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

Genomic heterogeneity of historical gene flow between two species of newts inferred from transcriptome data

The role of gene flow in species formation is a major unresolved issue in speciation biology. Progress in this area requires information on the long‐term patterns of gene flow between diverging species. Here, we used thousands of single‐nucleotide polymorphisms derived from transcriptome resequencing and a method modeling the joint frequency spectrum of these polymorphisms to reconstruct patterns of historical gene flow between two Lissotriton newts: L. vulgaris (Lv) and L. montandoni (Lm). We tested several models of divergence including complete isolation and various scenarios of historical gene flow. The model of secondary contact received the highest support. According to this model, the species split from their common ancestor ca. 5.5 million years (MY) ago, evolved in isolation for ca. 2 MY, and have been exchanging genes for the last 3.5 MY Demographic changes have been inferred in both species, with the current effective population size of ca. 0.7 million in Lv and 0.2 million in Lm. The postdivergence gene flow resulted in two‐directional introgression which affected the genomes of both species, but was more pronounced from Lv to Lm. Interestingly, we found evidence for genomic heterogeneity of interspecific gene flow. This study demonstrates the complexity of long‐term gene flow between distinct but incompletely reproductively isolated taxa which divergence was initiated millions of years ago

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

Distribution modelling and statistical phylogeography: an integrative framework for generating and testing alternative biogeographical hypotheses

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73644/1/j.1365-2699.2007.01814.x.pd

Evolutionary branching in a stochastic population model with discrete mutational steps

Evolutionary branching is analysed in a stochastic, individual-based population model under mutation and selection. In such models, the common assumption is that individual reproduction and life career are characterised by values of a trait, and also by population sizes, and that mutations lead to small changes in trait value. Then, traditionally, the evolutionary dynamics is studied in the limit of vanishing mutational step sizes. In the present approach, small but non-negligible mutational steps are considered. By means of theoretical analysis in the limit of infinitely large populations, as well as computer simulations, we demonstrate how discrete mutational steps affect the patterns of evolutionary branching. We also argue that the average time to the first branching depends in a sensitive way on both mutational step size and population size.Comment: 12 pages, 8 figures. Revised versio

Vulnerability to depression is associated with a failure to acquire implicit social appraisals

Major depressive disorder is frequently associated with disrupted relationships with spouses, partners, family and peers. These problems can precipitate the onset of clinical illness, influence severity and the prospects for treatment and recovery. Here, we investigated whether individuals who have recovered from depression use interpersonal signals to form favourable appraisals of others as social partners. Twenty recovered-depressed adults (with at least two adult episodes of major depressive disorder but euthymic and medication-free for six months) and twenty three healthy, never-depressed adults completed a reaction time task in which the gaze direction of some faces reliably cued the location a target (valid faces), whereas the gaze direction of other faces cued the opposite spatial location (invalid faces). None of the participants were aware of this contingency. Following this task, participants judged the trustworthiness of the faces. Both the recovered-depressed and healthy never-depressed participants were significantly faster to categorise targets following valid compared with invalid gaze cueing faces. Whereas the healthy never-depressed participants judged the valid faces to be significantly more trustworthy than the invalid faces; this implicit social appraisal was absent in the recovered-depressed participants. Individuals who have recovered from major depressive disorder are able to respond appropriately to joint attention with other people but appear to not use joint attention to form implicit trust appraisals of others as potential social partners

Evolutionary game dynamics in phenotype space

Evolutionary dynamics can be studied in well-mixed or structured populations. Population structure typically arises from the heterogeneous distribution of individuals in physical space or on social networks. Here we introduce a new type of space to evolutionary game dynamics: phenotype space. The population is well-mixed in the sense that everyone is equally likely to interact with everyone else, but the behavioral strategies depend on distance in phenotype space. Individuals might behave differently towards those who look similar or dissimilar. Individuals mutate to nearby phenotypes. We study the `phenotypic space walk' of populations. We present analytic calculations that bring together ideas from coalescence theory and evolutionary game dynamics. As a particular example, we investigate the evolution of cooperation in phenotype space. We obtain a precise condition for natural selection to favor cooperators over defectors: for a one-dimensional phenotype space and large population size the critical benefit-to-cost ratio is given by b/c=1+2/sqrt{3}. We derive the fundamental condition for any evolutionary game and explore higher dimensional phenotype spaces.Comment: version 2: minor changes; equivalent to final published versio

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

Thrombospondin-1 Type 1 Repeats in a Model of Inflammatory Bowel Disease: Transcript Profile and Therapeutic Effects

Thrombospondin-1 (TSP-1) is a matricellular protein with regulatory functions in inflammation and cancer. The type 1 repeats (TSR) domains of TSP-1 have been shown to interact with a wide range of proteins that result in the anti-angiogenic and anti-tumor properties of TSP-1. To ascertain possible functions and evaluate potential therapeutic effects of TSRs in inflammatory bowel disease, we conducted clinical, histological and microarray analyses on a mouse model of induced colitis. We used dextran sulfate sodium (DSS) to induce colitis in wild-type (WT) mice for 7 days. Simultaneously, mice were injected with either saline or one form of TSP-1 derived recombinant proteins, containing either (1) the three type 1 repeats of the TSP-1 (3TSR), (2) the second type 1 repeat (TSR2), or (3) TSR2 with the RFK sequence (TSR2+RFK). Total RNA isolated from the mice colons were processed and hybridized to mouse arrays. Array data were validated by real-time qPCR and immunohistochemistry. Histological and disease indices reveal that the mice treated with the TSRs show different patterns of leukocytic infiltration and that 3TSR treatment was the most effective in decreasing inflammation in DSS-induced colitis. Transcriptional profiling revealed differentially expressed (DE) genes, with the 3TSR-treated mice showing the least deviation from the WT-water controls. In conclusion, this study shows that 3TSR treatment is effective in attenuating the inflammatory response to DSS injury. In addition, the transcriptomics work unveils novel genetic data that suggest beneficial application of the TSR domains in inflammatory bowel disease