1) Micro-evolutionary predictions are complicated by ecological feedbacks like density dependence, while ecological predictions can be complicated by evolutionary change. A widely used approach in micro-evolution, quantitative genetics, struggles to incorporate ecological processes into predictive models, while structured population modelling, a tool widely used in ecology, rarely incorporates evolution explicitly.
2) In this paper we develop a flexible, general framework that links quantitative genetics and structured population models. We use the quantitative genetic approach to write down the phenotype as an additive map. We then construct integral projection models for each component of the phenotype. The dynamics of the distribution of the phenotype are generated by combining distributions of each of its components. Population projection models can be formulated on per generation or on shorter time steps.
3) We introduce the framework before developing example models with parameters chosen to exhibit specific dynamics. These models reveal (i) how evolution of a phenotype can cause populations to move from one dynamical regime to another (e.g. from stationarity to cycles), (ii) how additive genetic variances and covariances (the G matrix) are expected to evolve over multiple generations, (iii) how changing heritability with age can maintain additive genetic variation in the face of selection and (iii) life history, population dynamics, phenotypic characters and parameters in ecological models will change as adaptation occurs.
4) Our approach unifies population ecology and evolutionary biology providing a framework allowing a very wide range of questions to be addressed. The next step is to apply the approach to a variety of laboratory and field systems. Once this is done we will have a much deeper understanding of eco-evolutionary dynamics and feedbacks.
We give a overview of stochastic models of evolution that have found applications in genetics, ecology and linguistics for an audience of nonspecialists, especially statistical physicists. In particular, we focus mostly on neutral models in which no intrinsic advantage is ascribed to a particular type of the variable unit, for example a gene, appearing in the theory. In many cases these models are exactly solvable and furthermore go some way to describing observed features of genetic, ecological and linguistic systems.
Patterns of biodiversity predicted by the neutral theory rely on a simple phenomenological model of speciation. To further investigate the effect of speciation on neutral biodiversity, we analyze a spatially-explicit neutral model based on population genetics. We define the metacommunity as a system of populations exchanging migrants and we use this framework to introduce speciation with little or no gene flow (allopatric and parapatric speciation). We find that with realistic mutation rates, our metacommunity model driven by neutral processes cannot support more than a few species. Adding nat…
A birth-death process is a continuous-time Markov chain that counts the number of particles in a system over time. In the general process with $n$ current particles, a new particle is born with instantaneous rate $λ_n$ and a particle dies with instantaneous rate $μ_n$. Currently no robust and efficient method exists to evaluate the finite-time transition probabilities in a general birth-death process with arbitrary birth and death rates. In this paper, we first revisit the theory of continued fractions to obtain expressions for the Laplace transforms of these transition probabilities and make …
Populations can be genetically isolated both by geographic distance and by differences in their ecology or environment that decrease the rate of successful migration. Empirical studies often seek to investigate the relationship between genetic differentiation and some ecological variable(s) while accounting for geographic distance, but common approaches to this problem (such as the partial Mantel test) have a number of drawbacks. In this article, we present a Bayesian method that enables users to quantify the relative contributions of geographic distance and ecological distance to genetic diff…
The biological world, especially its majority microbial component, is strongly interacting and may be dominated by collective effects. In this review, we provide a brief introduction for statistical physicists of the way in which living cells communicate genetically through transferred genes, as well as the ways in which they can reorganize their genomes in response to environmental pressure. We discuss how genome evolution can be thought of as related to the physical phenomenon of annealing, and describe the sense in which genomes can be said to exhibit an analogue of information entropy. As …
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…
We have developed a mathematical model that captures stress-induced mutagenesis, a fundamental aspect of pathogenic and neoplastic evolutionary dynamics, on the fitness landscape with multiple relevant genetic traits as a high-dimensional Euclidean space. In this framework, stress-induced mutagenesis manifests as a heterogeneous diffusion process. We show how increasing mutations, and thus reducing exploitation, in a static ecology with fixed carrying capacity and maximum growth rates, can paradoxically boost population size. Remarkably, this unexpected biophysical phenomenon applies universal…
The ability of random environmental variation to stabilize competitor coexistence was pointed out long ago and, in recent years, has received considerable attention. Analyses have focused on variations in the log-abundances of species, with mean logarithmic growth rates when rare, $\mathbb{E}[r]$, used as metrics for persistence. However, invasion probabilities and the times to extinction are not single-valued functions of $\mathbb{E}[r]$ and, in some cases, decrease as $\mathbb{E}[r]$ increases. Here, we present a synthesis of stochasticity-induced stabilization (SIS) phenomena based on the r…
Many questions that we have about the history and dynamics of organisms have a geographical component: How many are there, and where do they live? How do they move and interbreed across the landscape? How were they moving a thousand years ago, and where were the ancestors of a particular individual alive today? Answers to these questions can have profound consequences for our understanding of history, ecology, and the evolutionary process. In this review, we discuss how geographic aspects of the distribution, movement, and reproduction of organisms are reflected in their pedigree across space …
