S. Cebrat, D. Stauffer
Computer simulations of the Penna ageing model suggest that already a small fraction of births with enhanced number of new mutations can negatively influence the whole population.
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The Weismann barrier, or the impossibility of inheritance of acquired traits, comprises a foundation of modern biology, and it has been a major obstacle in establishing the connection between evolution and ontogenesis. We propose the cooperative model based on the assumption that evolution is achieved by a cooperation between genetic mutations and acquired changes (phenotypic plasticity). It is also assumed in this model that natural selection operates on phenotypes, rather than genotypes, of individuals, and that the relationship between phenotypes and genotypes is one-to-many. In the simulat…
Genetic drift is stochastic fluctuations of alleles frequencies in a population due to sampling effects. We consider a model of drift in an equilibrium population, with high mutation rates: few functional mutations per generation. Such mutation rates are common in multicellular organisms including humans, however they are not explicitly considered in most population genetics models. Under these assumptions the drift shows properties distinct from the classical drift models, which ignore realistic mutation rates: i) All (non-lethal) variants of a site have a characteristic average frequencies, …
In genetic drift of small population, it is well known that even when the ratio of alleles is 0.5, specific genes are fixed in or disappear from the population. It seems the reason why inbreeding is avoided. On the other hand, this phenomenon suggests an interesting possibility. The mutant gene does not increase the number of genes at once in a large population. A gene is partially fixed by increasing the number within a small population because of inbreeding, and the gene increases in a large group by Darwin's natural selection. It would be more reasonable to think in this way. We studied thi…
In this work, we aim to study that the dynamics behavior for cumulative number of SARS-CoV-2 pandemic can provide information on the overall behavior of the spread over daily time.The cumulative data can be synthesized in an empirical form obtained from a Susceptible-Infected-Recovered (SIR) model previously studied on a Euclidean network. From the study we carried out, we can conclude that the SIR model on the Euclidean network can reproduce data from several countries with a deviation of precision for given parameter values. This gives an insight into the different agents that influence the …
Some species exhibit very high levels of DNA sequence variability; there is also evidence for the existence of heritable epigenetic variants that experience state changes at a much higher rate than sequence variants. In both cases, the resulting high diversity levels within a population (hyperdiversity) mean that standard population genetics methods are not trustworthy. We analyze a population genetics model that incorporates purifying selection, reversible mutations and genetic drift, assuming a stationary population size. We derive analytical results for both population parameters and sample…
The accumulation of beneficial mutations on many competing genetic backgrounds in rapidly adapting populations has a striking impact on evolutionary dynamics. This effect, known as clonal interference, causes erratic fluctuations in the frequencies of observed mutations, randomizes the fixation times of successful mutations, and leaves distinct signatures on patterns of genetic variation. Here, we show how this form of `genetic draft' affects the forward-time dynamics of site frequencies in rapidly adapting asexual populations. We calculate the probability that mutations at individual sites sh…
Non-genetic perturbations, such as environmental change or developmental noise, can induce novel phenotypes. If an induced phenotype confers a fitness advantage, selection may promote its genetic stabilization. Non-genetic perturbations can thus initiate evolutionary innovation. Genetic variation that is not usually phenotypically visible may play an important role in this process. Populations under stabilizing selection on a phenotype that is robust to mutations can accumulate such variation. After non-genetic perturbations, this variation can become a source of new phenotypes. We here study …
The evolution of drug resistance in HIV occurs by the fixation of specific, well-known, drug-resistance mutations, but the underlying population genetic processes are not well understood. By analyzing within-patient longitudinal sequence data, we make four observations that shed a light on the underlying processes and allow us infer the short-term effective population size of the viral population in a patient. Our first observation is that the evolution of drug resistance usually occurs by the fixation of one drug-resistance mutation at a time, as opposed to several changes simultaneously. Sec…
