This manuscript contains nothing new, but synthesizes known results: For the theoretical population geneticist with a probabilistic background, we provide a summary of some key results on stochastic differential equations. For the evolutionary game theorist, we give a new perspective on the derivations of results obtained when using discrete birth-death processes. For the theoretical biologist familiar with deterministic modeling, we outline how to derive and work with stochastic versions of classical ecological and evolutionary processes.
Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these models revolve around speciation, dispersal, and extinction, but they usually neglect trophic structure. Here, we propose and study a spatially extended evolutionary food web model that allows us to study large spatial systems with several trophic layers. Our computer simulations show that the model gives rise simultaneously to several biodiversity patterns …
The central goal of a dynamical theory of evolution is to abstract the mean evolutionary trajectory in the trait space by considering ecological processes at the level of the individual. In this work, we develop such a theory for a new class of deterministic individual based models describing individual births and deaths, which captures the essential features of standard stochastic individual-based models and become identical with the latter under maximal competition. The key motivation is to derive the canonical equation of adaptive dynamics from this microscopic ecological model, which can b…
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…
A biologically motivated individual-based framework for evolution in network-structured populations is developed that can accommodate eco-evolutionary dynamics. This framework is used to construct a network birth and death model. The evolutionary graph theory model, which considers evolutionary dynamics only, is derived as a special case, highlighting additional assumptions that diverge from real biological processes. This is achieved by introducing a negative ecological feedback loop that suppresses ecological dynamics by forcing births and deaths to be coupled. We also investigate how fitnes…
Science at Risk: The Urgent Need for Institutional Support of Long-Term Ecological and Evolutionary Research in an Era of Data Manipulation and Disinformation
Social dilemmas are an integral part of social interactions. Cooperative actions, ranging from secreting extra-cellular products in microbial populations to donating blood in humans, are costly to the actor and hence create an incentive to shirk and avoid the costs. Nevertheless, cooperation is ubiquitous in nature. Both costs and benefits often depend non-linearly on the number and types of individuals involved -- as captured by idioms such as `too many cooks spoil the broth' where additional contributions are discounted, or `two heads are better than one' where cooperators synergistically en…
Taylor's Law (TL) relates the variance to the mean of a random variable via power law. In ecology it applies to populationsand it is a common empirical pattern shared among different ecosystems. Measurements give power law exponent to be between 1 and 2, and more often to cluster around 2, whereas theoretical models predict TL exponent can assume any real value. In this paper, adopting the framework of multiplicative growth models in a Markovian environment, we investigate the possibility of evolutionary strategies to be responsible for TL exponent to be in a finite range. We implement three d…
Mitochondrial and nuclear genomes must be co-adapted to ensure proper cellular respiration and energy production. Mito-nuclear incompatibility reduces individual fitness and induces hybrid infertility, suggesting a possible role in reproductive barriers and speciation. Here we develop a birth-death model for evolution in spatially extended populations under selection for mito-nuclear co-adaptation. Mating is constrained by physical and genetic proximity, and offspring inherit nuclear genomes from both parents, with recombination. The model predicts macroscopic patterns including a community's …
Marine viruses shape the structure of the microbial community. They are, thus, a key determinant of the most important biogeochemical cycles in the planet. Therefore, a correct description of the ecological and evolutionary behavior of these viruses is essential to make reliable predictions about their role in marine ecosystems. The infection cycle, for example, is indistinctly modeled in two very different ways. In one representation, the process is described including explicitly a fixed delay between infection and offspring release. In the other, the offspring are released at exponentially d…
Residential mobility is deeply entangled with all aspects of hunter-gatherer life ways, and is therefore an issue of central importance in hunter-gatherer studies. Hunter-gatherers vary widely in annual rates of residential mobility, and understanding the sources of this variation has long been of interest to anthropologists and archaeologists. Since mobility is, to a large extent, driven by the need for a continuous supply of food, a natural framework for addressing this question is provided by the metabolic theory of ecology. This provides a powerful framework for formulating formal testable…
The mechanisms underlying eco-evolutionary dynamics (the feedback between ecological and evolutionary processes) are often unknown. Here, we propose that classical theory from behavioral ecology can provide a greater understanding of the mechanisms underlying eco-evolutionary dynamics, and thus improve predictions about the outcomes of these dynamics.
