Asymmetrical Damage Partitioning in Bacteria: A Model for the Evolution of Stochasticity,Determinism, and Genetic Assimilation

Non-genetic phenotypic variation is common in biological organisms. The variation is potentially beneficial if the environment is changing. If the benefit is large, selection can favor the evolution of genetic assimilation, the process by which the expression of a trait is transferred from environmental to genetic control. Genetic assimilation is an important evolutionary transition, but it is poorly understood because the fitness costs and benefits of variation are often unknown. Here we show that the partitioning of damage by a mother bacterium to its two daughters can evolve through genetic assimilation. Bacterial phenotypes are also highly variable. Because gene-regulating elements can have low copy numbers, the variation is attributed to stochastic sampling. Extant Escherichia coli partition asymmetrically and deterministically more damage to the old daughter, the one receiving the mother’s old pole. By modeling in silico damage partitioning in a population, we show that deterministic asymmetry is advantageous because it increases fitness variance and hence the efficiency of natural selection. However, we find that symmetrical but stochastic partitioning can be similarly beneficial. To examine why bacteria evolved deterministic asymmetry, we modeled the effect of damage anchored to the mother’s old pole. While anchored damage strengthens selection for asymmetry by creating additional fitness variance, it has the opposite effect on symmetry. The difference results because anchored damage reinforces the polarization of partitioning in asymmetric bacteria. In symmetric bacteria, it dilutes the polarization. Thus, stochasticity alone may have protected early bacteria from damage, but deterministic asymmetry has evolved to be equally important in extant bacteria. We estimate that 47% of damage partitioning is deterministic in E. coli. We suggest that the evolution of deterministic asymmetry from stochasticity offers an example of Waddington’s genetic assimilation. Our model is able to quantify the evolution of the assimilation because it characterizes the fitness consequences of variation.     

Dimensionality reduction of longitudinal ’omics data using modern tensor factorizations

Longitudinal ’omics analytical methods are extensively used in the evolving field of precision medicine, by enabling ‘big data’ recording and high-resolution interpretation of complex datasets, driven by individual variations in response to perturbations such as disease pathogenesis, medical treatment or changes in lifestyle. However, inherent technical limitations in biomedical studies often result in the generation of feature-rich and sample-limited datasets. Analyzing such data using conventional modalities often proves to be challenging since the repeated, high-dimensional measurements overload the outlook with inconsequential variations that must be filtered from the data in order to find the true, biologically relevant signal. Tensor methods for the analysis and meaningful representation of multiway data may prove useful to the biological research community by their advertised ability to tackle this challenge. In this study, we present tcam—a new unsupervised tensor factorization method for the analysis of multiway data. Building on top of cutting-edge developments in the field of tensor-tensor algebra, we characterize the unique mathematical properties of our method, namely, 1) preservation of geometric and statistical traits of the data, which enable uncovering information beyond the inter-individual variation that often takes over the focus, especially in human studies. 2) Natural and straightforward out-of-sample extension, making tcam amenable for integration in machine learning workflows. A series of re-analyses of real-world, human experimental datasets showcase these theoretical properties, while providing empirical confirmation of tcam’s utility in the analysis of longitudinal ’omics data.     

Intrinsic and realized generation intervals in infectious-disease transmission

The generation interval is the interval between the time when an individual is infected by an infector and the time when this infector was infected. Its distribution underpins estimates of the reproductive number and hence informs public health strategies. Empirical generation-interval distributions are often derived from contact-tracing data. But linking observed generation intervals to the underlying generation interval required for modelling purposes is surprisingly not straightforward, and misspecifications can lead to incorrect estimates of the reproductive number, with the potential to misguide interventions to stop or slow an epidemic. Here, we clarify the theoretical framework for three conceptually different generation-interval distributions: the ‘intrinsic’ one typically used in mathematical models and the ‘forward’ and ‘backward’ ones typically observed from contact-tracing data, looking, respectively, forward or backward in time. We explain how the relationship between these distributions changes as an epidemic progresses and discuss how empirical generation-interval data can be used to correctly inform mathematical models.     

