Fixation and consensus times on a network: a unified approach

We investigate a set of stochastic models of biodiversity, population genetics, language evolution and opinion dynamics on a network within a common framework. Each node has a state, 0 < x_i < 1, with interactions specified by strengths m_{ij}. For any set of m_{ij} we derive an approximate expression for the mean time to reach fixation or consensus (all x_i=0 or 1). Remarkably in a case relevant to language change this time is independent of the network structure.Comment: 4+epsilon pages, two-column, RevTeX4, 3 eps figures; version accepted by Phys. Rev. Let

Random copying in space

Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We focus in particular on how a measure of the diversity in the population changes over time. We show that even when the vast majority of a population's history may be well-described by a spatially-unstructured model, spatial structure may nevertheless affect the expected level of diversity seen at a local scale. We demonstrate this phenomenon explicitly by examining the random copying process on small-world networks, and use our results to comment on the use of simple random-copying models in an empirical context.Comment: 26 pages, 11 figures. Based on invited talk at AHRC CECD Conference on "Cultural Evolution in Spatially Structured Populations" at UCL, September 2010. To appear in ACS - Advances in Complex System

The PDZ domain of the SpoIVB serine peptidase facilitates multiple functions

During spore formation in Bacillus subtilis, the SpoIVB protein is a critical component of the sigma (K) regulatory checkpoint. SpoIVB has been shown to be a serine peptidase that is synthesized in the spore chamber and which self-cleaves, releasing active forms. These forms can signal proteolytic processing of the transcription factor sigma (K) in the outer mother cell chamber of the sporulating cell. This forms the basis of the sigma (K) checkpoint and ensures accurate sigma (K)-controlled gene expression. SpoIVB has also been shown to activate a second distinct process, termed the second function, which is essential for the formation of heat-resistant spores. In addition to the serine peptidase domain, SpoIVB contains a PDZ domain. We have altered a number of conserved residues in the PDZ domain by site-directed mutagenesis and assayed the sporulation phenotype and signaling properties of mutant SpoIVB proteins. Our work has revealed that the SpoIVB PDZ domain could be used for up to four distinct processes, (i) targeting of itself for trans proteolysis, (11) binding to the protease inhibitor BofC, (iii) signaling of pro-sigma (K) processing, and (iv) signaling of the second function of SpoIVB

Ordering in voter models on networks: Exact reduction to a single-coordinate diffusion

We study the voter model and related random-copying processes on arbitrarily complex network structures. Through a representation of the dynamics as a particle reaction process, we show that a quantity measuring the degree of order in a finite system is, under certain conditions, exactly governed by a universal diffusion equation. Whenever this reduction occurs, the details of the network structure and random-copying process affect only a single parameter in the diffusion equation. The validity of the reduction can be established with considerably less information than one might expect: it suffices to know just two characteristic timescales within the dynamics of a single pair of reacting particles. We develop methods to identify these timescales, and apply them to deterministic and random network structures. We focus in particular on how the ordering time is affected by degree correlations, since such effects are hard to access by existing theoretical approaches.Comment: 37 pages, 10 figures. Revised version with additional discussion and simulation results to appear in J Phys

Evaluation of a candidate breast cancer associated SNP in ERCC4 as a risk modifier in BRCA1 and BRCA2 mutation carriers. Results from the Consortium of Investigators of Modifiers of BRCA1/BRCA2 (CIMBA)

