Investigating the Interactions of Yeast Prions: [SWI+], [PSI+], and [PIN+]

The relationship between quantitative genetics and population genetics has been studied for nearly a century, almost since the existence of these two disciplines. Here we ask to what extent quantitative genetic models in which selection is assumed to operate on a polygenic trait predict adaptive fixations that may lead to footprints in the genome (selective sweeps). We study two-locus models of stabilizing selection (with and without genetic drift) by simulations and analytically. For symmetric viability selection we find that ∼16% of the trajectories may lead to fixation if the initial allele frequencies are sampled from the neutral site-frequency spectrum and the effect sizes are uniformly distributed. However, if the population is preadapted when it undergoes an environmental change (i.e., sits in one of the equilibria of the model), the fixation probability decreases dramatically. In other two-locus models with general viabilities or an optimum shift, the proportion of adaptive fixations may increase to >24%. Similarly, genetic drift leads to a higher probability of fixation. The predictions of alternative quantitative genetics models, initial conditions, and effect-size distributions are also discussed.     

Clades, clans, and reciprocal monophyly under neutral evolutionary models

The Yule model and the coalescent model are two neutral stochastic models for generating trees in phylogenetics and population genetics, respectively. Although these models are quite different, they lead to identical distributions concerning the probability that pre-specified groups of taxa form monophyletic groups (clades) in the tree. We extend earlier work to derive exact formulae for the probability of finding one or more groups of taxa as clades in a rooted tree, or as ‘clans’ in an unrooted tree. Our findings are relevant for calculating the statistical significance of observed monophyly and reciprocal monophyly in phylogenetics.     

Relating interactions between neurofilaments to the structure of axonal neurofilament distributions through polymer brush models

Neurofilaments (NFs) have been proposed to interact with one another through mutual steric exclusion of their unstructured C-terminal "sidearm" domains, producing order in axonal NF distributions and conferring mechanical strength to the axon. Here we apply theory developed for polymer brushes to examine the relationship between the brush properties of the sidearms and NF organization in axons. We first measure NF-NF radial distribution functions and occupancy probability distributions for adult mice. Interpreting the probability distributions using information theory, we show that the NF distributions may be represented by a single pair potential of mean force. Then, to explore the relationship between model parameters and NF architecture, we conduct two-dimensional Monte Carlo simulations of NF cross-sectional distributions. We impose purely repulsive interaction potentials in which the sidearms are represented as neutral and polyelectrolyte chains. By treating the NFs as telechelic polymer brushes, we also incorporate cross-bridging interactions. Both repulsive potentials are capable of reproducing NF cross-sectional densities and their pair correlations. We find that NF structure is sensitive to changes in brush thickness mediated by chain charge, consistent with the experimental observation that sidearm phosphorylation regulates interfilament spacing. The presence of attractive cross-bridging interactions contributes only modestly to structure for moderate degrees of cross-bridging and leads to NF aggregation for extensive cross-bridging.     

The Effect of Single Recombination Events on Coalescent Tree Height and Shape

The coalescent with recombination is a fundamental model to describe the genealogical history of DNA sequence samples from recombining organisms. Considering recombination as a process which acts along genomes and which creates sequence segments with shared ancestry, we study the influence of single recombination events upon tree characteristics of the coalescent. We focus on properties such as tree height and tree balance and quantify analytically the changes in these quantities incurred by recombination in terms of probability distributions. We find that changes in tree topology are often relatively mild under conditions of neutral evolution, while changes in tree height are on average quite large. Our results add to a quantitative understanding of the spatial coalescent and provide the neutral reference to which the impact by other evolutionary scenarios, for instance tree distortion by selective sweeps, can be compared.     