The Geographic Distribution of a Tropical Montane Bird Is Limited by a Tree: Acorn Woodpeckers (Melanerpes formicivorus) and Colombian Oaks (Quercus humboldtii) in the Northern Andes

Species distributions are limited by a complex array of abiotic and biotic factors. In general, abiotic (climatic) factors are thought to explain species’ broad geographic distributions, while biotic factors regulate species’ abundance patterns at local scales. We used species distribution models to test the hypothesis that a biotic interaction with a tree, the Colombian oak (Quercus humboldtii), limits the broad-scale distribution of the Acorn Woodpecker (Melanerpes formicivorus) in the Northern Andes of South America. North American populations of Acorn Woodpeckers consume acorns from Quercus oaks and are limited by the presence of Quercus oaks. However, Acorn Woodpeckers in the Northern Andes seldom consume Colombian oak acorns (though may regularly drink sap from oak trees) and have been observed at sites without Colombian oaks, the sole species of Quercus found in South America. We found that climate-only models overpredicted Acorn Woodpecker distribution, suggesting that suitable abiotic conditions (e.g. in northern Ecuador) exist beyond the woodpecker’s southern range margin. In contrast, models that incorporate Colombian oak presence outperformed climate-only models and more accurately predicted the location of the Acorn Woodpecker’s southern range margin in southern Colombia. These findings support the hypothesis that a biotic interaction with Colombian oaks sets Acorn Woodpecker’s broad-scale geographic limit in South America, probably because Acorn Woodpeckers rely on Colombian oaks as a food resource (possibly for the oak’s sap rather than for acorns). Although empirical examples of particular plants limiting tropical birds’ distributions are scarce, we predict that similar biotic interactions may play an important role in structuring the geographic distributions of many species of tropical montane birds with specialized foraging behavior.     

Adaptive Lévy Processes and Area-Restricted Search in Human Foraging

A considerable amount of research has claimed that animals’ foraging behaviors display movement lengths with power-law distributed tails, characteristic of Lévy flights and Lévy walks. Though these claims have recently come into question, the proposal that many animals forage using Lévy processes nonetheless remains. A Lévy process does not consider when or where resources are encountered, and samples movement lengths independently of past experience. However, Lévy processes too have come into question based on the observation that in patchy resource environments resource-sensitive foraging strategies, like area-restricted search, perform better than Lévy flights yet can still generate heavy-tailed distributions of movement lengths. To investigate these questions further, we tracked humans as they searched for hidden resources in an open-field virtual environment, with either patchy or dispersed resource distributions. Supporting previous research, for both conditions logarithmic binning methods were consistent with Lévy flights and rank-frequency methods–comparing alternative distributions using maximum likelihood methods–showed the strongest support for bounded power-law distributions (truncated Lévy flights). However, goodness-of-fit tests found that even bounded power-law distributions only accurately characterized movement behavior for 4 (out of 32) participants. Moreover, paths in the patchy environment (but not the dispersed environment) showed a transition to intensive search following resource encounters, characteristic of area-restricted search. Transferring paths between environments revealed that paths generated in the patchy environment were adapted to that environment. Our results suggest that though power-law distributions do not accurately reflect human search, Lévy processes may still describe movement in dispersed environments, but not in patchy environments–where search was area-restricted. Furthermore, our results indicate that search strategies cannot be inferred without knowing how organisms respond to resources–as both patched and dispersed conditions led to similar Lévy-like movement distributions.     

A graphical simulation model of the entire DNA process associated with the analysis of short tandem repeat loci

The use of expert systems to interpret short tandem repeat DNA profiles in forensic, medical and ancient DNA applications is becoming increasingly prevalent as high-throughput analytical systems generate large amounts of data that are time-consuming to process. With special reference to low copy number (LCN) applications, we use a graphical model to simulate stochastic variation associated with the entire DNA process starting with extraction of sample, followed by the processing associated with the preparation of a PCR reaction mixture and PCR itself. Each part of the process is modelled with input efficiency parameters. Then, the key output parameters that define the characteristics of a DNA profile are derived, namely heterozygote balance (Hb) and the probability of allelic drop-out p(D). The model can be used to estimate the unknown efficiency parameters, such as π_extraction. ‘What-if’ scenarios can be used to improve and optimize the entire process, e.g. by increasing the aliquot forwarded to PCR, the improvement expected to a given DNA profile can be reliably predicted. We demonstrate that Hb and drop-out are mainly a function of stochastic effect of pre-PCR molecular selection. Whole genome amplification is unlikely to give any benefit over conventional PCR for LCN.     

Discriminating between Light- and Heavy-Tailed Distributions with Limit Theorem

In this paper we propose an algorithm to distinguish between light- and heavy-tailed probability laws underlying random datasets. The idea of the algorithm, which is visual and easy to implement, is to check whether the underlying law belongs to the domain of attraction of the Gaussian or non-Gaussian stable distribution by examining its rate of convergence. The method allows to discriminate between stable and various non-stable distributions. The test allows to differentiate between distributions, which appear the same according to standard Kolmogorov–Smirnov test. In particular, it helps to distinguish between stable and Student’s t probability laws as well as between the stable and tempered stable, the cases which are considered in the literature as very cumbersome. Finally, we illustrate the procedure on plasma data to identify cases with so-called L-H transition.     