We have analyzed the relations between the mutational pressure, recombination and selection pressure in the bit-string model with sexual reproduction. For specific sets of these parameters we have found three phase transitions with one phase where populations can survive. In this phase, recombination enhances the survival probability. Even if recombination is associated, to some extent, with additional mutations it could be advantageous to reproduction, indicating that the frequencies of recombinations and recombination-associated mutations can self-organize in Nature. Partitioning the diploid…
We have investigated the role that the mutation rate and the structure of genetic variation at a locus play in determining whether a gene is involved in disease. We predict that the mutation rate and its genetic diversity should be higher in genes associated with disease, unless all genes that could cause disease have already been identified. Consistent with our predictions we find that genes associated with Mendelian and complex disease are substantially longer than non-disease genes. However, we find that both Mendelian and complex disease genes are found in regions of the genome with relati…
Background: Acceleration of adaptation dynamics by stress-induced hypermutation has been found experimentally. Evolved evolvability is a prominent explanation. We investigate a more generally applicable explanation by a physical constraint. Methods and Results: A generic thermodynamical analysis of genetic information storage obviates physical constraints on the integrity of genetic information. The capability to employ metabolic resources is found as a major determinant of mutation probability in stored genetic information. Incorporation into a non-recombinant, asexual adaptation toy model pr…
In order to analyze data from cancer genome sequencing projects, we need to be able to distinguish causative, or "driver," mutations from "passenger" mutations that have no selective effect. Toward this end, we prove results concerning the frequency of neutural mutations in exponentially growing multitype branching processes that have been widely used in cancer modeling. Our results yield a simple new population genetics result for the site frequency spectrum of a sample from an exponentially growing population.
While Neutral Theory famously describes the number of discrete genetic differences in populations, we consider the number of genetic backgrounds under which such differences are observed - setting limits to the generalizability of their effects. This allow us to determine which population structures and diversity rates have maximal effect generalization across (1) environmental and (2) genetic variation, and to demonstrate that they correspond asymptotically to those of populations under (1) natural selection and (2) drift. At the same time, these results suggest distinct limits to the predict…
The persistence of life requires populations to adapt at a rate commensurate with the dynamics of their environment. Successful populations that inhabit highly variable environments have evolved mechanisms to increase the likelihood of successful adaptation. We introduce a $64 \times 64$ matrix to quantify base-specific mutation potential, analyzing four different replicative systems, error-prone PCR, mouse antibodies, a nematode, and Drosophila. Mutational tendencies are correlated with the structural evolution of proteins. In systems under strong selective pressure, mutational biases are sho…
So far mutations analysis was performed in terms of transitions and trasversions, so on the basis of the molecule, or in terms of GC-content and isochors, through the quantification of GC->AT mutations over AT->GC mutations. We tried a different approach hypothesizing that probably we are partially protected (by the genetic code) from amyloid fibrils formation.
Conventional population genetics considers the evolution of a limited number of genotypes corresponding to phenotypes with different fitness. As model phenotypes, in particular RNA secondary structure, have become computationally tractable, however, it has become apparent that the context dependent effect of mutations and the many-to-one nature inherent in these genotype-phenotype maps can have fundamental evolutionary consequences. It has previously been demonstrated that populations of genotypes evolving on the neutral networks corresponding to all genotypes with the same secondary structure…
By exploiting an analogy between population genetics and statistical mechanics, we study the evolution of a polygenic trait under stabilizing selection, mutation, and genetic drift. This requires us to track only four macroscopic variables, instead of the distribution of all the allele frequencies that influence the trait. These macroscopic variables are the expectations of: the trait mean and its square, the genetic variance, and of a measure of heterozygosity, and are derived from a generating function that is in turn derived by maximizing an entropy measure. These four macroscopics are enou…
Do Species Evolve Through Mutations Guided by Non-Coding RNAs?
