Expected Shannon Entropy and Shannon Differentiation between Subpopulations for Neutral Genes under the Finite Island Model

Modelling the structure and evolution of cultural information as quasispecies

We present a novel mode of cultural evolution whereby some forms of transmission may be modelled as quasispecies. The model incorporates the effect of high rates of error in certain forms of communication; while also building on the structural similarities between biological molecules and written language. Firstly, both written language and key biological molecules, such as RNA and proteins, are modular. Within these molecules, structural domains may be recombined, while retaining their function. Likewise, sentences are structured as combinations of clauses, in which each clause contains a domain of information. The clausal structure permits the recombination of information to adopt different meanings, while allowing each unit to retain its identity. Secondly, by virtue of intrinsically-high error rates, we show that some, but not all, aspects of communicated culture information exists as rapidly evolving clouds within the population. These clouds of cultural information behave as quasispecies, which we model with varying mutation rates and suitable selection coefficients. We then integrate these ideas with the application of Shannon Diversity Index to produce a more holistic view of culture that is centred on the evolution of its information. Re-imagining culture, as evolving clouds of information, unifies the mode in which information is stored culturally and biologically, and opens up new avenues of comparative analysis.

A Comparison of Entropic Diversity and Variance in the Study of Population Structure

AMOVA is a widely used approach that focuses on variance within and among strata to study the hierarchical genetic structure of populations. The recently developed Shannon Informational Diversity Translation Analysis (SIDTA) instead tackles exploration of hierarchical genetic structure using entropic allelic diversity. A mix of artificial and natural population data sets (including allopolyploids) is used to compare the performance of SIDTA (a 'q = 1' diversity measure) vs. AMOVA (a 'q = 2' measure) under different conditions. An additive allelic differentiation index based on entropic allelic diversity measuring the mean difference among populations (Ω_AP) was developed to facilitate the comparison of SIDTA with AMOVA. These analyses show that the genetic population structure seen by AMOVA is notably different in many ways from that provided by SIDTA, and the extent of this difference is greatly affected by the stability of the markers employed. Negative among group values are lacking with SIDTA but occur with AMOVA, especially with allopolyploids. To provide more focus on measuring allelic differentiation among populations, additional measures were also tested including Bray-Curtis Genetic Differentiation (BCGD) and several expected heterozygosity-based indices (e.g., G_ST, G″_ST, Jost's D, and D_EST). Corrections, such as almost unbiased estimators, that were designed to work with heterozygosity-based fixation indices (e.g., F_ST, G_ST) are problematic when applied to differentiation indices (eg., D_EST, G″_ST, G'_STH).

Robustness and predictability of evolution in bottlenecked populations

Deterministic and stochastic evolutionary processes drive adaptation in natural populations. The strength of each component process is determined by the population size: deterministic components prevail in very large populations, while stochastic components are the driving mechanisms in small ones. Many natural populations, however, experience intermittent periods of growth, moving through states in which either stochastic or deterministic processes prevail. This growth is often countered by population bottlenecks, which abound in both natural and laboratory populations. Here we investigate how population bottlenecks shape the process of adaptation. We demonstrate that adaptive trajectories in populations experiencing regular bottlenecks can be naturally scaled in time units of generations; with this scaling the time courses of adaptation, fitness variance, and genetic diversity all become relatively insensitive to the timing of population bottlenecks, provided the bottleneck size exceeds a few thousand individuals. We also include analyses at the genotype level to investigate the impact of population bottlenecks on the predictability and distribution of evolutionary pathways. Irrespective of the timing of population bottlenecks, we find that predictability increases with population size. We also find that predictability of the adaptive pathways increases in increasingly rugged fitness landscapes. Overall, our work reveals that both the adaptation rate and the predictability of evolutionary trajectories are relatively robust to population bottlenecks.

Information Entropy as a Reliable Measure of Nanoparticle Dispersity

Nanoparticle size impacts properties vital to applications ranging from drug delivery to diagnostics and catalysis. As such, evaluating nanoparticle size dispersity is of fundamental importance. Conventional approaches, such as standard deviation, usually require the nanoparticle population to follow a known distribution and are ill-equipped to deal with highly poly- or heterodisperse populations. Herein, we propose the use of information entropy as an alternative and assumption-free method for describing nanoparticle size distributions. This measure works equally well for mono-, poly-, and heterodisperse populations and represents an unbiased route to evaluation and optimization of nanoparticle synthesis. We provide intuitive software tools for analysis and supply guidelines for interpretation with respect to known standards.