Modeling Invasion Dynamics with Spatial Random-Fitness Due to Micro-Environment

Numerous experimental studies have demonstrated that the microenvironment is a key regulator influencing the proliferative and migrative potentials of species. Spatial and temporal disturbances lead to adverse and hazardous microenvironments for cellular systems that is reflected in the phenotypic heterogeneity within the system. In this paper, we study the effect of microenvironment on the invasive capability of species, or mutants, on structured grids (in particular, square lattices) under the influence of site-dependent random proliferation in addition to a migration potential. We discuss both continuous and discrete fitness distributions. Our results suggest that the invasion probability is negatively correlated with the variance of fitness distribution of mutants (for both advantageous and neutral mutants) in the absence of migration of both types of cells. A similar behaviour is observed even in the presence of a random fitness distribution of host cells in the system with neutral fitness rate. In the case of a bimodal distribution, we observe zero invasion probability until the system reaches a (specific) proportion of advantageous phenotypes. Also, we find that the migrative potential amplifies the invasion probability as the variance of fitness of mutants increases in the system, which is the exact opposite in the absence of migration. Our computational framework captures the harsh microenvironmental conditions through quenched random fitness distributions and migration of cells, and our analysis shows that they play an important role in the invasion dynamics of several biological systems such as bacterial micro-habitats, epithelial dysplasia, and metastasis. We believe that our results may lead to more experimental studies, which can in turn provide further insights into the role and impact of heterogeneous environments on invasion dynamics.     

Predictions of Taylor's power law, density dependence and pink noise from a neutrally modeled time series

There has recently been increasing interest in neutral models of biodiversity and their ability to reproduce the patterns observed in nature, such as species abundance distributions. Here we investigate the ability of a neutral model to predict phenomena observed in single-population time series, a study complementary to most existing work that concentrates on snapshots in time of the whole community. We consider tests for density dependence, the dominant frequencies of population fluctuation (spectral density) and a relationship between the mean and variance of a fluctuating population (Taylor's power law). We simulated an archipelago model of a set of interconnected local communities with variable mortality rate, migration rate, speciation rate, size of local community and number of local communities. Our spectral analysis showed ‘pink noise’: a departure from a standard random walk dynamics in favor of the higher frequency fluctuations which is partly consistent with empirical data. We detected density dependence in local community time series but not in metacommunity time series. The slope of the Taylor's power law in the model was similar to the slopes observed in natural populations, but the fit to the power law was worse. Our observations of pink noise and density dependence can be attributed to the presence of an upper limit to community sizes and to the effect of migration which distorts temporal autocorrelation in local time series. We conclude that some of the phenomena observed in natural time series can emerge from neutral processes, as a result of random zero-sum birth, death and migration. This suggests the neutral model would be a parsimonious null model for future studies of time series data.     

Emergence of structural patterns in neutral trophic networks

Interaction networks are central elements of ecological systems and have very complex structures. Historically, much effort has focused on niche-mediated processes to explain these structures, while an emerging consensus posits that both niche and neutral mechanisms simultaneously shape many features of ecological communities. However, the study of interaction networks still lacks a comprehensive neutral theory. Here we present a neutral model of predator-prey interactions and analyze the structural characteristics of the simulated networks. We find that connectance values (complexity) and complexity-diversity relationships of neutral networks are close to those observed in empirical bipartite networks. High nestedness and low modularity values observed in neutral networks fall in the range of those from empirical antagonist bipartite networks. Our results suggest that, as an alternative to niche-mediated processes that induce incompatibility between species ("niche forbidden links"), neutral processes create "neutral forbidden links" due to uneven species abundance distributions and the low probability of interaction between rare species. Neutral trophic networks must be seen as the missing endpoint of a continuum from niche to purely stochastic approaches of community organization.     