针对现有进化论无法解释进化新特征出现的问题，本文提出并证实了一个新理论：物种进化中的突变由环境引导，环境与生殖系通过非编码RNA等信使连接，生殖系基因组基于接收的表观遗传信息经历表观修饰、基因突变和新基因产生三个阶段的可遗传变化以产生适应性更强的后代。
Phenotype of biological systems needs to be robust against mutation in order to sustain themselves between generations. On the other hand, phenotype of an individual also needs to be robust against fluctuations of both internal and external origins that are encountered during growth and development. Is there a relationship between these two types of robustness, one during a single generation and the other during evolution? Could stochasticity in gene expression have any relevance to the evolution of these robustness? Robustness can be defined by the sharpness of the distribution of phenotype; …
The fitness landscape - the mapping between genotypes and fitness - determines properties of the process of adaptation. Several small genetic fitness landscapes have recently been built by selecting a handful of beneficial mutations and measuring fitness of all combinations of these mutations. Here we generate several testable predictions for the properties of these landscapes under Fisher's geometric model of adaptation (FGMA). When far from the fitness optimum, we analytically compute the fitness effect of beneficial mutations and their epistatic interactions. We show that epistasis may be n…
Human populations have undergone dramatic changes in population size in the past 100,000 years, including a severe bottleneck of non-African populations and recent explosive population growth. There is currently great interest in how these demographic events may have affected the burden of deleterious mutations in individuals and the allele frequency spectrum of disease mutations in populations. Here we use population genetic models to show that--contrary to previous conjectures--recent human demography has likely had very little impact on the average burden of deleterious mutations carried by…
Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of deleterious variation, as well as the number, frequencies, and effect sizes of mutations that contribute risk to complex traits. Here I use simulations under population genetic models where a proportion of the heritability of the trait is accounted for by mutations in a subset of the exome. I show that recent population growth increases the proportion of nonsynony…
Genetic interactions pervade every aspect of biology, from evolutionary theory where they determine the accessibility of evolutionary paths, to medicine where they contribute to complex genetic diseases. Until very recently, studies on epistatic interactions have been based on a handful of mutations, providing at best anecdotal evidence about the frequency and the typical strength of genetic interactions. In this study we analyze the publicly available Data Repository of Yeast Genetic INteractions (DRYGIN), which contains the growth rates of over five million double gene knockout mutants. We d…
Self-Replication, Spontaneous Mutations, and Exponential Genetic Drift in Neural Cellular Automata
本文首次利用神经细胞自动机实现了自我复制、自发突变和指数遗传漂变，即使模型未受显式训练且自动机是确定性的，也展现出进化动力学，从而拓展了变异空间与开放式进化的机会。
Two important problems affect the ability of asexual populations to accumulate beneficial mutations, and hence to adapt. First, clonal interference causes some beneficial mutations to be outcompeted by more-fit mutations which occur in the same genetic background. Second, multiple mutations occur in some individuals, so even mutations of large effect can be outcompeted unless they occur in a good genetic background which contains other beneficial mutations. In this paper, we use a Monte Carlo simulation to study how these two factors influence the adaptation of asexual populations. We find tha…
Cancer results from genetic alterations that disturb the normal cooperative behavior of cells. Recent high-throughput genomic studies of cancer cells have shown that the mutational landscape of cancer is complex and that individual cancers may evolve through mutations in as many as 20 different cancer-associated genes. We use data published by Sjoblom et al. (2006) to develop a new mathematical model for the somatic evolution of colorectal cancers. We employ the Wright-Fisher process for exploring the basic parameters of this evolutionary process and derive an analytical approximation for the …
In population genetics, extant samples are usually used for inference of past population genetic forces. With the Kingman coalescent and the backward diffusion equation, inference of the marginal likelihood proceeds from an extant sample backward in time. Conditional on an extant sample, the Moran model can also be used backward in time with identical results, up to a scaling of time. In particular, all three approaches -- the coalescent, the backward diffusion, and the Moran model -- lead to the identical marginal likelihood of the sample. If probabilities of ancestral states are also inferre…
Lotka-Volterra Model with Mutations and Generative Adversarial Networks
本文提出统计流形上带突变的 Lotka-Volterra 群体遗传学模型，利用 Fisher-Rao 度量下的 Laplace-Beltrami 扩散融合信息几何，将 GAN 推广到网络群体情形以控制过拟合。
Mutation and Random Matrix Theory
本文在多体系统框架下探讨遗传演化与随机矩阵理论的联系，提出突变对应 Gross-Witten-Wadia 相变的统计描述。
Recent microbial experiments suggest that enhanced genetic drift at the frontier of a two-dimensional range expansion can cause genetic sectoring patterns with fractal domain boundaries. Here, we propose and analyze a simple model of asexual biological evolution at expanding frontiers to explain these neutral patterns and predict the effect of natural selection. Our model attributes the observed gradual decrease in the number of sectors at the leading edge to an unbiased random walk of sector boundaries. Natural selection introduces a deterministic bias in the wandering of domain boundaries th…