The urinary microbiome shows different bacterial genera in renal transplant recipients and non-transplant patients at time of acute kidney injury - a pilot study

Background

In the past urine was considered sterile. Through the introduction of next generation sequencing, it has become clear that a urinary microbiome exists. Acute kidney injury (AKI) represents a major threat to kidney transplant recipients. Remarkable changes in the urinary metabolome occur during AKI, which may influence the urinary microbiome. To our knowledge, this is the first study that examines the urinary microbiome in renal transplant recipients (RTX) and non-transplant recipients (nRTX) at time of AKI.

Methods

In this cross-sectional pilot-study the urinary microbiome of 21 RTX and 9 nRTX with AKI was examined. Clean catch morning urine samples were obtained from all patients on the first day of AKI diagnosis. AKI was defined according to KDIGO guidelines. Urinary microbiota and the urinary metabolome during AKI were assessed in one patient. 16S rRNA sequencing was performed. Sequences were processed using UPARSE-pipeline for operational taxonomic units (OTU) and taxon finding.

Results

We successfully extracted and sequenced bacterial DNA from 100% of the urine samples. All 30 patients revealed at least 106,138 reads. 319 OTU and 211 different genera were identified. The microbiotic diversity richness in the RTX group was no different from the nRTX group. Eighteen genera were solely present in nRTX and 7 in RTX.

Conclusions

The urinary microbiome at time of AKI showed different bacterial genera in RTX compared to nRTX. The nRTX group exhibited no different diversity to the RTX group. Irrespective of the status of a previous renal transplantation, the urinary microbiome comprised > 210 different genera. An intraindividual change in microbiota diversity and richness was observed in one study patient during recovery from AKI.

Increase in the genetic polymorphism of varicella-zoster virus after passaging in in vitro cell culture

Primary infections with the varicella-zoster virus (VZV) result in varicella, while latent reactivation leads to herpes zoster. Both varicella and zoster can be prevented by live attenuated vaccines. There have been reports suggesting that both clinical VZV strains and those in vaccine preparations are genetically polymorphic, containing mixtures of both wild-type and vaccine-type sequences at certain vaccine-specific sites. In this study, the genetic polymorphism of the VZV genome was examined by analyzing the frequencies of minor alleles at each nucleotide position. Next-generation sequencing of the clinical VZV strain YC02 passaged in an in vitro cell culture was used to identify genetically polymorphic sites (GPS), where the minor allele frequency (MAF) exceeded 5%. The number of GPS increased by 7.3-fold at high passages (p100) when compared to low passages (p17), although the average MAF remained similar. GPS were found in 6 open reading frames (ORFs) in p17, 35, and 54 ORFs in p60 and p100, respectively. GPS were found more frequently in the dispensable gene group than the essential gene group, but the average MAF was greater in the essential gene group. The most common two major/minor base pairs were A/g and T/c. GPS were found in all three passages at 16 positions, all located in the reiterated (R) region. The population diversity as measured by Shannon entropy increased in p60 and p100. However, the entropy remained unchanged in the R regions.

High-throughput sequencing of IgG B-cell receptors reveals frequent usage of the rearranged IGHV4-28/IGHJ4 gene in primary immune thrombocytopenia

Primary immune thrombocytopenia (ITP) is an acquired form of thrombocytopenia caused by IgG anti-platelet autoantibodies and represents an organ-specific autoimmune disorder. Although the glycoprotein (GP)IIb/IIIa and GPIb/IX have been shown to be targets for autoantibodies, the antigen specificity of autoantibodies is not fully elucidated. To identify the characteristics of IgG B-cell receptor (BCR) repertoires in ITP, we took advantage of adaptor-ligation PCR and high-throughput DNA sequencing methods for analyzing the clone-based repertoires of IgG-expressing peripheral blood B cells. A total of 2,009,943 in-frame and 315,469 unique reads for IGH (immunoglobulin heavy) were obtained from twenty blood samples. Comparison of the IGHV repertoires between patients and controls revealed an increased usage of IGHV4–28 in ITP patients. One hundred eighty-six distinct IGHV4–28-carrying sequences were identified in ITP patients and the majority of these clones used an IGHJ4 segment. The IGHV4–28/IGHJ4-carrying B-cell clones were found in all ITP patients. Oligoclonal expansions of IGHV4–28/IGHJ4-carrying B cells were accompanied by multiple related clones with single amino substitution in the CDR3 region suggesting somatic hypermutation. Taken together, the expansion of IGHV4–28/IGHJ4-carrying IgG-expressing B cells in ITP may be the result of certain antigenic pressure and may provide a clue for the immune pathophysiology of ITP.