One of the properties that make ecological systems so unique is the range of complex behavioural patterns that can be exhibited by even the simplest communities with only a few species. Much of this complexity is commonly attributed to stochastic factors which have very high-degrees of freedom. Orthodox study of the evolution of these simple networks has generally been limited in its ability to explain complexity, since it restricts evolutionary adaptation to an inertia-free process with few degrees of freedom in which only gradual, moderately complex behaviours are possible. We propose a mode…
Evolutionary and ecosystem dynamics are often treated as different processes --operating at separate timescales-- even if evidence reveals that rapid evolutionary changes can feed back into ecological interactions. A recent long-term field experiment has explicitly shown that communities of competing plant species can experience very fast phenotypic diversification, and that this gives rise to enhanced complementarity in resource exploitation and to enlarged ecosystem-level productivity. Here, we build on progress made in recent years in the integration of eco-evolutionary dynamics, and presen…
Identifying undocumented or potential future interactions among species is a challenge facing modern ecologists. Recent link prediction methods rely on trait data, however large species interaction databases are typically sparse and covariates are limited to only a fraction of species. On the other hand, evolutionary relationships, encoded as phylogenetic trees, can act as proxies for underlying traits and historical patterns of parasite sharing among hosts. We show that using a network-based conditional model, phylogenetic information provides strong predictive power in a recently published g…
1. Theoretical models pertaining to feedbacks between ecological and evolutionary processes are prevalent in multiple biological fields. An integrative overview is currently lacking, due to little crosstalk between the fields and the use of different methodological approaches. 2. Here we review a wide range of models of eco-evolutionary feedbacks and highlight their underlying assumptions. We discuss models where feedbacks occur both within and between hierarchical levels of ecosystems, including populations, communities, and abiotic environments, and consider feedbacks across spatial scales. …
The networks of predator-prey interactions in ecological systems are remarkably complex, but nevertheless surprisingly stable in terms of long term persistence of the system as a whole. In order to understand the mechanism driving the complexity and stability of such food webs, we developed an eco-evolutionary model in which new species emerge as modifications of existing ones and dynamic ecological interactions determine which species are viable. The food-web structure thereby emerges from the dynamical interplay between speciation and trophic interactions. The proposed model is less abstract…
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）
Reinforcement Learning for Control of Evolutionary and Ecological Processes
Mathematical Medicine Group, Stanford University（斯坦福大学数学医学组）；Department of Neurosurgery, Stanford Medical School（斯坦福医学院神经外科部门）；Physician-Scientist Training Program, Stanford Medical School（斯坦福医学院医师-科学家培训计划）；Maternal & Child Health Research Institute, Stanford University School of Medicine（斯坦福大学医学院母婴健康研究所）；Stanford Cancer Institute, Stanford University School of Medicine（斯坦福大学医学院癌症研究所）
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 t…
The evolutionary spread of cheater strategies can destabilize populations engaging in cooperative behaviors, thus demonstrating that evolutionary changes can have profound implications for populations dynamics. At the same time, the relative fitness of cooperative traits often depends upon population density, thus leading to the potential for bidirectional coupling between population density and the evolution of a cooperative trait. Despite the potential importance of these eco evolutionary feedback loops, they have not yet been demonstrated experimentally in social species and their ecologica…
This paper proposed a discrete stochastic dynamic programming (SDP) model for sustainable ecosystem (SE) planning of the Loess Plateau in Northwestern, China, and analyzed the ecological resource planning by the evolutionary game model in the decision-making process. The main objective is to explore a new approach of SE planning from a viewpoint of discrete SDP and evolutionary game theory, with a specific application in the area of ecological resource planning such as water management problems. In contrast to previous work, the proposed SDP method focuses on the transition probability matrix …
Understanding how the structure of community interactions is modified by coevolution is vital for understanding system responses to change at all scales. However, in absence of a group selection process, collective community behaviours cannot be organised or adapted in a Darwinian sense. An open question thus persists: are there alternative organising principles that enable us to understand how coevolution of component species creates complex collective behaviours exhibited at the community level? We address this issue using principles from connectionist learning, a discipline with well-develo…
