Guillaume Achaz, Julien Dutheil
In this article, we review the different models and methods to understand and estimate correlated evolution within the same genome, individual or species. We describe correlated evolution among traits, among genetic components and finally between traits and genetics.
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Inferences about the evolution of continuous traits based on reconstruction of ancestral states has often been considered more error-prone than analysis of independent contrasts. Here we show that both methods in fact yield identical estimators for the correlation coefficient and regression gradient of correlated traits, indicating that reconstructed ancestral states are a valid source of information about correlated evolution. We show that the independent contrast associated with a pair of sibling nodes on a phylogenetic tree can be expressed in terms of the maximum likelihood ancestral state…
Sexual selection theory models evolution of sexual signals and preferences using simple life histories. However, life-history models predict that males benefit from increasing sexual investment approaching old age, producing age-dependent sexual traits. Age-dependent traits require time and energy to grow, and will not fully mature before individuals enter mating competition. Early evolutionary stages pose several problems for these traits. Age-dependent traits suffer from strong viability selection and gain little benefit from mate choice when rare. Few males will grow large traits, and they …
We consider a simple mathematical model of gradual Darwinian evolution in continuous time and continuous trait space, due to intraspecific competition for common resource in an asexually reproducing population in constant environment, while far from evolutionary stable equilibrium. The model admits exact analytical solution. In particular, Gaussian distribution of the trait emerges from generic initial conditions.
Exact Expressions for the Log-likelihood's Hessian in Multivariate Continuous-Time Continuous-Trait Gaussian Evolution along a Phylogeny
本文推导多变量连续性状高斯马尔可夫系统发育演化模型似然 Hessian 的闭式表达式，并发布 R 包 glinvci 以支持近似置信域、缺失数据和多演化机制分析。
Genetic association data from national biobanks and large-scale association studies have provided new prospects for understanding the genetic evolution of complex traits and diseases in humans. In turn, genomes from ancient human archaeological remains are now easier than ever to obtain, and provide a direct window into changes in frequencies of trait-associated alleles in the past. This has generated a new wave of studies aiming to analyse the genetic component of traits in historic and prehistoric times using ancient DNA, and to determine whether any such traits were subject to natural selec…
In the classic view introduced by R. A. Fisher, a quantitative trait is encoded by many loci with small, additive effects. Recent advances in QTL mapping have begun to elucidate the genetic architectures underlying vast numbers of phenotypes across diverse taxa, producing observations that sometimes contrast with Fisher's blueprint. Despite these considerable empirical efforts to map the genetic determinants of traits, it remains poorly understood how the genetic architecture of a trait should evolve, or how it depends on the selection pressures on the trait. Here we develop a simple, populati…
Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a quantitative trait under time-dependent selection, which arises from environmental changes or through fitness interactions with other co-evolving phenotypes. We analyze a model of trait evolution under mutations and genetic drift in a single-peak fitness seascape. The fitness peak performs a constrained random walk in the trait amplitude, which determines the time-dep…
The selection pressures that have shaped the evolution of complex traits in humans remain largely unknown, and in some contexts highly contentious, perhaps above all where they concern mean trait differences among groups. To date, the discussion has focused on whether such group differences have any genetic basis, and if so, whether they are without fitness consequences and arose via random genetic drift, or whether they were driven by selection for different trait optima in different environments. Here, we highlight a plausible alternative, that many complex traits evolve under stabilizing se…
Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. We review recent developments in evolutionary theory and experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis, which is often at least par…
A tumor can be thought of as an ecosystem, which critically means that we cannot just consider it as a collection of mutated cells but more as a complex system of many interacting cellular and microenvironmental elements. At its simplest, a growing tumor with increased proliferation capacity must compete for space as a limited resource. Hypercellularity leads to a contact-inhibited core with a competitive proliferating rim. Evolution and selection occurs, and an individual cell's capacity to survive and propagate is determined by its combination of traits and interaction with the environment. …
Concomitant with the evolution of biological diversity must have been the evolution of mechanisms that facilitate evolution, due to the essentially infinite complexity of protein sequence space. We describe how evolvability can be an object of Darwinian selection, emphasizing the collective nature of the process. We quantify our theory with computer simulations of protein evolution. These simulations demonstrate that rapid or dramatic environmental change leads to selection for greater evolvability. The selective pressure for large scale genetic moves, such as DNA exchange, becomes increasingl…