Integrating population genetics into community ecology theory is a major goal in ecology and evolution, but analyzing the resulting models is computationally daunting. Here we describe sPEGG ($\underline{\textrm{s}}\textrm{imulating}$ $\underline{\textrm{P}}\textrm{henotypic}$ $\underline{\textrm{E}}\textrm{volution}$ on $\underline{\textrm{G}}\textrm{eneral Purpose}$ $\underline{\textrm{G}}\textrm{raphics Processing Units}$ (GPGPUs)), an open-source, multi-species forward-time population genetics simulator. Using a single commodity GPGPU instead of a single central processor, we find sPEGG ca…
Both evolution and ecology have long been concerned with the impact of variable environmental conditions on observed levels of genetic diversity within and between species. We model the evolution of a quantitative trait under selection that fluctuates in space and time, and derive an analytical condition for when these fluctuations promote genetic diversification. As ecological scenario we use a generalized island model with soft selection within patches in which we incorporate generation overlap. We allow for arbitrary fluctuations in the environment including spatio-temporal correlations and…
Whether or not biodiversity dynamics tend toward stable equilibria remains an unsolved question in ecology and evolution with important implications for our understanding of diversity and its conservation. Phylo/population genetic models and macroecological theory represent two primary lenses through which we view biodiversity. While phylo/population genetics provide an averaged view of changes in demography and diversity over timescales of generations to geological epochs, macroecology provides an ahistorical description of commonness and rarity across contemporary co-occurring species. Our g…
Evolution is the fundamental physical process that gives rise to biological phenomena. Yet it is widely treated as a subset of population genetics, and thus its scope is artificially limited. As a result, the key issues of how rapidly evolution occurs, and its coupling to ecology have not been satisfactorily addressed and formulated. The lack of widespread appreciation for, and understanding of, the evolutionary process has arguably retarded the development of biology as a science, with disastrous consequences for its applications to medicine, ecology and the global environment. This review fo…
Markov chains are a common framework for individual-based state and time discrete models in ecology and evolution. Their use, however, is largely limited to systems with a low number of states, since the transition matrices involved pose considerable challenges as their size and their density increase. Big, dense transition matrices may easily defy both the computer's memory and the scientists' ability to interpret them, due to the very high amount of information they contain; yet approximations using other types of models are not always the best solution. We propose a set of methods to overco…
Evolution has fascinated quantitative and physical scientists for decades: how can the random process of mutation, recombination, and duplication of genetic information generate the diversity of life? What determines the rate of evolution? Are there quantitative laws that govern and constrain evolution? Is evolution repeatable or predictable? Historically, the study of evolution involved classifying and comparing species, typically based on morphology. In addition to phenotypes on the organismal and molecular scales, we now use whole-genome sequencing to uncover not only the differences betwee…
Continuous-time birth-death-shift (BDS) processes are frequently used in stochastic modeling, with many applications in ecology and epidemiology. In particular, such processes can model evolutionary dynamics of transposable elements - important genetic markers in molecular epidemiology. Estimation of the effects of individual covariates on the birth, death, and shift rates of the process can be accomplished by analyzing patient data, but inferring these rates in a discretely and unevenly observed setting presents computational challenges. We propose a mutli-type branching process approximation…
Neutral models, in which individual agents with equal fitness undergo a birth-death-mutation process, are very popular in population genetics and community ecology. Usually these models are applied to populations and communities with spatial structure, but the analytic results presented so far are limited to well-mixed or mainland-island scenarios. Here we present a new technique, based on interface dynamics analysis, and apply it to the neutral dynamics in one, two and three spatial dimensions. New results are derived for the correlation length and for the main characteristics of the communit…
The growth and evolution of microbial populations is often subjected to advection by fluid flows in spatially extended environments, with immediate consequences for questions of spatial population genetics in marine ecology, planktonic diversity and origin of life scenarios. Here, we review recent progress made in understanding this rich problem in the simplified setting of two competing genetic microbial strains subjected to fluid flows. As a pedagogical example we focus on antagonsim, i.e., two killer microorganism strains, each secreting toxins that impede the growth of their competitors (c…
The identification of key populations shaping the structure and connectivity of metapopulation systems is a major challenge in population ecology. The use of molecular markers in the theoretical framework of population genetics has allowed great advances in this field, but the prime question of quantifying the role of each population in the system remains unresolved. Furthermore, the use and interpretation of classical methods are still bounded by the need for a priori information and underlying assumptions that are seldom respected in natural systems. Network theory was applied to map the gen…
