Probability and Statistics for Particle Physicists

Lectures presented at the 1st CERN Asia-Europe-Pacific School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. A pedagogical selection of topics in probability and statistics is presented. Choice and emphasis are driven by the author's personal experience, predominantly in the context of physics analyses using experimental data from high-energy physics detectors.Comment: Updated version of lectures given at the First Asia-Europe-Pacific School of High-Energy Physics, Fukuoka, Japan, 14-27 October 2012. Published as a CERN Yellow Report (CERN-2014-001) and KEK report (KEK-Proceedings-2013-8), K. Kawagoe and M. Mulders (eds.), 2014, p. 219. Total 28 pages, 36 figure

Inferring the Distribution of Selective Effects from a Time Inhomogeneous Model

We have developed a Poisson random field model for estimating the distribution of selective effects of newly arisen nonsynonymous mutations that could be observed as polymorphism or divergence in samples of two related species under the assumption that the two species populations are not at mutation-selection-drift equilibrium. The model is applied to 91Drosophila genes by comparing levels of polymorphism in an African population of D. melanogaster with divergence to a reference strain of D. simulans. Based on the difference of gene expression level between testes and ovaries, the 91 genes were classified as 33 male-biased, 28 female-biased, and 30 sex-unbiased genes. Under a Bayesian framework, Markov chain Monte Carlo simulations are implemented to the model in which the distribution of selective effects is assumed to be Gaussian with a mean that may differ from one gene to the other to sample key parameters. Based on our estimates, the majority of newly-arisen nonsynonymous mutations that could contribute to polymorphism or divergence in Drosophila species are mildly deleterious with a mean scaled selection coefficient of -2.81, while almost 86% of the fixed differences between species are driven by positive selection. There are only 16.6% of the nonsynonymous mutations observed in sex-unbiased genes that are under positive selection in comparison to 30% of male-biased and 46% of female-biased genes that are beneficial. We also estimated that D. melanogaster and D. simulans may have diverged 1.72 million years ago

Evolution of female multiple mating : A quantitative model of the “sexually selected sperm” hypothesis

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Sex Differences in Recombination in Sticklebacks.

Recombination often differs markedly between males and females. Here we present the first analysis of sex-specific recombination in Gasterosteus sticklebacks. Using whole-genome sequencing of 15 crosses between G. aculeatus and G. nipponicus, we localized 698 crossovers with a median resolution of 2.3 kb. We also used a bioinformatic approach to infer historical sex-averaged recombination patterns for both species. Recombination is greater in females than males on all chromosomes, and overall map length is 1.64 times longer in females. The locations of crossovers differ strikingly between sexes. Crossovers cluster toward chromosome ends in males, but are distributed more evenly across chromosomes in females. Suppression of recombination near the centromeres in males causes crossovers to cluster at the ends of long arms in acrocentric chromosomes, and greatly reduces crossing over on short arms. The effect of centromeres on recombination is much weaker in females. Genomic differentiation between G. aculeatus and G. nipponicus is strongly correlated with recombination rate, and patterns of differentiation along chromosomes are strongly influenced by male-specific telomere and centromere effects. We found no evidence for fine-scale correlations between recombination and local gene content in either sex. We discuss hypotheses for the origin of sexual dimorphism in recombination and its consequences for sexually antagonistic selection and sex chromosome evolution