The Ingenuity of Bacterial Genomes.

The genomes of bacteria contain fewer genes and substantially less noncoding DNA than those of eukaryotes, and as a result, they have much less raw material to invent new traits. Yet, bacteria are vastly more taxonomically diverse, numerically abundant, and globally successful in colonizing new habitats compared to eukaryotes. Although bacterial genomes are generally considered to be optimized for efficient growth and rapid adaptation, nonadaptive processes have played a major role in shaping the size, contents, and compact organization of bacterial genomes and have allowed the establishment of deleterious traits that serve as the raw materials for genetic innovation.

Influence of selection on the probability of fixation at a locus with multiple alleles.

BACKGROUND: Genes exist in a population in a variety of forms (alleles), as a consequence of multiple mutation events that have arisen over the course of time. In this work we consider a locus that is subject to either multiplicative or additive selection, and has n alleles, where n can take the values 2, 3, 4, … . We focus on determining the probability of fixation of each of the n alleles. For n = 2 alleles, analytical results, that are 'exact', under the diffusion approximation, can be found for the fixation probability. However generally there are no equally exact results for n ≥ 3 alleles. In the absence of such exact results, we proceed by finding results for the fixation probability, under the diffusion approximation, as a power series in scaled strengths of selection such as R i , j = 2 N e ( s i - s j ) , where N e is the effective population size, while s i and s j are the selection coefficients associated with alleles i and j, respectively. RESULTS: We determined the fixation probability when all terms up to second order in the R i , j are kept. The truncation of the power series requires that the R i , j cannot be indefinitely large. For magnitudes of the R i , j up to a value of approximately 1, numerical evidence suggests that the results work well. Additionally, results given for the particular case of n = 3 alleles illustrate a general feature that holds for n ≥ 3 alleles, that the fixation probability of a particular allele depends on that allele's initial frequency, but generally, this fixation probability also depends on the initial frequencies of other alleles at the locus, as well as their selective effects. CONCLUSIONS: We have analytically exposed the leading way the probability of fixation, at a locus with multiple alleles, is affected by selection. This result may offer important insights into CDCV traits that have extreme phenotypic variance due to numerous, low-penetrance susceptibility alleles.

The evolutionary scaling of cellular traits imposed by the drift barrier.

Owing to internal homeostatic mechanisms, cellular traits may experience long periods of stable selective pressures, during which the stochastic forces of drift and mutation conspire to generate variation. However, even in the face of invariant selection, the drift barrier defined by the genetic effective population size, which is negatively associated with organism size, can have a substantial influence on the location and dispersion of the long-term steady-state distribution of mean phenotypes. In addition, for multilocus traits, the multiplicity of alternative, functionally equivalent states can draw mean phenotypes away from selective optima, even in the absence of mutation bias. Using a framework for traits with an additive genetic basis, it is shown that 1) optimal phenotypic states may be only rarely achieved; 2) gradients of mean phenotypes with respect to organism size (i.e., allometric relationships) are likely to be molded by differences in the power of random genetic drift across the tree of life; and 3) for any particular set of population-genetic conditions, significant variation in mean phenotypes may exist among lineages exposed to identical selection pressures. These results provide a potentially useful framework for understanding numerous aspects of cellular diversification and illustrate the risks of interpreting such variation in a purely adaptive framework.

Constructive Neutral Evolution 20 Years Later.

Evolution has led to a great diversity that ranges from elegant simplicity to ornate complexity. Many complex features are often assumed to be more functional or adaptive than their simpler alternatives. However, in 1999, Arlin Stolzfus published a paper in the Journal of Molecular Evolution that outlined a framework in which complexity can arise through a series of non-adaptive steps. He called this framework Constructive Neutral Evolution (CNE). Despite its two-decade-old roots, many evolutionary biologists still appear to be unaware of this explanatory framework for the origins of complexity. In this perspective piece, we explain the theory of CNE and how it changes the order of events in narratives that describe the evolution of complexity. We also provide an extensive list of cellular features that may have become more complex through CNE. We end by discussing strategies to determine whether complexity arose through neutral or adaptive processes.

A New Formulation of Random Genetic Drift and Its Application to the Evolution of Cell Populations.