Allele Frequency Difference AFD⁻An Intuitive Alternative to FST for Quantifying Genetic Population Differentiation

Measuring the magnitude of differentiation between populations based on genetic markers is commonplace in ecology, evolution, and conservation biology. The predominant differentiation metric used for this purpose is F_ST. Based on a qualitative survey, numerical analyses, simulations, and empirical data, I here argue that F_ST does not express the relationship to allele frequency differentiation between populations generally considered interpretable and desirable by researchers. In particular, F_ST (1) has low sensitivity when population differentiation is weak, (2) is contingent on the minor allele frequency across the populations, (3) can be strongly affected by asymmetry in sample sizes, and (4) can differ greatly among the available estimators. Together, these features can complicate pattern recognition and interpretation in population genetic and genomic analysis, as illustrated by empirical examples, and overall compromise the comparability of population differentiation among markers and study systems. I argue that a simple differentiation metric displaying intuitive properties, the absolute allele frequency difference AFD, provides a valuable alternative to F_ST. I provide a general definition of AFD applicable to both bi- and multi-allelic markers and conclude by making recommendations on the sample sizes needed to achieve robust differentiation estimates using AFD.

Genetic Diversity of Verticillium dahliae Populations From Olive and Potato in Lebanon

Verticillium dahliae is widely distributed in potato and olive fields in Lebanon, causing serious economic losses. However, little is known about the inoculum source, population structure, and genetic diversity of the pathogen or the mechanisms of dissemination within Lebanon. To understand the population structure, a total of 203 isolates sampled from olive (n = 78) and potato (n = 125) were characterized for species, mating type, and race, and the genetic relationships were delineated using 13 microsatellite markers. All isolates except one from potato were V. dahliae, with 55.1 and 12.1% race 1, and 43.6 and 83.1% race 2 in olive and potato, respectively. The genetic structure of the studied population was best described by two large and two small clusters. Membership in the two large clusters was determined by the presence or absence of the effector gene Ave1. Furthermore, genetic structure was moderately associated with the host of origin but was weakly associated with the geographic origin. All but four isolates represented by three multilocus haploid genotypes were MAT1-2. This study identified a clear lack of gene flow between virulence genotypes of V. dahliae despite the proximity of these cropping systems and the wide distribution of genetic diversity among hosts and geographic regions in Lebanon.

Automatic anesthesia depth staging using entropy measures and relative power of electroencephalogram frequency bands

Many of the surgeries performed under general anesthesia are aided by electroencephalogram (EEG) monitoring. With increased focus on detecting the anesthesia states of patients in the course of surgery, more attention has been paid to analyzing the power spectra and entropy measures of EEG signal during anesthesia. In this paper, by using the relative power of EEG frequency bands and the EEG entropy measures, a new method for detecting the depth of anesthesia states has been presented based on the least squares support vector machine (LS-SVM) classifiers. EEG signals were recorded from 20 patients before, during and after general anesthesia in the operating room at a sampling rate of 200 Hz. Then, 12 features were extracted from each EEG segment, 10 s in length, which are used for anesthesia state monitoring. No significant difference was observed (p > 0.05) between these features and the bispectral index (BIS), which is the commonly used measure of anesthetic effect. The used LS-SVM classifier based method is able to identify the anesthesia states with an accuracy of 80% with reference to the BIS index. Since the underlying equation of the utilized LS-SVM is linear, the computational time of the algorithm is not significant and therefore it can be used for online application in operation rooms.

