Full likelihood inference from the site frequency spectrum based on the optimal tree resolution.

We develop a novel importance sampler to compute the full likelihood function of a demographic or structural scenario given the site frequency spectrum (SFS) at a locus free of intra-locus recombination. This sampler, instead of representing the hidden genealogy of a sample of individuals by a labelled binary tree, uses the minimal level of information about such a tree that is needed for the likelihood of the SFS and thus takes advantage of the huge reduction in the size of the state space that needs to be integrated. We assume that the population may have demographically changed and may be non-panmictically structured, as reflected by the branch lengths and the topology of the genealogical tree of the sample, respectively. We also assume that mutations conform to the infinitely-many-sites model. We achieve this by a controlled Markov process that generates 'particles' in the hidden space of SFS histories which are always compatible with the observed SFS. To produce the particles, we use Aldous' Beta-splitting model for a one parameter family of prior distributions over genealogical topologies or shapes (including that of the Kingman coalescent) and allow the branch lengths or epoch times to have a parametric family of priors specified by a model of demography (including exponential growth and bottleneck models). Assuming independence across unlinked loci, we can estimate the likelihood of a population scenario based on a large collection of independent SFS by an importance sampling scheme, using the (unconditional) distribution of the genealogies under this scenario when the latter is available. When it is not available, we instead compute the joint likelihood of the tree balance parameter ß assuming that the tree topology follows Aldous' Beta-splitting model, and of the demographic scenario determining the distribution of the inter-coalescence times or epoch times in the genealogy of a sample, in order to at least distinguish different equivalence classes of population scenarios leading to different tree balances and epoch times. Simulation studies are conducted to demonstrate the capabilities of the approach with publicly available code.

A nonlinear dynamical system approach for the yielding behaviour of a viscoplastic material.

A nonlinear dynamical system model that approximates a microscopic Gibbs field model for the yielding of a viscoplastic material subjected to varying external stresses recently reported in R. Sainudiin, M. Moyers-Gonzalez and T. Burghelea, Soft Matter, 2015, 11(27), 5531-5545 is presented. The predictions of the model are in fair agreement with microscopic simulations and are in very good agreement with the micro-structural semi-empirical model reported in A. M. V. Putz and T. I. Burghelea, Rheol. Acta, 2009, 48, 673-689. With only two internal parameters, the nonlinear dynamical system model captures several key features of the solid-fluid transition observed in experiments: the effect of the interactions between microscopic constituents on the yield point, the abruptness of solid-fluid transition and the emergence of a hysteresis of the micro-structural states upon increasing/decreasing external forces. The scaling behaviour of the magnitude of the hysteresis with the degree of the steadiness of the flow is consistent with previous experimental observations. Finally, the practical usefulness of the approach is demonstrated by fitting a rheological data set measured with an elasto-viscoplastic material.

The transmission process: A combinatorial stochastic process for the evolution of transmission trees over networks.

We derive a combinatorial stochastic process for the evolution of the transmission tree over the infected vertices of a host contact network in a susceptible-infected (SI) model of an epidemic. Models of transmission trees are crucial to understanding the evolution of pathogen populations. We provide an explicit description of the transmission process on the product state space of (rooted planar ranked labelled) binary transmission trees and labelled host contact networks with SI-tags as a discrete-state continuous-time Markov chain. We give the exact probability of any transmission tree when the host contact network is a complete, star or path network - three illustrative examples. We then develop a biparametric Beta-splitting model that directly generates transmission trees with exact probabilities as a function of the model parameters, but without explicitly modelling the underlying contact network, and show that for specific values of the parameters we can recover the exact probabilities for our three example networks through the Markov chain construction that explicitly models the underlying contact network. We use the maximum likelihood estimator (MLE) to consistently infer the two parameters driving the transmission process based on observations of the transmission trees and use the exact MLE to characterize equivalence classes over the space of contact networks with a single initial infection. An exploratory simulation study of the MLEs from transmission trees sampled from three other deterministic and four random families of classical contact networks is conducted to shed light on the relation between the MLEs of these families with some implications for statistical inference along with pointers to further extensions of our models. The insights developed here are also applicable to the simplest models of "meme" evolution in online social media networks through transmission events that can be distilled from observable actions such as "likes", "mentions", "retweets" and "+1s" along with any concomitant comments.