Zipf’s Law: Balancing Signal Usage Cost and Communication Efficiency

We propose a model that explains the reliable emergence of power laws (e.g., Zipf’s law) during the development of different human languages. The model incorporates the principle of least effort in communications, minimizing a combination of the information-theoretic communication inefficiency and direct signal cost. We prove a general relationship, for all optimal languages, between the signal cost distribution and the resulting distribution of signals. Zipf’s law then emerges for logarithmic signal cost distributions, which is the cost distribution expected for words constructed from letters or phonemes.     

Spontaneous Facial Mimicry Is Enhanced by the Goal of Inferring Emotional States: Evidence for Moderation of “Automatic” Mimicry by Higher Cognitive Processes

A number of studies have shown that individuals often spontaneously mimic the facial expressions of others, a tendency known as facial mimicry. This tendency has generally been considered a reflex-like “automatic” response, but several recent studies have shown that the degree of mimicry may be moderated by contextual information. However, the cognitive and motivational factors underlying the contextual moderation of facial mimicry require further empirical investigation. In this study, we present evidence that the degree to which participants spontaneously mimic a target’s facial expressions depends on whether participants are motivated to infer the target’s emotional state. In the first study we show that facial mimicry, assessed by facial electromyography, occurs more frequently when participants are specifically instructed to infer a target’s emotional state than when given no instruction. In the second study, we replicate this effect using the Facial Action Coding System to show that participants are more likely to mimic facial expressions of emotion when they are asked to infer the target’s emotional state, rather than make inferences about a physical trait unrelated to emotion. These results provide convergent evidence that the explicit goal of understanding a target’s emotional state affects the degree of facial mimicry shown by the perceiver, suggesting moderation of reflex-like motor activities by higher cognitive processes.     

Dwell Time Distributions of the Molecular Motor Myosin V

The dwell times between two successive steps of the two-headed molecular motor myosin V are governed by non-exponential distributions. These distributions have been determined experimentally for various control parameters such as nucleotide concentrations and external load force. First, we use a simplified network representation to determine the dwell time distributions of myosin V, with the associated dynamics described by a Markov process on networks with absorbing boundaries. Our approach provides a direct relation between the motor’s chemical kinetics and its stepping properties. In the absence of an external load, the theoretical distributions quantitatively agree with experimental findings for various nucleotide concentrations. Second, using a more complex branched network, which includes ADP release from the leading head, we are able to elucidate the motor’s gating effect. This effect is caused by an asymmetry in the chemical properties of the leading and the trailing head of the motor molecule. In the case of an external load acting on the motor, the corresponding dwell time distributions reveal details about the motor’s backsteps.     

Two dominant forms of multisite similarity decline – Their origins and interpretation

The number of species shared by two or more sites is a fundamental measure of spatial variation in species composition. As more sites are included in the comparison of species composition, the average number of species shared across them declines, with a rate increasingly dependent on only the most widespread species. In over 80% of empirical communities, models of decline in shared species across multiple sites (multisite similarity decline) follow one of two distinct forms. An exponential form is assumed to reflect stochastic assembly and a power law form niche‐based sorting, yet these explanations are largely untested, and little is known of how the two forms arise in nature. Using simulations, we first show that the distribution of the most widespread species largely differentiates the two forms, with the power law increasingly favored where such species occupy more than ~75% of sites. We reasoned the less cosmopolitan distribution of widespread species within exponential communities would manifest as differences in community biodiversity properties, specifically more aggregated within‐species distributions, less even relative abundance distributions, and weaker between‐species spatial associations. We tested and largely confirmed these relationships using 80 empirical datasets, suggesting that the form of multisite similarity decline offers a basis to predict how landscape‐scale loss or gain of widespread species is reflected in different local‐scale community structures. Such understanding could, for example, be used to predict changes in local‐scale competitive interactions following shifts in widespread species'' distributions. We propose multiple explanations for the origin of exponential decline, including high among‐site abiotic variation, sampling of highly specialized (narrow niche width) taxa, and strong dispersal limitation. We recommend these are evaluated as alternative hypotheses to stochastic assembly.     