In his highly influential view of evolution, G. G. Simpson hypothesized that clades of species evolve in adaptive zones, defined as collections of niches occupied by species with similar traits and patterns of habitat use. Simpson hypothesized that species enter new adaptive zones in one of three ways: extinction of competitor species, dispersal to a new geographic region, or the evolution of a key trait that allows species to exploit resources in a new way. However, direct tests of Simpson's hypotheses for the entry into new adaptive zones remain elusive. Here we evaluate the fit of a Simpson…
Several studies question the adaptive value of female preferences for older males. Theory and evidence show that older males carry more deleterious mutations in their sperm than younger males carry. These mutations are not visible to females choosing mates. Germ-line mutations could oppose preferences for "good genes." Choosy females run the risk that offspring of older males will be no more attractive or healthy than offspring of younger males. Germ-line mutations could pose a particular problem when females can only judge male trait size, rather than assessing age directly. I ask whether or …
The presence of phenomena analogous to phase transition in Statistical Mechanics, has been suggested in the evolution of a polygenic trait under stabilizing selection, mutation and genetic drift. By using numerical simulations of a model system, we analyze the evolution of a population of $N$ diploid hermaphrodites in random mating regime. The population evolves under the effect of drift, selective pressure in form of viability on an additive polygenic trait, and mutation. The analysis allows to determine a phase diagram in the plane of mutation rate and strength of selection. The involved pat…
The evolution of complex molecular traits such as disulphide bridges often requires multiple mutations. The intermediate steps in such evolutionary trajectories are likely to be selectively neutral or deleterious. Therefore, large populations and long times may be required to evolve such traits. We propose that errors in transcription and translation may allow selection for the intermediate mutations if the final trait provides a large enough selective advantage. We test this hypothesis using a population based model of protein evolution. If an individual acquires one of two mutations needed f…
The interplay of network structure and correlated infectious traits in epidemic models
研究网络结构与个体传染性特征的相互作用，通过SIR模型分析群体结构和度异质性的影响，推导基本再生数并验证社会干预的有效性。
Many biological characteristics of evolutionary interest are not scalar variables but continuous functions. Given a dataset of function-valued traits generated by evolution, we develop a practical statistical approach to infer ancestral function-valued traits, and estimate the generative evolutionary process. We do this by combining dimension reduction and phylogenetic Gaussian process regression, a nonparametric procedure which explicitly accounts for known phylogenetic relationships. We test the methods' performance on simulated function-valued data generated from a stochastic evolutionary m…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this work, we present a probabilistic modeling framework for binary trait, random species trees, in which the number of species and their traits are represented by a two-type, continuous time Markov branching process. We develop our model by considering the impact of mating systems on dN/dS, the ratio of nonsynonymous to synonymous substitutions. A methodology is int…
Stochasticity and Environmental Switching Shape Quorum Sensing Evolution in Bacterial Populations
本研究通过个体模型和自适应动力学，揭示环境频率与噪声不对称性决定细菌群体感应中膜通透性双性状的进化与共存。
Limits on the Evolutionary Rates of Biological Traits
本文推导了自然选择、突变和遗传漂变下生物性状进化速率的不等式，将种群变异性与进化速度联系起来，并推广了 Fisher 基本定理。
Adapting cluster graphs for inference of continuous trait evolution on phylogenetic networks
本文提出利用非树状聚类图优化高斯性状进化模型的因子化能量近似，探讨最大聚类大小对估计精度与运行时间的权衡影响，并证明同质布朗运动模型的参数估计等价性。
We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which heterogeneity is described by an individual specific parameter that differs in general from individual to individual, but does not change with time for the whole lifespan of this individual. Such a restriction allows obtaining a number of simple and yet important analytical results. In particular we show that initial assumptions on time-dependent behavior of various…
We present a mathematical simplification for the evolutionary dynamics of a heritable trait within a two-sex population. This trait is assumed to control the timing of sex-specific life-history events, such as the age of sexual maturity and end of female fertility, and each sex has a distinct fitness tradeoff associated with the trait. We provide a formula for the fitness landscape of the population and show a natural extension of the result to an arbitrary number of heritable traits. Our method can be viewed as a dynamical systems generalisation of the Price Equation to include two sexes{, ag…
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species' range dynamics is a major goal of spatial ecology. Previous mathematical models have jointly captured the dynamic changes in species' population distributions and the selective evolution of fitness-related phenotypic traits in the presence of an environmental gradient. These models inevitably include some unrealistic assumptions, and biologically reasonable ranges of values for their parameters are not easy to specify. As a …