A microscopic Gibbs field model for the macroscopic yielding behaviour of a viscoplastic fluid.

We present a Gibbs random field model for the microscopic interactions in a viscoplastic fluid. The model has only two parameters which are sufficient to describe the internal energy of the material in the absence of external stress and a third parameter for a constant externally applied stress. The energy function is derived from the Gibbs potential in terms of the external stress and internal energy. The resulting Gibbs distribution, over a configuration space of microscopic interactions, can mimic experimentally observed macroscopic behavioural phenomena that depend on the externally applied stress. A simulation algorithm that can be used to approximate samples from the Gibbs distribution is given and it is used to gain several insights about the model. Corresponding to weak interactions between the microscopic solid units, our model reveals a smooth solid-fluid transition which is fully reversible upon increasing/decreasing external stresses. If the interaction between neighbouring microscopic constituents exceeds a critical threshold the solid-fluid transition becomes abrupt and a hysteresis of the deformation states is observed even at the asymptotic limit of steady forcing. Quite remarkably, in spite of the limited number of parameters involved, the predictions of our model are in a good qualitative agreement with macro rheological experimental results on the solid-fluid transition in various yield stress materials subjected to an external stress.

Finding the best resolution for the Kingman-Tajima coalescent: theory and applications.

Many summary statistics currently used in population genetics and in phylogenetics depend only on a rather coarse resolution of the underlying tree (the number of extant lineages, for example). Hence, for computational purposes, working directly on these resolutions appears to be much more efficient. However, this approach seems to have been overlooked in the past. In this paper, we describe six different resolutions of the Kingman-Tajima coalescent together with the corresponding Markov chains, which are essential for inference methods. Two of the resolutions are the well-known n-coalescent and the lineage death process due to Kingman. Two other resolutions were mentioned by Kingman and Tajima, but never explicitly formalized. Another two resolutions are novel, and complete the picture of a multi-resolution coalescent. For all of them, we provide the forward and backward transition probabilities, the probability of visiting a given state as well as the probability of a given realization of the full Markov chain. We also provide a description of the state-space that highlights the computational gain obtained by working with lower-resolution objects. Finally, we give several examples of summary statistics that depend on a coarser resolution of Kingman's coalescent, on which simulations are usually based.

Experiments with the site frequency spectrum.

Evaluating the likelihood function of parameters in highly-structured population genetic models from extant deoxyribonucleic acid (DNA) sequences is computationally prohibitive. In such cases, one may approximately infer the parameters from summary statistics of the data such as the site-frequency-spectrum (SFS) or its linear combinations. Such methods are known as approximate likelihood or Bayesian computations. Using a controlled lumped Markov chain and computational commutative algebraic methods, we compute the exact likelihood of the SFS and many classical linear combinations of it at a non-recombining locus that is neutrally evolving under the infinitely-many-sites mutation model. Using a partially ordered graph of coalescent experiments around the SFS, we provide a decision-theoretic framework for approximate sufficiency. We also extend a family of classical hypothesis tests of standard neutrality at a non-recombining locus based on the SFS to a more powerful version that conditions on the topological information provided by the SFS.

Simple models of genomic variation in human SNP density.

BACKGROUND: Descriptive hierarchical Poisson models and population-genetic coalescent mixture models are used to describe the observed variation in single-nucleotide polymorphism (SNP) density from samples of size two across the human genome. RESULTS: Using empirical estimates of recombination rate across the human genome and the observed SNP density distribution, we produce a maximum likelihood estimate of the genomic heterogeneity in the scaled mutation rate theta. Such models produce significantly better fits to the observed SNP density distribution than those that ignore the empirically observed recombinational heterogeneities. CONCLUSION: Accounting for mutational and recombinational heterogeneities can allow for empirically sound null distributions in genome scans for "outliers", when the alternative hypotheses include fundamentally historical and unobserved phenomena.

Relative Contribution of Seed-Transmitted Inoculum to Foliar Populations of Phaeosphaeria nodorum.