Effects of stochastic channel gating and distribution on the cardiac action potential

Ion channels exhibit stochastic conformational changes determining their gating behavior. In addition, the process of protein turnover leads to a natural variability of the number of membrane and gap junctional channels. Nevertheless, in computational models, these two aspects are scarcely considered and their impacts are largely unknown. We investigated the effects of stochastic current fluctuations and channel distributions on action potential duration (APD), intercellular conduction delays (ICDs) and conduction blocks using a modified ventricular cell model (Rudy et al.) with Markovian formulations of the principal ion currents (to simulate their stochastic open-close gating behavior) and with channel counts drawn from Poisson distributions (to simulate their natural variability). In single cells, APD variability (coefficient of variation: 1.6% at BCL=1000 ms) was essentially caused by stochastic channel gating of I_Ks, persistent I_Na and I_Ca,L. In cell strands, ICD variability induced by stochastic channel gating and Poissonian channel distributions was low under normal conditions. Nonetheless, at low intercellular coupling levels, Poissonian gap junctional channel distribution resulted in a large ICD variability (coefficient of variation >20%), highly heterogeneous conduction patterns and conduction blocks. Therefore, the stochastic behavior of current fluctuations and channel distributions can contribute to the heterogeneity of conduction patterns and to conduction block, as observed previously in experiments in cardiac tissue with altered intercellular coupling.     

The Measurement of the Effect on Citation Inequality of Differences in Citation Practices across Scientific Fields

This paper has two aims: (i) to introduce a novel method for measuring which part of overall citation inequality can be attributed to differences in citation practices across scientific fields, and (ii) to implement an empirical strategy for making meaningful comparisons between the number of citations received by articles in 22 broad fields. The number of citations received by any article is seen as a function of the article’s scientific influence, and the field to which it belongs. A key assumption is that articles in the same quantile of any field citation distribution have the same degree of citation impact in their respective field. Using a dataset of 4.4 million articles published in 1998–2003 with a five-year citation window, we estimate that differences in citation practices between the 22 fields account for 14% of overall citation inequality. Our empirical strategy is based on the strong similarities found in the behavior of citation distributions. We obtain three main results. Firstly, we estimate a set of average-based indicators, called exchange rates, to express the citations received by any article in a large interval in terms of the citations received in a reference situation. Secondly, using our exchange rates as normalization factors of the raw citation data reduces the effect of differences in citation practices to, approximately, 2% of overall citation inequality in the normalized citation distributions. Thirdly, we provide an empirical explanation of why the usual normalization procedure based on the fields’ mean citation rates is found to be equally successful.     

Virio- and Bacterioplankton Microscale Distributions at the Sediment-Water Interface

The marine sediment-water interface is an important location for microbially controlled nutrient and gas exchange processes. While microbial distributions on the sediment side of the interface are well established in many locations, the distributions of microbes on the water side of the interface are less well known. Here, we measured that distribution for marine virio- and bacterioplankton with a new two-dimensional technique. Our results revealed higher heterogeneity in sediment-water interface biomass distributions than previously reported with a greater than 45– and 2500-fold change cm⁻¹ found within bacterial and viral subpopulations compared to previous maxima of 1.5- and 1.4-fold cm⁻¹ in bacteria and viruses in the same environments. The 45-fold and 2500-fold changes were due to patches of elevated and patches of reduced viral and bacterial abundance. The bacterial and viral hotspots were found over single and multiple sample points and the two groups often coincided whilst the coldspots only occurred over single sample points and the bacterial and viral abundances showed no correlation. The total mean abundances of viruses strongly correlated with bacteria (r = 0.90, p<0.0001, n = 12) for all three microplates (n = 1350). Spatial autocorrelation analysis via Moran’s I and Geary’s C revealed non-random distributions in bacterial subpopulations and random distributions in viral subpopulations. The variable distributions of viral and bacterial abundance over centimetre-scale distances suggest that competition and the likelihood of viral infection are higher in the small volumes important for individual cell encounters than bulk measurements indicate. We conclude that large scale measurements are not an accurate measurement of the conditions under which microbial dynamics exist. The high variability we report indicates that few microbes experience the ‘average’ concentrations that are frequently measured.     

Weevil x Insecticide: Does ‘Personality’ Matter?