Entropy, or Information, Unifies Ecology and Evolution and Beyond

This article discusses how entropy/information methods are well-suited to analyzing and forecasting the four processes of innovation, transmission, movement, and adaptation, which are the common basis to ecology and evolution. Macroecologists study assemblages of differing species, whereas micro-evolutionary biologists study variants of heritable information within species, such as DNA and epigenetic modifications. These two different modes of variation are both driven by the same four basic processes, but approaches to these processes sometimes differ considerably. For example, macroecology often documents patterns without modeling underlying processes, with some notable exceptions. On the other hand, evolutionary biologists have a long history of deriving and testing mathematical genetic forecasts, previously focusing on entropies such as heterozygosity. Macroecology calls this Gini-Simpson, and has borrowed the genetic predictions, but sometimes this measure has shortcomings. Therefore it is important to note that predictive equations have now been derived for molecular diversity based on Shannon entropy and mutual information. As a result, we can now forecast all major types of entropy/information, creating a general predictive approach for the four basic processes in ecology and evolution. Additionally, the use of these methods will allow seamless integration with other studies such as the physical environment, and may even extend to assisting with evolutionary algorithms.

Diversity from genes to ecosystems: A unifying framework to study variation across biological metrics and scales

Biological diversity is a key concept in the life sciences and plays a fundamental role in many ecological and evolutionary processes. Although biodiversity is inherently a hierarchical concept covering different levels of organization (genes, population, species, ecological communities and ecosystems), a diversity index that behaves consistently across these different levels has so far been lacking, hindering the development of truly integrative biodiversity studies. To fill this important knowledge gap, we present a unifying framework for the measurement of biodiversity across hierarchical levels of organization. Our weighted, information-based decomposition framework is based on a Hill number of order q = 1, which weights all elements in proportion to their frequency and leads to diversity measures based on Shannon's entropy. We investigated the numerical behaviour of our approach with simulations and showed that it can accurately describe complex spatial hierarchical structures. To demonstrate the intuitive and straightforward interpretation of our diversity measures in terms of effective number of components (alleles, species, etc.), we applied the framework to a real data set on coral reef biodiversity. We expect our framework will have multiple applications covering the fields of conservation biology, community genetics and eco-evolutionary dynamics.

Differentiation measures for conservation genetics

We compare the two main classes of measures of population structure in genetics: (i) fixation measures such as FST,GST, and θ and (ii) allelic differentiation measures such as Jost's D and entropy differentiation. These two groups of measures quantify complementary aspects of population structure, which have no necessary relationship with each other. We focus especially on empirical aspects of population structure relevant to conservation analyses. At the empirical level, the first set of measures quantify nearness to fixation, while the second set of measures quantify relative degree of allelic differentiation. The two sets of measures do not compete with each other. Fixation measures are often misinterpreted as measures of allelic differentiation in conservation applications; we give examples and theoretical explanations showing why this interpretation can mislead. This misinterpretation has led to the mistaken belief that the absolute number of migrants determines allelic differentiation between demes when mutation rate is low; we show that in the finite island model, the absolute number of migrants determines nearness to fixation, not allelic differentiation. We show that a different quantity, the factor that controls Jost's D, is a good predictor of the evolution of the actual genetic divergence between demes at equilibrium in this model. We also show that when conservation decisions require judgments about differences in genetic composition between demes, allelic differentiation measures should be used instead of fixation measures. Allelic differentiation of fast-mutating markers can be used to rank pairs or sets of demes according to their differentiation, but the allelic differentiation at coding loci of interest should be directly measured in order to judge its actual magnitude at these loci.

Information Theory Broadens the Spectrum of Molecular Ecology and Evolution

Information or entropy analysis of diversity is used extensively in community ecology, and has recently been exploited for prediction and analysis in molecular ecology and evolution. Information measures belong to a spectrum (or q profile) of measures whose contrasting properties provide a rich summary of diversity, including allelic richness (q=0), Shannon information (q=1), and heterozygosity (q=2). We present the merits of information measures for describing and forecasting molecular variation within and among groups, comparing forecasts with data, and evaluating underlying processes such as dispersal. Importantly, information measures directly link causal processes and divergence outcomes, have straightforward relationship to allele frequency differences (including monotonicity that q=2 lacks), and show additivity across hierarchical layers such as ecology, behaviour, cellular processes, and nongenetic inheritance.