Background: In this study we aimed to evaluate the role of a SNP in intron 1 of the ERCC4 gene (rs744154), previously reported to be associated with a reduced risk of breast cancer in the general population, as a breast cancer risk modifier in BRCA1 and BRCA2 mutation carriers. Methods: We have genotyped rs744154 in 9408 BRCA1 and 5632 BRCA2 mutation carriers from the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA) and assessed its association with breast cancer risk using a retrospective weighted cohort approach. Results: We found no evidence of association with breast cancer risk for BRCA1 (per-allele HR: 0.98, 95% CI: 0.93–1.04, P=0.5) or BRCA2 (per-allele HR: 0.97, 95% CI: 0.89–1.06, P=0.5) mutation carriers. Conclusion: This SNP is not a significant modifier of breast cancer risk for mutation carriers, though weak associations cannot be ruled out. A Osorio1, R L Milne2, G Pita3, P Peterlongo4,5, T Heikkinen6, J Simard7, G Chenevix-Trench8, A B Spurdle8, J Beesley8, X Chen8, S Healey8, KConFab9, S L Neuhausen10, Y C Ding10, F J Couch11,12, X Wang11, N Lindor13, S Manoukian4, M Barile14, A Viel15, L Tizzoni5,16, C I Szabo17, L Foretova18, M Zikan19, K Claes20, M H Greene21, P Mai21, G Rennert22, F Lejbkowicz22, O Barnett-Griness22, I L Andrulis23,24, H Ozcelik24, N Weerasooriya23, OCGN23, A-M Gerdes25, M Thomassen25, D G Cruger26, M A Caligo27, E Friedman28,29, B Kaufman28,29, Y Laitman28, S Cohen28, T Kontorovich28, R Gershoni-Baruch30, E Dagan31,32, H Jernström33, M S Askmalm34, B Arver35, B Malmer36, SWE-BRCA37, S M Domchek38, K L Nathanson38, J Brunet39, T Ramón y Cajal40, D Yannoukakos41, U Hamann42, HEBON37, F B L Hogervorst43, S Verhoef43, EB Gómez García44,45, J T Wijnen46,47, A van den Ouweland48, EMBRACE37, D F Easton49, S Peock49, M Cook49, C T Oliver49, D Frost49, C Luccarini50, D G Evans51, F Lalloo51, R Eeles52, G Pichert53, J Cook54, S Hodgson55, P J Morrison56, F Douglas57, A K Godwin58, GEMO59,60,61, O M Sinilnikova59,60, L Barjhoux59,60, D Stoppa-Lyonnet61, V Moncoutier61, S Giraud59, C Cassini62,63, L Olivier-Faivre62,63, F Révillion64, J-P Peyrat64, D Muller65, J-P Fricker65, H T Lynch66, E M John67, S Buys68, M Daly69, J L Hopper70, M B Terry71, A Miron72, Y Yassin72, D Goldgar73, Breast Cancer Family Registry37, C F Singer74, D Gschwantler-Kaulich74, G Pfeiler74, A-C Spiess74, Thomas v O Hansen75, O T Johannsson76, T Kirchhoff77, K Offit77, K Kosarin77, M Piedmonte78, G C Rodriguez79, K Wakeley80, J F Boggess81, J Basil82, P E Schwartz83, S V Blank84, A E Toland85, M Montagna86, C Casella87, E N Imyanitov88, A Allavena89, R K Schmutzler90, B Versmold90, C Engel91, A Meindl92, N Ditsch93, N Arnold94, D Niederacher95, H Deißler96, B Fiebig97, R Varon-Mateeva98, D Schaefer99, U G Froster100, T Caldes101, M de la Hoya101, L McGuffog49, A C Antoniou49, H Nevanlinna6, P Radice4,5 and J Benítez1,3 on behalf of CIMB

GENOMEPOP: A program to simulate genomes in populations

<p>Abstract</p> <p>Background</p> <p>There are several situations in population biology research where simulating DNA sequences is useful. Simulation of biological populations under different evolutionary genetic models can be undertaken using backward or forward strategies. Backward simulations, also called coalescent-based simulations, are computationally efficient. The reason is that they are based on the history of lineages with surviving offspring in the current population. On the contrary, forward simulations are less efficient because the entire population is simulated from past to present. However, the coalescent framework imposes some limitations that forward simulation does not. Hence, there is an increasing interest in forward population genetic simulation and efficient new tools have been developed recently. Software tools that allow efficient simulation of large DNA fragments under complex evolutionary models will be very helpful when trying to better understand the trace left on the DNA by the different interacting evolutionary forces. Here I will introduce GenomePop, a forward simulation program that fulfills the above requirements. The use of the program is demonstrated by studying the impact of intracodon recombination on global and site-specific <it>dN/dS </it>estimation.</p> <p>Results</p> <p>I have developed algorithms and written software to efficiently simulate, forward in time, different Markovian nucleotide or codon models of DNA mutation. Such models can be combined with recombination, at inter and intra codon levels, fitness-based selection and complex demographic scenarios.</p> <p>Conclusion</p> <p>GenomePop has many interesting characteristics for simulating SNPs or DNA sequences under complex evolutionary and demographic models. These features make it unique with respect to other simulation tools. Namely, the possibility of forward simulation under General Time Reversible (GTR) mutation or GTR×MG94 codon models with intra-codon recombination, arbitrary, user-defined, migration patterns, diploid or haploid models, constant or variable population sizes, etc. It also allows simulation of fitness-based selection under different distributions of mutational effects. Under the 2-allele model it allows the simulation of recombination hot-spots, the definition of different frequencies in different populations, etc. GenomePop can also manage large DNA fragments. In addition, it has a scaling option to save computation time when simulating large sequences and population sizes under complex demographic and evolutionary situations. These and many other features are detailed in its web page <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>.</p