Random genetic drift, or stochastic change in gene frequency, is a fundamental evolutionary force that is usually defined within the ideal Wright-Fisher (WF) population. However, as the theory is increasingly applied to populations that deviate strongly from the ideal model, a paradox of random drift has emerged. When drift is defined by the WF model, it becomes stronger as the population size, N, decreases. However, the intensity of competition decreases when N decreases and, hence, drift might become weaker. To resolve the paradox, we propose that random drift be defined by the variance of "individual output", V(k) [k being the progeny number of each individual with the mean of E(k)], rather than by the WF sampling. If the distribution of k is known for any population, its strength of drift relative to a WF population of the same size, N, can be calculated. Generally, E(k) and V(k) should be density dependent but their relationships are different with or without competition, leading to opposite predictions on the efficiency of random drift as N changes. We apply the "individual output" model to asexual cell populations that are either unregulated (such as tumors) or negatively density-dependent (e.g., bacteria). In such populations, the efficiency of drift could be as low as <10% of that in WF populations. Interestingly, when N is below the carrying capacity, random drift could in fact increase as N increases. Growing asexual populations, especially tumors, may therefore be genetically even more heterogeneous than the high diversity estimated by some conventional models.

Evolutionary meandering of intermolecular interactions along the drift barrier.

Many cellular functions depend on highly specific intermolecular interactions, for example transcription factors and their DNA binding sites, microRNAs and their RNA binding sites, the interfaces between heterodimeric protein molecules, the stems in RNA molecules, and kinases and their response regulators in signal-transduction systems. Despite the need for complementarity between interacting partners, such pairwise systems seem to be capable of high levels of evolutionary divergence, even when subject to strong selection. Such behavior is a consequence of the diminishing advantages of increasing binding affinity between partners, the multiplicity of evolutionary pathways between selectively equivalent alternatives, and the stochastic nature of evolutionary processes. Because mutation pressure toward reduced affinity conflicts with selective pressure for greater interaction, situations can arise in which the expected distribution of the degree of matching between interacting partners is bimodal, even in the face of constant selection. Although biomolecules with larger numbers of interacting partners are subject to increased levels of evolutionary conservation, their more numerous partners need not converge on a single sequence motif or be increasingly constrained in more complex systems. These results suggest that most phylogenetic differences in the sequences of binding interfaces are not the result of adaptive fine tuning but a simple consequence of random genetic drift.

Evolutionary control: Targeted change of allele frequencies in natural populations using externally directed evolution.

Random processes in biology, in particular random genetic drift, often make it difficult to predict the fate of a particular mutation in a population. Using principles of theoretical population genetics, we present a form of biological control that ensures a focal allele's frequency, at a given locus, achieves a prescribed probability distribution at a given time. This control is in the form of an additional evolutionary force that acts on a population. We provide the mathematical framework that determines the additional force. Our analysis indicates that generally the additional force depends on the frequency of the focal allele, and it may also depend on the time. We argue that translating this additional force into an externally controlled process, which has the possibility of being implemented in a number of different ways corresponding to selection, migration, mutation, or a combination of these, may provide a flexible instrument for targeted change of traits of interest in natural populations. This framework may be applied, or used as an informed form of guidance, in a variety of different biological scenarios including: yield and pesticide optimisation in crop production, biofermentation, the local regulation of human-associated natural populations, such as parasitic animals, or bacterial communities in hospitals.

Exact results for the probability and stochastic dynamics of fixation in the Wright-Fisher model.

In this work we consider fixation of an allele in a population. Fixation is key to understanding the way long-term evolutionary change occurs at the gene and molecular levels. Two basic aspects of fixation are: (i) the chance it occurs and (ii) the way the gene frequency progresses to fixation. We present exact results for both aspects of fixation for the Wright-Fisher model. We give the exact fixation probability for some different schemes of frequency-dependent selection. We also give the corresponding exact stochastic difference equation that generates frequency trajectories which ultimately fix. Exactness of the results means selection need not be weak. There are possible applications of this work to data analysis, modelling, and tests of approximations. The methodology employed illustrates that knowledge of the fixation probability, for all initial frequencies, fully characterises the dynamics of the Wright-Fisher model. The stochastic equations for fixing trajectories allow insight into the way fixation occurs. They provide the alternative picture that fixation is driven by the injection of one carrier of the fixing allele into the population each generation. The stochastic equations allow explicit calculation of some properties of fixing trajectories and their efficient simulation. The results are illustrated and tested with simulations.

Evolutionary cell biology: two origins, one objective.