Quantifying Population Genetic Differentiation from Next-Generation Sequencing Data

Over the past few years, new high-throughput DNA sequencing technologies have dramatically increased speed and reduced sequencing costs. However, the use of these sequencing technologies is often challenged by errors and biases associated with the bioinformatical methods used for analyzing the data. In particular, the use of naïve methods to identify polymorphic sites and infer genotypes can inflate downstream analyses. Recently, explicit modeling of genotype probability distributions has been proposed as a method for taking genotype call uncertainty into account. Based on this idea, we propose a novel method for quantifying population genetic differentiation from next-generation sequencing data. In addition, we present a strategy for investigating population structure via principal components analysis. Through extensive simulations, we compare the new method herein proposed to approaches based on genotype calling and demonstrate a marked improvement in estimation accuracy for a wide range of conditions. We apply the method to a large-scale genomic data set of domesticated and wild silkworms sequenced at low coverage. We find that we can infer the fine-scale genetic structure of the sampled individuals, suggesting that employing this new method is useful for investigating the genetic relationships of populations sampled at low coverage.     

Confronting different models of community structure to species-abundance data: a Bayesian model comparison

Species abundances are undoubtedly the most widely available macroecological data, but can we use them to distinguish among several models of community structure? Here we present a Bayesian analysis of species‐abundance data that yields a full joint probability distribution of each model's parameters plus a relatively parameter‐independent criterion, the posterior Bayes factor, to compare these models. We illustrate our approach by comparing three classical distributions: the zero‐sum multinomial (ZSM) distribution, based on Hubbell's neutral model, the multivariate Poisson lognormal distribution (MPLN), based on niche arguments, and the discrete broken stick (DBS) distribution, based on MacArthur's broken stick model. We give explicit formulas for the probability of observing a particular species‐abundance data set in each model, and argue that conditioning on both sample size and species count is needed to allow comparisons between the two distributions. We apply our approach to two neotropical communities (trees, fish). We find that DBS is largely inferior to ZSM and MPLN for both communities. The tree data do not allow discrimination between ZSM and MPLN, but for the fish data ZSM (neutral model) overwhelmingly outperforms MPLN (niche model), suggesting that dispersal plays a previously underestimated role in structuring tropical freshwater fish communities. We advocate this approach for identifying the relative importance of dispersal and niche‐partitioning in determining diversity of different ecological groups of species under different environmental conditions.     

Optimal design of experiments with anticipated pattern of missing observations

We propose a general method of designing an experiment when there are potentially failing trials. We use polynomial models and the Michaelis-Menten model as examples and construct different types of optimal designs under a broad class of response probability functions. We show that the usual optimal designs, that assume all observations are available at the end of the experiment, can be quite inefficient if the anticipated missingness pattern is not accounted for at the design stage. We also investigate robustness properties of the proposed designs to specification of their nominal values and the response probability functions.     

Neutral Models with Generalised Speciation

Hubbell’s neutral theory claims that ecological patterns such as species abundance distributions can be explained by a stochastic model based on simple assumptions. One of these assumptions, the point mutation assumption, states that every individual has the same probability to speciate. Etienne et al. have argued that other assumptions on the speciation process could be more realistic, for example, that every species has the same probability to speciate (Etienne, et al. in Oikos 116:241–258, 2007). They introduced a number of neutral community models with a different speciation process, and conjectured formulas for their stationary species abundance distribution. Here we study a generalised neutral community model, encompassing these modified models, and derive its stationary distribution, thus proving the conjectured formulas.     

The coherence problem with the Unified Neutral Theory of Biodiversity

The Unified Neutral Theory of Biodiversity (UNTB), proposed as an alternative to niche theory, has been viewed as a theory that species coexist without niche differences, without fitness differences, or with equal probability of success. Support is claimed when models lacking species differences predict highly aggregated metrics, such as species abundance distributions (SADs) or species area distributions (SARs). Here, I summarize why UNTB generates confusion, and is not actually relevant to niche theory (i.e. an explanation for why and how many species coexist). Equal probability is not a theory, but lack of one; it does not include or exclude any process relevant to coexistence of competitors. Models lacking explicit species can make useful predictions, but this does not support neutral theory. I provide s suggestions that could help reduce confusion generated by the debate.     