Understanding the processes that give rise to quantitative measurements associated with molecular sequence data remains an important issue in statistical phylogenetics. Examples of such measurements include geographic coordinates in the context of phylogeography and phenotypic traits in the context of comparative studies. A popular approach is to model the evolution of continuously varying traits as a Brownian diffusion process. However, standard Brownian diffusion is quite restrictive and may not accurately characterize certain trait evolutionary processes. Here, we relax one of the major res…
From trees to traits: A review of advances in PhyloG2P methods and future directions
本综述回顾PhyloG2P方法在识别基因型-表型关联中的进展，强调简单性状、连续性状建模及多方法联合应用，并展望整合群体变异与环境信息的未来方向。
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…
Under constant selection, each trait has a fixed fitness, and small mutation rates allow populations to efficiently exploit the optimal trait. Therefore it is reasonable to expect mutation rates will evolve downwards. However, we find this need not be the case, examining several models of mutation. While upwards evolution of mutation rate has been found with frequency or time dependent fitness, we demonstrate its possibility in a much simpler context. This work uses adaptive dynamics to study the evolution of mutation rate, and the replicator-mutator equation to model trait evolution. Our appr…
The evolution of parasite virulence and host defences is affected by population structure. This effect has been confirmed in studies focusing on large spatial scales, whereas the importance of local structure is not well understood. Slavemaking ants are social parasites that exploit workers of another species to rear their offspring. Enslaved workers of the host species Temnothorax longispinosus have been found to exhibit an effective post-enslavement defence behaviour: enslaved workers were observed killing a large proportion of the parasites' offspring. Since enslaved workers do not reproduc…
An explicit bound is given for the Kolmogorov distance between a mixture of normal distributions and a normal distribution with properly chosen parameter values. A random variable X has a mixture of normal distributions if its conditional distribution given some sigma-algebra is normal. The bound depends only on the first two moments of the first two conditional moments of X given this sigma-algebra. As an application, the Yule-Ornstein-Uhlenbeck model, used in the field of phylogenetic comparative methods, is considered. A bound is derived for the Kolmogorov distance between the distribution …
Novel models of trait evolution via an expansion of Lande's fitness function: The Ornstein-Uhlenbeck process meets the Little Prince's boa
该研究扩展兰德适应度函数，结合OU模型构建性状演化新随机微分方程模型，解释非高斯适应度函数机制，为相关演化假说检验及生态与演化动态研究提供了新途径。
We consider an interacting particle Markov process for Darwinian evolution in an asexual population with non-constant population size, involving a linear birth rate, a density-dependent logistic death rate, and a probability $μ$ of mutation at each birth event. We introduce a renormalization parameter $K$ scaling the size of the population, which leads, when $K\to+\infty$, to a deterministic dynamics for the density of individuals holding a given trait. By combining in a non-standard way the limits of large population ($K\to+\infty$) and of small mutations ($μ\to 0$), we prove that a time scal…
Every now and then the cultural paradigm of a society changes. Human history can be regarded as a sequence of long periods of cultural stasis punctuated by paradigm shifts that transform culture upside-down over the turn of a few generations. We propose here a population dynamics model devised to analyse paradigm shifts. In this model individuals are defined by a vector of cultural traits that can change mainly through imitation of other individuals' traits. The novelty of the model is that cultural traits may interact reinforcing or hindering each other. Imitation is then biased by the 'cultu…
Evolving genealogies in cultural evolution, the descendant process, and the number of cultural traits
本文研究了文化进化中谱系的动态行为，通过分析谱系长度的变化，揭示了文化特征数量的亚稳态特性。
Information Theory in a Darwinian Evolution Population Dynamics Model
本研究将信息论应用于达尔文进化种群动力学模型，提出基于Fisher信息的性状参数估计方法，可得到单/多性状物种的估计误差，并通过仿真验证了方法有效性。
Evolution of distribution of strategies in game theory is an interesting question that has been studied only for specific cases. Here I develop a general method to extend analysis of the evolution of continuous strategy distributions given bi-linear and quadratic payoff functions for any initial distribution to answer the following question: given the initial distribution of strategies in a game, how will it evolve over time? I look at several specific examples, including normal distribution on the entire line, normal truncated distribution, as well as exponential, uniform and Gamma distributi…
Organisms result from adaptive processes interacting across different time scales. One such interaction is that between development and evolution. Models have shown that development sweeps over several traits in a single agent, sometimes exposing promising static traits. Subsequent evolution can then canalize these rare traits. Thus, development can, under the right conditions, increase evolvability. Here, we report on a previously unknown phenomenon when embodied agents are allowed to develop and evolve: Evolution discovers body plans robust to control changes, these body plans become genetic…
A stochastic field theory for the evolution of quantitative traits in finite populations