Shannon information has, in the past, been applied to quantify the genetic diversity of many natural populations. Here, we apply the Shannon concept to consecutive generations of alleles as they evolve over time. We suppose a genetic system analogous to the discrete noisy channel of Shannon, where the signal emitted by the input (mother population) is a number of alleles that will form the next generation (offspring). The alleles received at a given generation are conditional upon the previous generation. Knowledge of this conditional probability law allows us to track the evolution of the all…
Diffusion theory is a central tool of modern population genetics, yielding simple expressions for fixation probabilities and other quantities that are not easily derived from the underlying Wright-Fisher model. Unfortunately, the textbook derivation of diffusion equations as scaling limits requires evolutionary parameters (selection coefficients, mutation rates) to scale like the inverse population size -- a severe restriction that does not always reflect biological reality. Here we note that the Wright-Fisher model can be approximated by diffusion equations under more general conditions, incl…
When polygenic traits are under stabilizing selection, many different combinations of alleles allow close adaptation to the optimum. If alleles have equal effects, all combinations that result in the same deviation from the optimum are equivalent. Furthermore, the genetic variance that is maintained by mutation-selection balance is $2 μ/S$ per locus, where $μ$ is the mutation rate and $S$ the strength of stabilizing selection. In reality, alleles vary in their effects, making the fitness landscape asymmetric, and complicating analysis of the equilibria. We show that that the resulting genetic …
GWAS in humans are revealing the genetic architecture of biomedical and anthropomorphic traits, i.e., the frequencies and effect sizes of variants that contribute to heritable variation in a trait. To interpret these findings, we need to understand how genetic architecture is shaped by basic population genetics processes-notably, by mutation, natural selection and genetic drift. Because many quantitative traits are subject to stabilizing selection and genetic variation that affects one trait often affects many others, we model the genetic architecture of a focal trait that arises under stabili…
We study the population genetics of two neutral alleles under reversible mutation in the Λ-processes, a population model that features a skewed offspring distribution. We describe the shape of the equilibrium allele frequency distribution as a function of the model parameters. We show that the mutation rates can be uniquely identified from the equilibrium distribution, but that the form of the offspring distribution itself cannot be uniquely identified. We also introduce an infinite-sites version of the Λ-process, and we use it to study how reproductive skew influences standing genetic diversi…
The frequencies of A, C, G and T in mitochondrial DNA vary among species due to unequal rates of mutation between the bases. The frequencies of bases at four-fold degenerate sites respond directly to mutation pressure. At 1st and 2nd positions, selection reduces the degree of frequency variation. Using a simple evolutionary model, we show that 1st position sites are less constrained by selection than 2nd position sites, and therefore that the frequencies of bases at 1st position are more responsive to mutation pressure than those at 2nd position. We define a similarity measure between amino ac…
Cancer progression is an evolutionary process that is driven by mutation and selection in a population of tumor cells. We discuss mathematical models of cancer progression, starting from traditional multistage theory. Each stage is associated with the occurrence of genetic alterations and their fixation in the population. We describe the accumulation of mutations using conjunctive Bayesian networks, an exponential family of waiting time models in which the occurrence of mutations is constrained to a partial temporal order. Two opposing limit cases arise if mutations either follow a linear orde…
Dominant negative mutations in the insulin gene are the second most common cause of permanent neonatal diabetes. However, variation in severity and penetrance of neonatal diabetes, as in other complex genetic diseases, cannot be accounted for by known disease mutations. In a novel approach to this problem, we have utilized the genetic tools available in Drosophila to model the effects of the C96Y mutation, a cysteine to tyrosine mutation in the insulin protein that can cause permanent neonatal diabetes in humans. This mutation, which disrupts a disulfide bridge in the proinsulin molecule, has …
We propose that the evolutionary purpose of junk DNA is to protect the gene. Mutation agents, such as retro-viruses, hit ``decoy'' DNA most of the time. Although the argument is far from general, we propose that the percentage of junk DNA should correlate with the number of retroviruses attacking a given species. It should also anti-correlate with the ideal mutation rates (higher in insects than in mammals).