Analyzing tropical forest tree species abundance distributions using a nonneutral model and through approximate Bayesian inference

The neutral theory of biodiversity challenges the classical niche-based view of ecological communities, where species attributes and environmental conditions jointly determine community composition. Functional equivalence among species, as assumed by neutral ecological theory, has been recurrently falsified, yet many patterns of tropical tree communities appear consistent with neutral predictions. This may mean that neutral theory is a good first-approximation theory or that species abundance data sets contain too little information to reject neutrality. Here we present a simple test of neutrality based on species abundance distributions in ecological communities. Based on this test, we show that deviations from neutrality are more frequent than previously thought in tropical forest trees, especially at small spatial scales. We then develop a nonneutral model that generalizes Hubbell's dispersal-limited neutral model in a simple way by including one additional parameter of frequency dependence. We also develop a statistical method to infer the parameters of this model from empirical data by approximate Bayesian computation. In more than half of the permanent tree plots, we show that our new model fits the data better than does the neutral model. Finally, we discuss whether observed deviations from neutrality may be interpreted as the signature of environmental filtering on tropical tree species abundance distributions.     

GENE GENEALOGIES WITHIN THE ORGANISMAL PEDIGREES OF RANDOM-MATING POPULATIONS

Using computer simulations, we generated and analyzed genetic distances among selectively neutral haplotypes transmitted through gene genealogies with random-mating organismal pedigrees. Constraints and possible biases on haplotype distances due to correlated ancestry were evaluated by comparing observed distributions of distances to those predicted from an inbreeding theory that assumes independence among haplotype pairs. Results suggest that: 1) mean time to common ancestry of neutral haplotypes can be a reasonably good predictor of evolutionary effective population size; 2) the nonindependence of haplotype paths of descent within a given gene genealogy typically produces significant departures from the theoretical probability distributions of haplotype distances; 3) frequency distributions of distances between haplotypes drawn from “replicate” organismal pedigrees or from multiple unlinked loci within an organismal pedigree exhibit very close agreement with the theory for independent haplotypes. These results are relevant to interpretations of current molecular data on genetic distances among nonrecombining haplotypes at either nuclear or cytoplasmic loci.     

Estimating the distribution of selection coefficients from phylogenetic data using sitewise mutation-selection models

Estimation of the distribution of selection coefficients of mutations is a long-standing issue in molecular evolution. In addition to population-based methods, the distribution can be estimated from DNA sequence data by phylogenetic-based models. Previous models have generally found unimodal distributions where the probability mass is concentrated between mildly deleterious and nearly neutral mutations. Here we use a sitewise mutation-selection phylogenetic model to estimate the distribution of selection coefficients among novel and fixed mutations (substitutions) in a data set of 244 mammalian mitochondrial genomes and a set of 401 PB2 proteins from influenza. We find a bimodal distribution of selection coefficients for novel mutations in both the mitochondrial data set and for the influenza protein evolving in its natural reservoir, birds. Most of the mutations are strongly deleterious with the rest of the probability mass concentrated around mildly deleterious to neutral mutations. The distribution of the coefficients among substitutions is unimodal and symmetrical around nearly neutral substitutions for both data sets at adaptive equilibrium. About 0.5% of the nonsynonymous mutations and 14% of the nonsynonymous substitutions in the mitochondrial proteins are advantageous, with 0.5% and 24% observed for the influenza protein. Following a host shift of influenza from birds to humans, however, we find among novel mutations in PB2 a trimodal distribution with a small mode of advantageous mutations.     