本文提出有限种群一维数量性状生态-进化动力学的随机场理论，推导随机场方程描述种群密度、性状频率及均值的演化，揭示自然选择、噪声诱导选择、生态-进化反馈与中性漂变的相互作用，并在无限种群极限下恢复复制-突变方程、Price方程等经典结果。
Phylogenetic comparative methods for real-valued traits usually make use of stochastic process whose trajectories are continuous. This is despite biological intuition that evolution is rather punctuated than gradual. On the other hand, there has been a number of recent proposals of evolutionary models with jump components. However, as we are only beginning to understand the behaviour of branching Ornstein-Uhlenbeck (OU) processes the asymptotics of branching OU processes with jumps is an even greater unknown. In this work we build up on a previous study concerning OU with jumps evolution on a …
A key goal in studies of ecology and evolution is understanding the causes of phenotypic diversity in nature. Most traits of interest, such as those relating to morphology, life-history, immunity and behaviour are quantitative, and phenotypic variation is driven by the cumulative effects of genetic and environmental variation. The field of quantitative genetics aims to quantify the additive genetic component of this trait variance (i.e. the "heritability"), often with the underlying assumption that trait variance is driven by many loci of infinitesimal effects throughout the genome. This appro…
Evolution of a trait distributed over a large fragmented population: Propagation of chaos meets adaptive dynamics
本文研究大型片段化集合种群中的数量性状演化，通过混沌传播与自适应动力学建立空间Moran模型的积分微分及McKean–Vlasov极限，并导出含选择、漂变与迁移效应的新正则方程。
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population of discrete individuals characterized by one or several adaptive traits. The population is modelled as a stochastic point process whose generator captures the probabilistic dynamics over continuous time of birth, mutation, and death, as influenced by each individual's trait values, and interactions between individuals. An offspring usually inherits the trai…
Cultural traits such as words, names, decorative styles, and technical standards often assume arbitrary values and are thought to evolve neutrally. But neutral evolution cannot explain why some traits come and go in cycles of popularity while others become entrenched. Here we study frequency-dependent selection (FDS)--where a trait's tendency to be copied depends on its current frequency regardless of the trait value itself. We develop a maximum-likelihood method to infer the precise form of FDS from time series of trait abundance, and we apply the method to data on baby names and pet dog bree…
Non-selective effects, like genetic drift, are an important factor in modern conceptions of evolution, and have been extensively studied for constant population sizes. Here, we consider non-selective evolution in the case of growing populations that are of small size and have varying trait compositions (e.g. after a population bottleneck). We find that, in these conditions, populations never fixate to a trait, but tend to a random limit composition, and that the distribution of compositions 'freezes' to a steady state This final state is crucially influenced by the initial conditions. We obtai…
The gene's-eye view of quantitative genetics
本文从基因视角出发，通过有限位点模型探讨连续性状的进化，利用麦肯纳-瓦拉斯科斯随机微分方程和福克-普朗克方程分析极限行为，揭示了选择对典型位点的影响及等位频率的稳态分布。
The adaptation of biological species to their environment depends on their traits. When various biological processes occur (survival, reproduction, migration, etc.), the trait distribution may change with respect to time and space. In the context of invasions, when considering the evolution of a heritable trait that encodes the dispersive ability of individuals, the trait distribution develops a particular spatial structure that leads to the acceleration of the front propagation. That phenomenon is known as spatial sorting. Many biological examples can be cited like the bush cricket in Britain…
Evaluating Phylogenetic Comparative Methods under Reticulate Evolutionary Scenarios
本文研究了在网状进化情景下系统发育比较方法的性能，发现杂交和快速进化特征导致估计误差增加，提出了研究复杂进化历史系统的建议。
The distribution and heritability of many traits depends on numerous loci in the genome. In general, the astronomical number of possible genotypes makes the system with large numbers of loci difficult to describe. Multilocus evolution, however, greatly simplifies in the limit of weak selection and frequent recombination. In this limit, populations rapidly reach Quasi-Linkage Equilibrium (QLE) in which the dynamics of the full genotype distribution, including correlations between alleles at different loci, can be parameterized by the allele frequencies. This review provides a simplified exposit…
Sol argues that innovation propensity is not a specialized adaptation resulting from targeted selection but an instance of exaptation because selection cannot act on situations that are only encountered once. In exaptation, a trait that originally evolved to solve one problem is co-opted to solve a new problem; thus the trait or traits in question must be necessary and sufficient to solve the new problem. Sol claims that traits such as persistence and neophilia, are necessary and sufficient for animal innovation, which is a matter of trial and error. We suggest that this explanation does not e…
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of individuals to infinity we obtain a nonlinear transport equation, which describes the evolution of distribution of phenotypic traits. Existence of an one-dimensional attractor is proved and the formula for the density of phenotypic traits in the limiting (asymptotic) population is derived in some particular case.