Genes are information, so information theory is coming to the aid of evolutionary biology

Speciation is central to evolutionary biology, and to elucidate it, we need to catch the early genetic changes that set nascent taxa on their path to species status (Via 2009). That challenge is difficult, of course, for two chief reasons: (i) serendipity is required to catch speciation in the act; and (ii) after a short time span with lingering gene flow, differentiation may be low and/or embodied only in rare alleles that are difficult to sample. In this issue of Molecular Ecology Resources, Smouse et al. (2015) have noted that optimal assessment of differentiation within and between nascent species should be robust to these challenges, and they identified a measure based on Shannon's information theory that has many advantages for this and numerous other tasks. The Shannon measure exhibits complete additivity of information at different levels of subdivision. Of all the family of diversity measures ('0' or allele counts, '1' or Shannon, '2' or heterozygosity, F(ST) and related metrics) Shannon's measure comes closest to weighting alleles by their frequencies. For the Shannon measure, rare alleles that represent early signals of nascent speciation are neither down-weighted to the point of irrelevance, as for level 2 measures, nor up-weighted to overpowering importance, as for level 0 measures (Chao et al. 2010, )2015. Shannon measures have a long history in population genetics, dating back to Shannon's PhD thesis in 1940 (Crow 2001), but have received only sporadic attention, until a resurgence of interest in the last ten years, as reviewed briefly by Smouse et al. (2015).

Integrated network-diversity analyses suggest suppressive effect of Hodgkin's lymphoma and slightly relieving effect of chemotherapy on human milk microbiome

We aim to investigate the effects of Hodgkin’s lymphoma and the chemotherapy for treating the disease on the human milk microbiome through integrated network and community diversity analyses. Our analyses suggest that Hodgkin’s lymphoma seems to have a suppressing effect on the milk microbiome by lowering the milk microbial community diversity, as measured by the Hill numbers profiles. Although the diversity analysis did not reveal an effect of chemotherapy on community diversity, bacterial species interaction network analysis shows that chemotherapy may help to slightly restore the milk microbiome impacted by Hodgkin’s lymphoma through its influence on the interactions among species (or OTUs). We further constructed diversity-metabolites network, which suggests that the milk microbial diversity is positively correlated with some beneficial milk metabolites such as DHA (DocosaHexaenoic Acid), and that the diversity is negatively correlated with some potentially harmful metabolites such as Butanal. We hence postulate that higher milk microbial diversity should be a signature of healthy mothers and beneficial to infants. Finally, we constructed metabolites OTU correlation networks, from which we identified some special OTUs. These OTUs deserve further investigations given their apparent involvements in regulating the levels of critical milk metabolites such as DHA, Inositol and Butanal.

Identification and functional analysis of essential, conserved, housekeeping and duplicated genes

Gene conservation, duplication and constitutive expression are intricately linked and strong predictors of essentiality. Here, we introduce metrics based on diversity indices to measure gene conservation, duplication and constitutive expression and validate them by measuring their performance in prediction of essential genes. Conservation and duplication were measured using the diversity indices on the bit score profile of Escherichia coli K12 orthologues, across the genomes, and paralogues, within the genome respectively. Constitutive expression was measured using expression diversity of E. coli K12 genes across different conditions. In addition, we developed a systematic method for enrichment analysis of gene-sets in a given ranked list of genes. The method was used to identify genome-wide functions of essential, conserved, constitutively expressed and duplicated genes. Furthermore, we also ranked various operons, complexes and pathways according to their essentiality, conservation, constitutive expression and duplication.

Mathematical model for adaptive evolution of populations based on a complex domain

A mutation is ultimately essential for adaptive evolution in all populations. It arises all the time, but is mostly fixed by enzymes. Further, most do consider that the evolution mechanism is by a natural assortment of variations in organisms in line for random variations in their DNA, and the suggestions for this are overwhelming. The altering of the construction of a gene, causing a different form that may be communicated to succeeding generations, produced by the modification of single base units in DNA, or the deletion, insertion, or rearrangement of larger units of chromosomes or genes. This altering is called a mutation. In this paper, a mathematical model is introduced to this reality. The model describes the time and space for the evolution. The tool is based on a complex domain for the space. We show that the evolution is distributed with the hypergeometric function. The Boundedness of the evolution is imposed by utilizing the Koebe function.