolites species from biological systems. Here we report a large-scale analysis of the population abundance distributions of the transcriptomes, proteomes, and metabolomes from varied biological systems. Results: We compared the observed empirical distributions with a number of distributions: power law, lognormal, loglogistic, loggamma, right Pareto-lognormal, and double Pareto-lognormal. The best-fit for mRNA, protein, and metabolite population abundance distributions was found to be the double Pareto-lognormal. This distribution behaves like a lognormal distribution around the centre, and like a power law distribution in the tails. To better understand the cause of this observed distribution we explored a simple stochastic model based on geometric Brownian motion. The distribution indicates that multiplicative effects are causally dominant in biological systems. We speculate that these effects arise from chemical reactions: the central-limit theorem then explains the central lognormal, and a number of possible mechanisms could explain the long tails - positivefeedback effects, network topology, etc. Many of the components in the central lognormal parts of the empirical distributions are unidentified and/or have unknown function. This indicates that much more biology awaits discovery.

Malthus qui n'était pas un mathématicien a fourni une description courte mais élaborée du rapport entre ressources, population et progrès technique dont on a retenu la célèbre opposition des deux progressions arithmétiques et géométriques. Quetelet puis Verhulst, en tentant de donner une expression plus mathématique aux idées de Malthus les ont simplifiées et déformées. Les économistes modernes, de Solow à R.D. Lee ont accentué cette dérive. Pour que les mathématiques puissent « passer » et respecter l'orthodoxie économique, ils ont déformé un peu plus l'idée originale de Malthus jusqu'à l'inverser pour l'opposer aux idées d'Ester Boserup, elles aussi inversées pour les besoins de la cause. Cette dérive n'est sans doute pas limitée au modèle malthusien ou boserupien mais montre le danger fréquent en mathématiques sociales de préférer l'élégance mathématique et le respect des théories en vigueur au simple déroulement des faits, et plus précisément de croire qu'en introduisant le temps t dans les équations, on traduit la dynamique profonde des phénomènes

A characterization of the genetic variation of recently admixed populations may reveal historical population events, and is useful for the detection of single nucleotide polymorphisms (SNPs) associated with diseases through association studies and admixture mapping. Inference of locus-specific ancestry is key to our understanding of the genetic variation of such populations. While a number of methods for the inference of locus-specific ancestry are accurate when the ancestral populations are quite distant (e.g. African–Americans), current methods incur a large error rate when inferring the locus-specific ancestry in admixed populations where the ancestral populations are closely related (e.g. Americans of European descent). Results: In this work, we extend previous methods for the inference of locus-specific ancestry by the incorporation of a refined model of recombination events. We present an efficient dynamic programming algorithm to infer the locus-specific ancestries in this model, resulting in a method that attains improved accuracies; the improvement is most significant when the ancestral populations are closely related. An evaluation on a wide range of scenarios, including admixtures of the 52 population groups from the Human Genome Diversity Project demonstrates that locus-specific ancestry can indeed be accurately inferred in these admixtures using our method. Finally, we demonstrate that imputation methods can be improved by the incorporation of locus-specific ancestry, when applied to admixed populations. Availability: The implementation of the WINPOP model is available as part of the LAMP package at http://lamp.icsi.berkeley.edu/lamp

Motivation: A fundamental problem in population genetics, which being also of importance to forensic science, is to compute the match probability (MP) that two individuals randomly chosen from a population have identical alleles at a collection of loci. At present, 11–13 unlinked autosomal microsatellite loci are typed for forensic use. In a finite population, the genealogical relationships of individuals can create statistical non-independence of alleles at unlinked loci. However, the so-called product rule, which is used in courts in the USA, computes the MP for multiple unlinked loci by assuming statistical independence, multiplying the one-locus MPs at those loci. Analytically testing the accuracy of the product rule for more than five loci has hitherto remained an open problem. Results: In this article, we adopt a flexible graphical framework to compute multi-locus MPs analytically. We consider two standard models of random mating, namely the Wright–Fisher (WF) and Moran models. We succeed in computing haplotypic MPs for up to 10 loci in the WF model, and up to 13 loci in the Moran model. For a finite population and a large number of loci, we show that the MPs predicted by the product rule are highly sensitive to mutation rates in the range of interest, while the true MPs computed using our graphical framework are not. Furthermore, we show that the WF and Moran models may produce drastically different MPs for a finite population, and that this difference grows with the number of loci and mutation rates. Although the two models converge to the same coalescent or diffusion limit, in which the population size approaches infinity, we demonstrate that, when multiple loci are considered, the rate of convergence in the Moran model is significantly slower than that in the WF model. Availability: A C++ implementation of the algorithms discussed in this article is available at http://www.cs.berkeley.edu/~yss/software.html.

Background The pattern of single nucleotide polymorphisms, or SNPs, contains a tremendous amount of information with respect to the mechanisms of the micro-evolutionary process of a species. The inference of the roles of these mechanisms, including natural selection, relies heavily on computer simulations. A coalescent simulation is extremely powerful in generating a large number of samples of DNA sequences from a population (species) when all mutations are neutral, and Hudson's ms software is frequently used for this purpose. However, it has been difficult to incorporate natural selection into the coalescent framework. Results We herein present a software application to generate samples of DNA sequences when there is a biallelic site targeted by selection. This software application, referred to as mbs, is developed by modifying Hudson's ms. The mbs software is so flexible that it can incorporate any arbitrary histories of population size changes and any mode of selection as long as selection is operating on a biallelic site. Conclusions mbs provides opportunities to investigate the effect of any mode of selection on the pattern of SNPs under various demography.