Non-L\'evy mobility patterns of Mexican Me'Phaa peasants searching for fuelwood

We measured mobility patterns that describe walking trajectories of individual Me'Phaa peasants searching and collecting fuelwood in the forests of "La Monta\~na de Guerrero" in Mexico. These one-day excursions typically follow a mixed pattern of nearly-constant steps when individuals displace from their homes towards potential collecting sites and a mixed pattern of steps of different lengths when actually searching for fallen wood in the forest. Displacements in the searching phase seem not to be compatible with L\'evy flights described by power-laws with optimal scaling exponents. These findings however can be interpreted in the light of deterministic searching on heavily degraded landscapes where the interaction of the individuals with their scarce environment produces alternative searching strategies than the expected L\'evy flights. These results have important implications for future management and restoration of degraded forests and the improvement of the ecological services they may provide to their inhabitants.Comment: 15 pages, 4 figures. First version submitted to Human Ecology. The final publication will be available at http://www.springerlink.co

Composite likelihood estimation of demographic parameters

which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Background: Most existing likelihood-based methods for fitting historical demographic models to DNA sequence polymorphism data to do not scale feasibly up to the level of whole-genome data sets. Computational economies can be achieved by incorporating two forms of pseudo-likelihood: composite and approximate likelihood methods. Composite likelihood enables scaling up to large data sets because it takes the product of marginal likelihoods as an estimator of the likelihood of the complete data set. This approach is especially useful when a large number of genomic regions constitutes the data set. Additionally, approximate likelihood methods can reduce the dimensionality of the data by summarizing the information in the original data by either a sufficient statistic, or a set of statistics. Both composite and approximate likelihood methods hold promise for analyzing large data sets or for use in situations where the underlying demographic model is complex and has many parameters. This paper considers a simple demographic model of allopatric divergence between two populations, in which one of the population is hypothesized to have experienced a founder event, or population bottleneck. A large resequencing data set from human populations is summarized by the joint frequency spectrum, which is a matrix of the genomic frequency spectrum of derived base frequencies in two populations. A Bayesia

Estimating Parameters of Speciation Models Based on Refined Summaries of the Joint Site-Frequency Spectrum

Understanding the processes and conditions under which populations diverge to give rise to distinct species is a central question in evolutionary biology. Since recently diverged populations have high levels of shared polymorphisms, it is challenging to distinguish between recent divergence with no (or very low) inter-population gene flow and older splitting events with subsequent gene flow. Recently published methods to infer speciation parameters under the isolation-migration framework are based on summarizing polymorphism data at multiple loci in two species using the joint site-frequency spectrum (JSFS). We have developed two improvements of these methods based on a more extensive use of the JSFS classes of polymorphisms for species with high intra-locus recombination rates. First, using a likelihood based method, we demonstrate that taking into account low-frequency polymorphisms shared between species significantly improves the joint estimation of the divergence time and gene flow between species. Second, we introduce a local linear regression algorithm that considerably reduces the computational time and allows for the estimation of unequal rates of gene flow between species. We also investigate which summary statistics from the JSFS allow the greatest estimation accuracy for divergence time and migration rates for low (around 10) and high (around 100) numbers of loci. Focusing on cases with low numbers of loci and high intra-locus recombination rates we show that our methods for the estimation of divergence time and migration rates are more precise than existing approaches