The diffusion approximation (DA) is widely used in the analysis of stochastic population dynamics, from population genetics to ecology and evolution. DA is an uncontrolled approximation that assumes the smoothness of the calculated quantity over the relevant state space and fails when this property is not satisfied. This failure becomes severe in situations where the direction of selection switches sign. Here we employ the WKB (large-deviations) method, which requires only the logarithm of a given quantity to be smooth over its state space. Combining the WKB scheme with asymptotic matching tec…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts even if the system is away from the bifurcation points. In this paper, we propose a new quantitative measure, namely, the propensity transition point as an indicator of stochastic regime shifts. The concepts and the methodology are illustrated for the one-variable May model, a well-known model in ecology and the genetic toggle, a two-variable model of a simpl…
Population dynamics and evolutionary genetics underly the structure of ecosystems, changing on the same timescale for interacting species with rapid turnover, such as virus (e.g. HIV) and immune response. Thus, an important problem in mathematical modeling is to connect ecology, evolution and genetics, which often have been treated separately. Here, extending analysis of multiple virus and immune response populations in a resource - prey (consumer) - predator model from Browne and Smith \cite{browne2018dynamics}, we show that long term dynamics of viral mutants evolving resistance at distinct …
It is becoming widely accepted that very early in the origin of life, even before the emergence of genetic encoding, reaction networks of diverse small chemicals might have manifested key properties of life, namely self-propagation and adaptive evolution. To explore this possibility, we formalize the dynamics of chemical reaction networks within the framework of chemical ecosystem ecology. To capture the idea that life-like chemical systems are maintained out of equilibrium by fluxes of energy-rich food chemicals, we model chemical ecosystems in well-mixed containers that are subject to consta…
Emergent frequency-dependent selection predicts mutation outcomes in complex ecological communities
MIT Center for Theoretical Physics - a Leinweber Institute（麻省理工学院理论物理中心（莱因韦伯研究所））；Department of Physics, Boston University（波士顿大学物理系）；International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（塔塔基础研究院国际理论科学中心）；Faculty of Computing and Data Sciences, Boston University（波士顿大学计算与数据科学学院）
We investigate the stochastic dynamics of entities which are confined to a set of islands, between which they migrate. They are assumed to be one of two types, and in addition to migration, they also reproduce and die. Systems which fall into this class are common in biology and social science, occurring in ecology, population genetics, epidemiology, biochemistry, linguistics, opinion dynamics, and other areas. In all these cases the governing equations are intractable, consisting as they do of multidimensional Fokker-Planck equations or, equivalently, coupled nonlinear stochastic differential…
Population structure can be modelled by evolutionary graphs, which can have a substantial, but very subtle influence on the fate of the arising mutants. Individuals are located on the nodes of these graphs, competing with each other to eventually take over the graph via the links. Many applications for this framework can be envisioned, from the ecology of river systems and cancer initiation in colonic crypts to biotechnological search for optimal mutations. In all these applications, it is not only important where and when novel variants arise and how likely it is that they ultimately take ove…
The unwelcome evolution of malignancy during cancer progression emerges through a selection process in a complex heterogeneous population structure. In the present work, we investigate evolutionary dynamics in a phenotypically heterogeneous population of stem cells (SCs) and their associated progenitors. The fate of a malignant mutation is determined not only by overall stem cell and differentiated cell growth rates but also differentiation and dedifferentiation rates. We investigate the effect of such a complex population structure on the evolution of malignant mutations. We derive exact anal…
Populations are made up of an integer number of individuals and are subject to stochastic birth-death processes whose rates may vary in time. Useful quantities, like the chance of ultimate fixation, satisfy an appropriate difference (master) equation, but closed-form solutions of these equations are rare. Analytical insights in fields like population genetics, ecology and evolution rely, almost exclusively, on an uncontrolled application of the diffusion approximation (DA) which assumes the smoothness of the relevant quantities over the set of integers. Here we combine asymptotic matching tech…
In large clonal populations, several clones generally compete which results in complex evolutionary and ecological dynamics: experiments show successive selective sweeps of favorable mutations as well as long-term coexistence of multiple clonal strains. The mechanisms underlying either coexistence or fixation of several competing strains have rarely been studied altogether. Conditions for coexistence have mostly been studied by population and community ecology, while rates of invasion and fixation have mostly been studied by population genetics. In order to provide a global understanding of th…
University of Wisconsin–Madison（威斯康星大学麦迪逊分校）；University of Bath（巴斯大学）；CNRS, Université Paris-Saclay, AgroParisTech（法国国家科学研究中心，巴黎萨克雷大学，农业巴黎技术学院）；The University of Rhode Island（罗德岛大学）；University of Connecticut（康涅狄格大学）；University of Bristol（布里斯托大学）；Royal Netherlands Institute for Sea Research（荷兰皇家海洋研究所）；University of Amsterdam（阿姆斯特丹大学）；Virginia Tech（弗吉尼亚理工大学）；University of Minnesota（明尼苏达大学）；Stanford University（斯坦福大学）；Woods Hole Oceanographic Institution（伍兹霍尔海洋研究所）；University of Pittsburgh（匹兹堡大学）；Yale University（耶鲁大学）；University of California, Riverside（加州大学河滨分校）；University of Texas at Austin（德克萨斯大学奥斯汀分校）；University of Colorado, Boulder（科罗拉多大学博尔德分校）；National Library of Medicine, National Institutes of Health（美国国家医学图书馆，美国国立卫生研究院）；Arizona State University（亚利桑那州立大学）
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…