grenedalf: population genetic statistics for the next generation of pool sequencing
本文介绍 C++ 命令行工具 grenedalf，用于混合测序数据的 θ、Tajima’s D 和 FST 等群体遗传统计，兼具高速、可扩展与多格式支持。
Genetic robustness, the preservation of evolved phenotypes against genotypic mutations, is one of the central concepts in evolution. In recent years a large body of work has focused on the origins, mechanisms, and consequences of robustness in a wide range of biological systems. In particular, research on ncRNAs studied the ability of sequences to maintain folded structures against single-point mutations. In these studies, the structure is merely a reference. However, recent work revealed evidence that structure itself contributes to the genetic robustness of ncRNAs. We follow this line of tho…
Over time, a population acquires neutral genetic substitutions as a consequence of random drift. A famous result in population genetics asserts that the rate, $K$, at which these substitutions accumulate in the population coincides with the mutation rate, $u$, at which they arise in individuals: $K=u$. This identity enables genetic sequence data to be used as a "molecular clock" to estimate the timing of evolutionary events. While the molecular clock is known to be perturbed by selection, it is thought that $K=u$ holds very generally for neutral evolution. Here we show that asymmetric spatial …
We introduce and analyze a waiting time model for the accumulation of genetic changes. The continuous time conjunctive Bayesian network is defined by a partially ordered set of mutations and by the rate of fixation of each mutation. The partial order encodes constraints on the order in which mutations can fixate in the population, shedding light on the mutational pathways underlying the evolutionary process. We study a censored version of the model and derive equations for an EM algorithm to perform maximum likelihood estimation of the model parameters. We also show how to select the maximum l…
Pervasive natural selection can strongly influence observed patterns of genetic variation, but these effects remain poorly understood when multiple selected variants segregate in nearby regions of the genome. Classical population genetics fails to account for interference between linked mutations, which grows increasingly severe as the density of selected polymorphisms increases. Here, we describe a simple limit that emerges when interference is common, in which the fitness effects of individual mutations play a relatively minor role. Instead, molecular evolution is determined by the variance …
The phenotypic consequences of individual mutations are modulated by the wild type genetic background in which they occur.Although such background dependence is widely observed, we do not know whether general patterns across species and traits exist, nor about the mechanisms underlying it. We also lack knowledge on how mutations interact with genetic background to influence gene expression, and how this in turn mediates mutant phenotypes. Furthermore, how genetic background influences patterns of epistasis remains unclear. To investigate the genetic basis and genomic consequences of genetic ba…
Natural selection explains how life has evolved over millions of years from more primitive forms. The speed at which this happens, however, has sometimes defied formal explanations when based on random (uniformly distributed) mutations. Here we investigate the application of a simplicity bias based on a natural but algorithmic distribution of mutations (no recombination) in various examples, particularly binary matrices in order to compare evolutionary convergence rates. Results both on synthetic and on small biological examples indicate an accelerated rate when mutations are not statistical u…
The mutation process on the ancestral line under selection
本研究针对含突变与选择的Moran模型，借助修剪后的向下看祖先选择图分析远祖谱系的突变过程，发现选择导致有利型偏倚及突变率不对称，为系统发育与谱系研究的突变率差异提供新解释。
Although traditional models of epidemic spreading focus on the number of infected, susceptible and recovered individuals, a lot of attention has been devoted to integrate epidemic models with population genetics. Here we develop an individual-based model for epidemic spreading on networks in which viruses are explicitly represented by finite chains of nucleotides that can mutate inside the host. Under the hypothesis of neutral evolution we compute analytically the average pairwise genetic distance between all infecting viruses over time. We also derive a mean-field version of this equation tha…
The genetic composition of a naturally developing population is considered as due to mutation, selection, genetic drift and recombination. Selection is modeled as single-locus terms (additive fitness) and two-loci terms (pairwise epistatic fitness). The problem is posed to infer epistatic fitness from population-wide whole-genome data from a time series of a developing population. We generate such data in silico, and show that in the Quasi-Linkage Equilibrium (QLE) phase of Kimura, Neher and Shraiman, that pertains at high enough recombination rates and low enough mutation rates, epistatic fit…