ABSTRACT A marked-isolate, release-recapture experiment was conducted to assess the relative contributions of seed-transmitted (released isolates) versus all other inocula to foliar and grain populations of Phaeosphaeria nodorum in winter wheat rotated with nonsusceptible crops in New York and Georgia, United States. Seed infected with two distinct groups of marked isolates of P. nodorum containing rare alleles (identified by amplified fragment length polymorphisms [AFLPs]) and balanced for mating type were planted in experimental field plots in two locations in each state. Recapture was done by isolating P. nodorum from leaves showing necrotic lesions at spring tillering and flowering stages, and mature grains from spikes showing glume blotch. Isolates from these samples were genotyped by AFLPs and categorized as released or nonreleased to infer sources of inoculum. Both infected seed and other sources of the pathogen contributed significant primary inocula to populations recovered from leaves and harvested grain. Seed-transmitted genotypes accounted for a total of 57% of all isolates recovered from inoculated plots, with a range of 15 to 90% of the populations of P. nodorum collected over the season in individual, inoculated plots at the four locations. Plants in the noninoculated control plots also became diseased and 95% or more of the isolates recovered from these plots were nonreleased genotypes. Although other potential sources of P. nodorum within and adjacent to experimental plots were not ruled out, nonreleased genotypes likely were derived from immigrant ascospores potentially from sources at a considerable distance from the plots. Our results suggest that, although reduction of seedborne inoculum of P. nodorum may delay foliar epidemics, this strategy by itself is unlikely to result in high levels of control in eastern North America because of the additional contribution from alternative sources of inoculum.

Identification of physicochemical selective pressure on protein encoding nucleotide sequences.

BACKGROUND: Statistical methods for identifying positively selected sites in protein coding regions are one of the most commonly used tools in evolutionary bioinformatics. However, they have been limited by not taking the physiochemical properties of amino acids into account. RESULTS: We develop a new codon-based likelihood model for detecting site-specific selection pressures acting on specific physicochemical properties. Nonsynonymous substitutions are divided into substitutions that differ with respect to the physicochemical properties of interest, and those that do not. The substitution rates of these two types of changes, relative to the synonymous substitution rate, are then described by two parameters, gamma and omega respectively. The new model allows us to perform likelihood ratio tests for positive selection acting on specific physicochemical properties of interest. The new method is first used to analyze simulated data and is shown to have good power and accuracy in detecting physicochemical selective pressure. We then re-analyze data from the class-I alleles of the human Major Histocompatibility Complex (MHC) and from the abalone sperm lysine. CONCLUSION: Our new method allows a more flexible framework to identify selection pressure on particular physicochemical properties.

A Beta-splitting model for evolutionary trees.

In this article, we construct a generalization of the Blum-François Beta-splitting model for evolutionary trees, which was itself inspired by Aldous' Beta-splitting model on cladograms. The novelty of our approach allows for asymmetric shares of diversification rates (or diversification 'potential') between two sister species in an evolutionarily interpretable manner, as well as the addition of extinction to the model in a natural way. We describe the incremental evolutionary construction of a tree with n leaves by splitting or freezing extant lineages through the generating, organizing and deleting processes. We then give the probability of any (binary rooted) tree under this model with no extinction, at several resolutions: ranked planar trees giving asymmetric roles to the first and second offspring species of a given species and keeping track of the order of the speciation events occurring during the creation of the tree, unranked planar trees, ranked non-planar trees and finally (unranked non-planar) trees. We also describe a continuous-time equivalent of the generating, organizing and deleting processes where tree topology and branch lengths are jointly modelled and provide code in SageMath/Python for these algorithms.

Microsatellite mutation models: insights from a comparison of humans and chimpanzees.

Using genomic data from homologous microsatellite loci of pure AC repeats in humans and chimpanzees, several models of microsatellite evolution are tested and compared using likelihood-ratio tests and the Akaike information criterion. A proportional-rate, linear-biased, one-phase model emerges as the best model. A focal length toward which the mutational and/or substitutional process is linearly biased is a crucial feature of microsatellite evolution. We find that two-phase models do not lead to a significantly better fit than their one-phase counterparts. The performance of models based on the fit of their stationary distributions to the empirical distribution of microsatellite lengths in the human genome is consistent with that based on the human-chimp comparison. Microsatellites interrupted by even a single point mutation exhibit a twofold decrease in their mutation rate when compared to pure AC repeats. In general, models that allow chimps to have a larger per-repeat unit slippage rate and/or a shorter focal length compared to humans give a better fit to the human-chimp data as well as the human genomic data.

Terrorist attacks escalate in frequency and fatalities preceding highly lethal attacks.