All aspects of biological diversification ultimately trace to evolutionary modifications at the cellular level. This central role of cells frames the basic questions as to how cells work and how cells come to be the way they are. Although these two lines of inquiry lie respectively within the traditional provenance of cell biology and evolutionary biology, a comprehensive synthesis of evolutionary and cell-biological thinking is lacking. We define evolutionary cell biology as the fusion of these two eponymous fields with the theoretical and quantitative branches of biochemistry, biophysics, and population genetics. The key goals are to develop a mechanistic understanding of general evolutionary processes, while specifically infusing cell biology with an evolutionary perspective. The full development of this interdisciplinary field has the potential to solve numerous problems in diverse areas of biology, including the degree to which selection, effectively neutral processes, historical contingencies, and/or constraints at the chemical and biophysical levels dictate patterns of variation for intracellular features. These problems can now be examined at both the within- and among-species levels, with single-cell methodologies even allowing quantification of variation within genotypes. Some results from this emerging field have already had a substantial impact on cell biology, and future findings will significantly influence applications in agriculture, medicine, environmental science, and synthetic biology.

The evolution of recombination rates in finite populations during ecological speciation.

Recombination can impede ecological speciation with gene flow by mixing locally adapted genotypes with maladapted migrant genotypes from a divergent population. In such a scenario, suppression of recombination can be selectively favoured. However, in finite populations evolving under the influence of random genetic drift, recombination can also facilitate adaptation by reducing Hill-Robertson interference between loci under selection. In this case, increased recombination rates can be favoured. Although these two major effects on recombination have been studied individually, their joint effect on ecological speciation with gene flow remains unexplored. Using a mathematical model, we investigated the evolution of recombination rates in two finite populations that exchange migrants while adapting to contrasting environments. Our results indicate a two-step dynamic where increased recombination is first favoured (in response to the Hill-Robertson effect), and then disfavoured, as the cost of recombining locally with maladapted migrant genotypes increases over time (the maladaptive gene flow effect). In larger populations, a stronger initial benefit for recombination was observed, whereas high migration rates intensify the long-term cost of recombination. These dynamics may have important implications for our understanding of the conditions that facilitate incipient speciation with gene flow and the evolution of recombination in finite populations.

An informational transition in conditioned Markov chains: Applied to genetics and evolution.

In this work we assume that we have some knowledge about the state of a population at two known times, when the dynamics is governed by a Markov chain such as a Wright-Fisher model. Such knowledge could be obtained, for example, from observations made on ancient and contemporary DNA, or during laboratory experiments involving long term evolution. A natural assumption is that the behaviour of the population, between observations, is related to (or constrained by) what was actually observed. The present work shows that this assumption has limited validity. When the time interval between observations is larger than a characteristic value, which is a property of the population under consideration, there is a range of intermediate times where the behaviour of the population has reduced or no dependence on what was observed and an equilibrium-like distribution applies. Thus, for example, if the frequency of an allele is observed at two different times, then for a large enough time interval between observations, the population has reduced or no dependence on the two observed frequencies for a range of intermediate times. Given observations of a population at two times, we provide a general theoretical analysis of the behaviour of the population at all intermediate times, and determine an expression for the characteristic time interval, beyond which the observations do not constrain the population's behaviour over a range of intermediate times. The findings of this work relate to what can be meaningfully inferred about a population at intermediate times, given knowledge of terminal states.

Exact simulation of conditioned Wright-Fisher models.

Forward and backward simulations play an increasing role in population genetics, in particular when inferring the relative importance of evolutionary forces. It is therefore important to develop fast and accurate simulation methods for general population genetics models. Here we present an exact simulation method that generates trajectories of an allele׳s frequency in a finite population, as described by a general Wright-Fisher model. The method generates conditioned trajectories that start from a known frequency at a known time, and which achieve a specific final frequency at a known final time. The simulation method applies irrespective of the smallness of the probability of the transition between the initial and final states, because it is not based on rejection of trajectories. We illustrate the method on several different populations where a Wright-Fisher model (or related) applies, namely (i) a locus with 2 alleles, that is subject to selection and mutation; (ii) a locus with 3 alleles, that is subject to selection; (iii) a locus in a metapopulation consisting of two subpopulations of finite size, that are subject to selection and migration. The simulation method allows the generation of conditioned trajectories that can be used for the purposes of visualisation, the estimation of summary statistics, and the development/testing of new inferential methods. The simulated trajectories provide a very simple approach to estimating quantities that cannot easily be expressed in terms of the transition matrix, and can be applied to finite Markov chains other than the Wright-Fisher model.

Evolution of gene regulatory networks by means of selection and random genetic drift.