Phenotype Search Trajectory Networks for Linear Genetic Programming
本研究通过图模型可视化线性遗传编程的搜索轨迹，并量化表型复杂度与基因型丰度，发现复杂表型更难发现，简单表型更易作为进化垫脚石。
Genetic contribution of an advantaged mutant in the biparental Moran model -- finite selection
本研究针对带优势/劣势类型的双亲Moran模型种群，探究降低死亡概率的孟德尔式突变的遗传贡献，推导了大种群下突变固定后采样基因源自优势个体的概率与初始携带比例a的函数关系。
Genetic Composition of Supercritical Branching Populations under Power Law Mutation Rates
本文用有限有向图上的个体细胞分支模型刻画幂律突变率下的癌细胞演化，给出各亚群规模在对数与随机时间尺度上的一阶及数量级渐近结果。
We study a simple model of DNA evolution in a growing population of cells. Each cell contains a nucleotide sequence which randomly mutates at cell division. Cells divide according to a branching process. Following typical parameter values in bacteria and cancer cell populations, we take the mutation rate to zero and the final number of cells to infinity. We prove that almost every site (entry of the nucleotide sequence) is mutated in only a finite number of cells, and these numbers are independent across sites. However independence breaks down for the rare sites which are mutated in a positive…
We study the evolutionary dynamics of an asexual population of nonmutators and mutators on a class of epistatic fitness landscapes. We consider the situation in which all mutations are deleterious and mutators are produced from nonmutators continually at a constant rate. We find that in an infinitely large population, a minimum nonmutator-to-mutator conversion rate is required to fix the mutators but an arbitrarily small conversion rate results in the fixation of mutators in a finite population. We calculate analytical expressions for the mutator fraction at mutation-selection balance and fixa…
Motivated by present activities in (statistical) physics directed towards biological evolution, we review the interplay of three evolutionary forces: mutation, selection, and genetic drift. The review addresses itself to physicists and intends to bridge the gap between the biological and the physical literature. We first clarify the terminology and recapitulate the basic models of population genetics, which describe the evolution of the composition of a population under the joint action of the various evolutionary forces. Building on these foundations, we specify the ingredients explicitly, na…
We study the effect of spatial structure, genetic drift, mutation, and selective pressure on the evolutionary dynamics in a simplified model of asexual organisms colonizing a new territory. Under an appropriate coarse-graining, the evolutionary dynamics is related to the directed percolation processes that arise in voter models, the Domany-Kinzel (DK) model, contact process, etc. We explore the differences between linear (flat front) expansions and the much less familiar radial (curved front) range expansions. For the radial expansion, we develop a generalized, off-lattice DK model that minimi…
Emergent frequency-dependent selection predicts mutation outcomes in complex ecological communities
研究通过动态平均场理论将生态学整合到经典群体遗传学模型中，揭示生态互作导致的频率依赖选择如何影响突变结果，并展示了生态反馈对突变固定概率的抑制作用。
Very low levels of genetic diversity have been reported in vertebrates with large genomes, notably salamanders and lungfish [1-3]. Interpreting differences in heterozygosity, which reflects genetic diversity in a population, is complicated because levels of heterozygosity vary widely between conspecific populations, and correlate with many different physiological and demographic variables such as body size and effective population size. Here we return to the question of genetic variability in salamanders and report on the relationship between evolutionary rates and genome sizes in five differe…
We construct an individual-based metapopulation model of population genetics featuring migration, mutation, selection and genetic drift. In the case of a single `island', the model reduces to the Moran model. Using the diffusion approximation and timescale separation arguments, an effective one-variable description of the model is developed. The effective description bears similarities to the well-mixed Moran model with effective parameters which depend on the network structure and island sizes, and is amenable to analysis. Predictions from the reduced theory match the results from stochastic …
BACKGROUND: Many of the mutations accumulated by naturally evolving proteins are neutral in the sense that they do not significantly alter a protein's ability to perform its primary biological function. However, new protein functions evolve when selection begins to favor other, "promiscuous" functions that are incidental to a protein's biological role. If mutations that are neutral with respect to a protein's primary biological function cause substantial changes in promiscuous functions, these mutations could enable future functional evolution. RESULTS: Here we investigate this possibility exp…
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