Parameter-free testing of the shape of a probability distribution

The Kolmogorov-Smirnov test determines the consistency of empirical data with a particular probability distribution. Often, parameters in the distribution are unknown, and have to be estimated from the data. In this case, the Kolmogorov-Smirnov test depends on the form of the particular probability distribution under consideration, even when the estimated parameter-values are used within the distribution. In the present work, we address a less specific problem: to determine the consistency of data with a given functional form of a probability distribution (for example the normal distribution), without enquiring into values of unknown parameters in the distribution. For a wide class of distributions, we present a direct method for determining whether empirical data are consistent with a given functional form of the probability distribution. This utilizes a transformation of the data. If the data are from the class of distributions considered here, the transformation leads to an empirical distribution with no unknown parameters, and hence is susceptible to a standard Kolmogorov-Smirnov test. We give some general analytical results for some of the distributions from the class of distributions considered here. The significance level and power of the tests introduced in this work are estimated from simulations. Some biological applications of the method are given.     

On the conceptual basis of the self-thinning rule

We show a widely accepted proof of the self-thinning rule offered by Enquist et al. to be mathematically incomplete, as it does not identify the plant mass distributions that satisfy a condition implicitly used in the proof. We propose a method to guide the search for such mass distributions, based on a requirement of maximum mass diversity under the appropriate constraints. This generic method allows construction of a probability density that incorporates the available information on a given stochastic variable, and we illustrate its use through the calculation of a continuous mass distribution for the self-thinning rule that satisfies the implicit condition mentioned above. We suggest a biological justification of maximum mass diversity, as a corollary to the random and unbiased nature of the source of diversity in Darwin's principle.     

Ensemble-Biased Metadynamics: A Molecular Simulation Method to Sample Experimental Distributions

We introduce an enhanced-sampling method for molecular dynamics (MD) simulations referred to as ensemble-biased metadynamics (EBMetaD). The method biases a conventional MD simulation to sample a molecular ensemble that is consistent with one or more probability distributions known a priori, e.g., experimental intramolecular distance distributions obtained by double electron-electron resonance or other spectroscopic techniques. To this end, EBMetaD adds an adaptive biasing potential throughout the simulation that discourages sampling of configurations inconsistent with the target probability distributions. The bias introduced is the minimum necessary to fulfill the target distributions, i.e., EBMetaD satisfies the maximum-entropy principle. Unlike other methods, EBMetaD does not require multiple simulation replicas or the introduction of Lagrange multipliers, and is therefore computationally efficient and straightforward in practice. We demonstrate the performance and accuracy of the method for a model system as well as for spin-labeled T4 lysozyme in explicit water, and show how EBMetaD reproduces three double electron-electron resonance distance distributions concurrently within a few tens of nanoseconds of simulation time. EBMetaD is integrated in the open-source PLUMED plug-in (www.plumed-code.org), and can be therefore readily used with multiple MD engines.     

The impact of species-neutral stage structure on macroecological patterns

Despite its radical assumption of ecological equivalence between species, neutral biodiversity theory can often provide good fits to species abundance distributions observed in nature. Major criticisms of neutral theory have focused on interspecific differences, which are in conflict with ecological equivalence. However, neutrality in nature is also broken by differences between conspecific individuals at different life stages, which in many communities may vastly exceed interspecific differences between individuals at similar stages. These within-species asymmetries have not been fully explored in species-neutral models, and it is not known whether demographic stage structure affects macroecological patterns in neutral theory. Here, we present a two-stage neutral model where fecundity and mortality change as an individual transitions from one stage to the other. We explore several qualitatively different scenarios, and compare numerically obtained species abundance distributions to the predictions of unstructured neutral theory. We find that abundance distributions are generally robust to this kind of stage structure, but significant departures from unstructured predictions occur if adults have sufficiently low fecundity and mortality. In addition, we show that the cumulative number of births per species, which is distributed as a power law with a 3/2 exponent, is invariant even when the abundance distribution departs from unstructured model predictions. Our findings potentially explain power law-like abundance distributions in organisms with strong demographic structure, such as eusocial insects and humans, and partially rehabilitate species abundance distributions from past criticisms as to their inability to distinguish between biological mechanisms.