An insect’s behavior is the expression of its integrated physiology in response to external and internal stimuli, turning insect behavior into a potential determinant of insecticide exposure. Behavioral traits may therefore influence insecticide efficacy against insects, compromising the validity of standard bioassays of insecticide activity, which are fundamentally based on lethality alone. By extension, insect ‘personality’ (i.e., an individual’s integrated set of behavioral tendencies that is inferred from multiple empirical measures) may also be an important determinant of insecticide exposure and activity. This has yet to be considered because the behavioral studies involving insects and insecticides focus on populations rather than on individuals. Even among studies of animal ‘personality’, the relative contributions of individual and population variation are usually neglected. Here, we assessed behavioral traits (within the categories: activity, boldness/shyness, and exploration/avoidance) of individuals from 15 populations of the maize weevil (Sitophilus zeamais), an important stored-grain pest with serious problems of insecticide resistance, and correlated the behavioral responses with the activity of the insecticide deltamethrin. This analysis was performed at both the population and individual levels. There was significant variation in weevil ‘personality’ among individuals and populations, but variation among individuals within populations accounted for most of the observed variation (92.57%). This result emphasizes the importance of individual variation in behavioral and ‘personality’ studies. When the behavioral traits assessed were correlated with median lethal time (LT₅₀) at the population level and with the survival time under insecticide exposure, activity traits, particularly the distance walked, significantly increased survival time. Therefore, behavioral traits are important components of insecticide efficacy, and individual variation should be considered in such studies. This is so because population differences provided only crude approximation of the individual personality in a restrained experimental setting likely to restrict individual behavior favoring the transposition of the individual variation to the population.     

Moment closure approximations for stochastic kinetic models with rational rate laws

Stochastic models are often used when modelling chemical species that have low numbers of molecules. However, as these models become large, it can become computationally expensive to simulate even a single realisation of the system since even efficient simulation techniques have a high computational cost. One possible technique to approximate the stochastic system is moment closure. The moment closure approximation is used to provide analytic approximations to non-linear stochastic models. Until now, this approximation has only been applied to models with polynomial rate laws. In this paper we extend the moment closure method to cover models with rational rate laws.     

Curve Fitting of the Corporate Recovery Rates: The Comparison of Beta Distribution Estimation and Kernel Density Estimation

Recovery rate is essential to the estimation of the portfolio’s loss and economic capital. Neglecting the randomness of the distribution of recovery rate may underestimate the risk. The study introduces two kinds of models of distribution, Beta distribution estimation and kernel density distribution estimation, to simulate the distribution of recovery rates of corporate loans and bonds. As is known, models based on Beta distribution are common in daily usage, such as CreditMetrics by J.P. Morgan, Portfolio Manager by KMV and Losscalc by Moody’s. However, it has a fatal defect that it can’t fit the bimodal or multimodal distributions such as recovery rates of corporate loans and bonds as Moody’s new data show. In order to overcome this flaw, the kernel density estimation is introduced and we compare the simulation results by histogram, Beta distribution estimation and kernel density estimation to reach the conclusion that the Gaussian kernel density distribution really better imitates the distribution of the bimodal or multimodal data samples of corporate loans and bonds. Finally, a Chi-square test of the Gaussian kernel density estimation proves that it can fit the curve of recovery rates of loans and bonds. So using the kernel density distribution to precisely delineate the bimodal recovery rates of bonds is optimal in credit risk management.     

Gillespie eco‐evolutionary models (GEMs) reveal the role of heritable trait variation in eco‐evolutionary dynamics

Heritable trait variation is a central and necessary ingredient of evolution. Trait variation also directly affects ecological processes, generating a clear link between evolutionary and ecological dynamics. Despite the changes in variation that occur through selection, drift, mutation, and recombination, current eco‐evolutionary models usually fail to track how variation changes through time. Moreover, eco‐evolutionary models assume fitness functions for each trait and each ecological context, which often do not have empirical validation. We introduce a new type of model, Gillespie eco‐evolutionary models (GEMs), that resolves these concerns by tracking distributions of traits through time as eco‐evolutionary dynamics progress. This is done by allowing change to be driven by the direct fitness consequences of model parameters within the context of the underlying ecological model, without having to assume a particular fitness function. GEMs work by adding a trait distribution component to the standard Gillespie algorithm – an approach that models stochastic systems in nature that are typically approximated through ordinary differential equations. We illustrate GEMs with the Rosenzweig–MacArthur consumer–resource model. We show not only how heritable trait variation fuels trait evolution and influences eco‐evolutionary dynamics, but also how the erosion of variation through time may hinder eco‐evolutionary dynamics in the long run. GEMs can be developed for any parameter in any ordinary differential equation model and, furthermore, can enable modeling of multiple interacting traits at the same time. We expect GEMs will open the door to a new direction in eco‐evolutionary and evolutionary modeling by removing long‐standing modeling barriers, simplifying the link between traits, fitness, and dynamics, and expanding eco‐evolutionary treatment of a greater diversity of ecological interactions. These factors make GEMs much more than a modeling advance, but an important conceptual advance that bridges ecology and evolution through the central concept of heritable trait variation.