The evolution of a population by means of genetic drift and natural selection operating on a gene regulatory network (GRN) of an individual has not been scrutinized in depth. Thus, the relative importance of various evolutionary forces and processes on shaping genetic variability in GRNs is understudied. In this study, we implemented a simulation framework, called EvoNET, that simulates forward-in-time the evolution of GRNs in a population. The fitness effect of mutations is not constant, rather fitness of each individual is evaluated on the phenotypic level, by measuring its distance from an optimal phenotype. Each individual goes through a maturation period, where its GRN may reach an equilibrium, thus deciding its phenotype. Afterwards, individuals compete to produce the next generation. We examine properties of the GRN evolution, such as robustness against the deleterious effect of mutations and the role of genetic drift. We are able to confirm previous hypotheses regarding the effect of mutations and we provide new insights on the interplay between random genetic drift and natural selection.

Codon Usage Analysis Reveals Distinct Evolutionary Patterns and Host Adaptation Strategies in Duck Hepatitis Virus 1 (DHV-1) Phylogroups.

Duck hepatitis virus 1 (DHV-1) is a major threat to the global poultry industry, causing significant economic losses due to high mortality rates in young ducklings. To better understand the evolution and host adaptation strategies of DHV-1, we conducted a comprehensive codon usage analysis of DHV-1 genomes. Our phylogenetic analysis revealed three well-supported DHV-1 phylogroups (Ia, Ib, and II) with distinct genetic diversity patterns. Comparative analyses of the codon usage bias and dinucleotide abundance uncovered a strong preference for A/U-ended codons and a biased pattern of dinucleotide usage in the DHV-1 genome, with CG dinucleotides being extremely underrepresented. Effective number of codons (ENC) analysis indicated a low codon usage bias in the DHV-1 ORF sequences, suggesting adaptation to host codon usage preferences. PR2 bias, ENC plot, and neutrality analyses revealed that both mutation pressure and natural selection influence the codon usage patterns of DHV-1. Notably, the three DHV-1 phylogroups exhibited distinct evolutionary trends, with phylogroups Ia and Ib showing evidence of neutral evolution accompanied by selective pressure, while the phylogroup II evolution was primarily driven by random genetic drift. Comparative analysis of the codon usage indices (CAI, RCDI, and SiD) among the phylogroups highlighted significant differences between subgroups Ia and Ib, suggesting distinct evolutionary pressures or adaptations influencing their codon usage. These findings contribute to our understanding of DHV-1 evolution and host adaptation, with potential implications for the development of effective control measures and vaccines.

Information encoded in gene-frequency trajectories.

In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded within gene-frequency trajectories. We determine approximate, time-dependent, gene-frequency trajectory statistics, assuming additive selection. We use the probability of fixation to test and illustrate the approximation scheme introduced. For the case where the strength of selection and the effective population size have constant values, we show how a standard diffusion approximation result, for the probability of fixation, systematically emerges when increasing numbers of approximate trajectory statistics are taken into account. We then provide examples of how time-dependent parameters influence gene-frequency statistics.

The divergence of mean phenotypes under persistent directional selection.

Numerous organismal traits, particularly at the cellular level, are likely to be under persistent directional selection across phylogenetic lineages. Unless all mutations affecting such traits have large enough effects to be efficiently selected in all species, gradients in mean phenotypes are expected to arise as a consequence of differences in the power of random genetic drift, which varies by approximately five orders of magnitude across the Tree of Life. Prior theoretical work examining the conditions under which such gradients can arise focused on the simple situation in which all genomic sites affecting the trait have identical and constant mutational effects. Here, we extend this theory to incorporate the more biologically realistic situation in which mutational effects on a trait differ among nucleotide sites. Pursuit of such modifications leads to the development of semi-analytic expressions for the ways in which selective interference arises via linkage effects in single-effects models, which then extend to more complex scenarios. The theory developed clarifies the conditions under which mutations of different selective effects mutually interfere with each others' fixation and shows how variance in effects among sites can substantially modify and extend the expected scaling relationships between mean phenotypes and effective population sizes.

Genome-wide detection of changes in allelic frequency in Landrace pigs selected for resistance to mycoplasma pneumonia of swine.

Closed-pig line breeding could change the genetic structure at a genome-wide scale because of the selection in a pig breeding population. We investigated the changes in population structure among generations at a genome-wide scale and the selected loci across the genome by comparing the observed and expected allele frequency changes in mycoplasma pneumonia of swine (MPS)-selected pigs. Eight hundred and seventy-four Landrace pigs, selected for MPS resistance without reducing average daily gain over five generations, had 37,299 single nucleotide polymorphisms (SNPs) and were used for genomic analyses. Regarding population structure, individuals in the first generation were the most widely distributed and then converged into a specific group, as they were selected over five generations. For allele frequency changes, 96 and 14 SNPs had higher allele frequency changes than the 99.9% and 99.99% thresholds of the expected changes, respectively. These SNPs were evenly spread across the genome, and a few of these selected regions overlapped with previously detected quantitative trait loci for MPS and immune-related traits. Our results indicated that the considerable changes in allele frequency were identified in many regions across the genome by closed-pig line breeding based on estimated breeding value.