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the population is driven by births, deaths, competition, and mutations along the edges of $G$. We are interested in the large population limit under a mutation rate $μ_K$ given by a negative power of the carrying capacity $K$ of the system: $μ_K=K^{-1/α},α>0$. This results in several mutant traits being present at the same time and competing for invading the resid…
Understanding which phenotypic traits are consistently correlated throughout evolution is a highly pertinent problem in modern evolutionary biology. Here, we propose a multivariate phylogenetic latent liability model for assessing the correlation between multiple types of data, while simultaneously controlling for their unknown shared evolutionary history informed through molecular sequences. The latent formulation enables us to consider in a single model combinations of continuous traits, discrete binary traits and discrete traits with multiple ordered and unordered states. Previous approache…
The genetic and developmental enigma of rhizomes: crucial traits with limited understanding
研究揭示 rhizomes 的遗传和发育调控机制，强调植物激素的作用及多基因控制，提出 Mimulus 作为研究模型，推动 rhizome 发展的多组学整合方法。
Causes and consequences of dispersal in biodiverse spatially structured systems: what is old and what is new?
本文探讨单物种扩散进化理论在生物多样性空间结构化系统中的适用性，提出性状维度增加和协同扩散会调节扩散进化，并推测其可能导致进化更慢且更弥散。
The evolution of cooperation often depends upon population structure, yet nearly all models of cooperation implicitly assume that this structure remains static. This is a simplifying assumption, because most organisms possess genetic traits that affect their population structure to some degree. These traits, such as a group size preference, affect the relatedness of interacting individuals and hence the opportunity for kin or group selection. We argue that models that do not explicitly consider their evolution cannot provide a satisfactory account of the origin of cooperation, because they can…
We present a model for the dynamics of a population of bacteria with a continuum of traits, who compete for resources and exchange horizontally (transfer) an otherwise vertically inherited trait with possible mutations. Competition influences individual demographics, affecting population size, which feeds back on the dynamics of transfer. We consider a stochastic individual-based pure jump process taking values in the space of point measures, and whose jump events describe the individual reproduction, transfer and death mechanisms. In a large population scale, the stochastic process is proved …
When can we reconstruct the ancestral state? Beyond Brownian motion
本文将祖先状态准确重建的 big bang 条件从 Brownian motion 等模型推广到满足正则性条件的一般连续性状随机进化过程，并验证了多个常用模型。
Stochastic niche-based models for the evolution of species
本研究扩展了Price的适应性辐射模型，通过增加生态位维度并引入物种灭绝与生态位移除机制，利用连续时间随机过程生成系统发育树，并借助多种统计量评估其现实性。
Hierarchical Conditioning of Diffusion Models Using Tree-of-Life for Studying Species Evolution
本文提出Phylo-Diffusion框架，将生命之树的层级嵌入用于条件化扩散模型，并通过性状掩蔽与交换实验，从图像中可视化并揭示鱼类和鸟类的演化性状变异机制。
We consider a stochastic model for the evolution of a discrete population structured by a trait with values on a finite grid of the torus, and with mutation and selection. Traits are vertically inherited unless a mutation occurs, and influence the birth and death rates. We focus on a parameter scaling where population is large, individual mutations are small but not rare, and the grid mesh for the trait values is much smaller than the size of mutation steps. When considering the evolution of the population in a long time scale, the contribution of small sub-populations may strongly influence t…
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