Highly lethal terrorist attacks, which we define as those killing 21 or more people, account for 50% of the total number of people killed in all terrorist attacks combined, yet comprise only 3.5% of terrorist attacks. Given the disproportionate influence of these incidents, uncovering systematic patterns in attacks that precede and anticipate these highly lethal attacks may be of value for understanding attacks that exact a heavy toll on life. Here we examined whether the activity of terrorist groups escalates--both in the number of people killed per attack and in the frequency of attacks--leading up to highly lethal attacks. Analyses of terrorist attacks drawn from a state-of-the-art international terrorism database (The Global Terrorism Database) showed evidence for both types of escalation leading up to highly lethal attacks, though complexities to the patterns emerged as well. These patterns of escalation do not emerge among terrorist groups that never commit a highly lethal attack.

Human-assisted spread of a maladaptive behavior in a critically endangered bird.

Conservation management often focuses on counteracting the adverse effects of human activities on threatened populations. However, conservation measures may unintentionally relax selection by allowing the 'survival of the not-so-fit', increasing the risk of fixation of maladaptive traits. Here, we report such a case in the critically-endangered Chatham Island black robin (Petroica traversi) which, in 1980, was reduced to a single breeding pair. Following this bottleneck, some females were observed to lay eggs on the rims of their nests. Rim eggs left in place always failed to hatch. To expedite population recovery, rim eggs were repositioned inside nests, yielding viable hatchlings. Repositioning resulted in rapid growth of the black robin population, but by 1989 over 50% of all females were laying rim eggs. We used an exceptional, species-wide pedigree to consider both recessive and dominant models of inheritance over all plausible founder genotype combinations at a biallelic and possibly sex-linked locus. The pattern of rim laying is best fitted as an autosomal dominant Mendelian trait. Using a phenotype permutation test we could also reject the null hypothesis of non-heritability for this trait in favour of our best-fitting model of heritability. Data collected after intervention ceased shows that the frequency of rim laying has strongly declined, and that this trait is maladaptive. This episode yields an important lesson for conservation biology: fixation of maladaptive traits could render small threatened populations completely dependent on humans for reproduction, irreversibly compromising the long term viability of populations humanity seeks to conserve.

Auto-validating von Neumann rejection sampling from small phylogenetic tree spaces.

BACKGROUND: In phylogenetic inference one is interested in obtaining samples from the posterior distribution over the tree space on the basis of some observed DNA sequence data. One of the simplest sampling methods is the rejection sampler due to von Neumann. Here we introduce an auto-validating version of the rejection sampler, via interval analysis, to rigorously draw samples from posterior distributions over small phylogenetic tree spaces. RESULTS: The posterior samples from the auto-validating sampler are used to rigorously (i) estimate posterior probabilities for different rooted topologies based on mitochondrial DNA from human, chimpanzee and gorilla, (ii) conduct a non-parametric test of rate variation between protein-coding and tRNA-coding sites from three primates and (iii) obtain a posterior estimate of the human-neanderthal divergence time. CONCLUSION: This solves the open problem of rigorously drawing independent and identically distributed samples from the posterior distribution over rooted and unrooted small tree spaces (3 or 4 taxa) based on any multiply-aligned sequence data.

Detecting site-specific physicochemical selective pressures: applications to the Class I HLA of the human major histocompatibility complex and the SRK of the plant sporophytic self-incompatibility system.

Models of codon substitution are developed that incorporate physicochemical properties of amino acids. When amino acid sites are inferred to be under positive selection, these models suggest the nature and extent of the physicochemical properties under selection. This is accomplished by first partitioning the codons on the basis of some property of the encoded amino acids. This partition is used to parametrize the rates of property-conserving and property-altering base substitutions at the codon level by means of finite mixtures of Markov models that also account for codon and transition:transversion biases. Here, we apply this method to two positively selected receptors involved in ligand-recognition: the class I alleles of the human major histocompatibility complex (MHC) of known structure and the S-locus receptor kinase (SRK) of the sporophytic self-incompatibility system (SSI) in cruciferous plants (Brassicaceae), whose structure is unknown. Through likelihood ratio tests we demonstrate that at some sites, the positively selected MHC and SRK proteins are under physicochemical selective pressures to alter polarity, volume, polarity and/or volume, and charge to various extents. An empirical Bayes approach is used to identify sites that may be important for ligand recognition in these proteins.