Pedigree-based analyses of changes in genetic variability in three major swine breeds in Taiwan after a disease outbreak.

Pedigree analysis was performed in three major Taiwanese swine breeds to evaluate the genetic variability in the current population and determine the main reason for genetic diversity (GD) loss after the occurrence of foot-and-mouth disease (FMD) in Taiwan. The pedigree files of the Duroc, Landrace, and Yorkshire breeds, containing 60,237, 87,177, and 34,373 records, respectively, were analyzed. We divided the population into two subpopulations (pre-1998 and post-1998) to determine the role of FMD in GD loss. Pedigree completeness and related indicators were analyzed to evaluate the pedigree quality, and several parameters were used to measure the levels of GD and further used to determine the major cause of GD loss. The pedigree completeness indexes for the different breeds were higher than 0.60, and the trend was enhanced after the FMD outbreak. The estimated proportion of random genetic drift in GD loss increased in all breeds over time (from 62.64% to 78.44% in Duroc; from 26.26% to 57.99% in Landrace; and from 47.97% to 55.00% in Yorkshire, respectively). The effective population size of Duroc and Landrace were increased by the time (Duroc: from 61.73 to 84.75; Landrace: from 108.70 to 113.64); however, it shows opposite trend in Yorkshire population (decline from 86.21 to 50.00). In summary, the occurrence of FMD led to the major loss of GD loss by random genetic drift. Therefore, for the recovery of GD, breeders in Taiwan should increase the effective population size with newly imported genetic materials and adjust the breeding strategy to reduce the inbreeding rate.

Correcting Bias in Allele Frequency Estimates Due to an Observation Threshold: A Markov Chain Analysis.

There are many problems in biology and related disciplines involving stochasticity, where a signal can only be detected when it lies above a threshold level, while signals lying below threshold are simply not detected. A consequence is that the detected signal is conditioned to lie above threshold, and is not representative of the actual signal. In this work, we present some general results for the conditioning that occurs due to the existence of such an observational threshold. We show that this conditioning is relevant, for example, to gene-frequency trajectories, where many loci in the genome are simultaneously measured in a given generation. Such a threshold can lead to severe biases of allele frequency estimates under purifying selection. In the analysis presented, within the context of Markov chains such as the Wright-Fisher model, we address two key questions: (1) "What is a natural measure of the strength of the conditioning associated with an observation threshold?" (2) "What is a principled way to correct for the effects of the conditioning?". We answer the first question in terms of a proportion. Starting with a large number of trajectories, the relevant quantity is the proportion of these trajectories that are above threshold at a later time and hence are detected. The smaller the value of this proportion, the stronger the effects of conditioning. We provide an approximate analytical answer to the second question, that corrects the bias produced by an observation threshold, and performs to reasonable accuracy in the Wright-Fisher model for biologically plausible parameter values.

A dynamic ancestral graph model and GPU-based simulation of a community based on metagenomic sampling.

In this paper, we present an ancestral graph model of the evolution of a guild in an ecological community. The model is based on a metagenomic sampling design in that a random sample is taken at the community, as opposed the taxon, level and species are discovered by genetic sequencing. The specific implementation of the model envisions an ecological guild that was founded by colonization at some point in the past that then potentially undergoes diversification by natural selection. Within the graph, species emerge and evolve through the diversification process and their densities in the graph are dynamic and governed by both ecological drift and random genetic drift, as well as differential viability. We employ the 3% sequence divergence rule at a marker locus to identify operational taxonomic units. We then explore approaches to see whether there are indirect signals of the diversification process, including population genetic and ecological approaches. In terms of population genetics, we study the joint site frequency spectrum of OTUs, as well its associated statistics. In terms of ecology, we study the species (or OTU) abundance distribution. For both, we observe deviations from neutrality, which indicates that there may be signals of diversifying selection in metagenomic studies under certain conditions. The model is available as a GPU-based computer program in C/C++ and using OpenCL, with the long-term goal of adding functionality iteratively to model large-scale eco-evolutionary processes for metagenomic data.