Evolutionary tradeoff and equilibrium in an aquatic predator-prey system
由于生态（快速）和进化（缓慢）时间尺度之间的传统区别，迄今为止的生态和人口模型通常忽略了进化的影响。然而，最近已经确定了快速进化变化的潜力，这对于理解种群如何适应不断变化的环境可能至关重要。在本文中，我们研究生态和演化动力学之间的关系，重点是一个充分研究的实验水生捕食者-猎物系统（Fussmann et al. 2000; Shertzer et al. 2002; Yoshida et al. 2003）。食饵种群的持续演化动力学决定了该系统中捕食-食饵循环的主要性质。然而，在某些条件下，人口倾向于明显稳定的稳态密度。这就是本文件的主题。我们研究了以前开发的系统模型，以确定如何演变形状的平衡，特别是数量和身份共存的猎物基因型的属性。然后，我们应用这些结果来探索如何演化动力学可以塑造系统的“管理”的反应：外部强加的条件的改变。具体来说，我们比较了系统的行为，包括演化动力学，预测，如果快速进化变化的潜力是不确定的。最后，我们通过一些简单的实验来验证我们的预测，即进化可以对观察到的种群水平对变化条件的反应产生显着的定性影响。
To examine the co-evolution of quantitative traits in hosts and parasites, we present and study a co-evolutionary model of a social parasite-host system that incorporates (1) ecological dynamics that feed back into their co-evolutionary outcomes; (2) variation in whether the parasite is obligate or facultative; and (3) Holling Type II functional responses between host and parasite, which are particularly suitable for social parasites that face time costs for host location and its social manipulation. We perform local and global analyses for the co-evolutionary model and the corresponding ecolo…
Until recently, much of the microbial world was hidden from view. A global research effort has changed this, unveiling and quantifying microbial diversity across enormous range of critically-important contexts, from the human microbiome, to plant-soil interactions, to marine life. Yet what has remained largely hidden is the interplay of ecological and evolutionary processes that led to the diversity we observe in the present day. We introduce a theoretical framework to quantify the effect of ecological innovations in microbial evolutionary history, using a new, coarse-grained approach that is …
Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecological…
Predators often consume multiple prey and by mutually subsidizing a shared predator, the prey may reciprocally harm each other. When predation levels are high, this apparent competition can culminate in a prey species being displaced. Coupling quantitative genetics and Lotka-Volterra models, we study how predator evolution alters this and other ecological outcomes. These models account for a trade-off between the predator's attack rates on two prey species. We provide a mathematical characterization of a strong form of persistence--permanence--for which there is a global attractor bounded away…
Evolutionary transitions among ecological interactions are widely known, although their detailed dynamics remain absent for most population models. Adaptive dynamics has been used to illustrate how the parameters of population models might shift through evolution, but within an ecological regime. Here we use adaptive dynamics combined with a generalised logistic model of population dynamics to show that transitions of ecological interactions might appear as a consequence of evolution. To this purpose we introduce a two-microbial toy model in which population parameters are determined by a book…
The processes of ecological interactions, dispersal and mutations shape the dynamics of biological communities, and analogous eco-evolutionary processes acting upon economic entities have been proposed to explain economic change. This hypothesis is compelling because it explains economic change through endogenous mechanisms, but it has not been quantitatively tested at the global economy level. Here, we use an inverse modelling technique and 59 years of economic data covering 77 countries to test whether the collective dynamics of national economic activities can be characterised by eco-evolut…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on interactions between individuals within the population. This should be reflected in fluctuations of the population size even in constant environments. Here, we propose a stochastic model, which naturally combines these two evolutionary ingredients by assuming frequency dependent competition between different types in an individual-based model. In contrast to previous…
This paper further develops work from a previous article which introduced a new way of modelling evolutionary game models with an emphasis on ecological realism, concerned with how ecological factors determine payoffs in evolutionary games. The current paper is focused on the impact of selectively neutral factors (i.e. those that are the same for all strategies), such as background fitness and a neutral density dependence on game dynamics. In the previous paper background mortality was modelled by post-reproductive mortality describing aggregated mortality between game interactions. In this pa…
We perform individual-based Monte Carlo simulations in a community consisting of two predator species competing for a single prey species, with the purpose of studying biodiversity stabilization in this simple model system. Predators are characterized with predation efficiency and death rates, to which Darwinian evolutionary adaptation is introduced. Competition for limited prey abundance drives the populations' optimization with respect to predation efficiency and death rates. We study the influence of various ecological elements on the final state, finding that both indirect competition and …
How the neutral diversity is affected by selection and adaptation is investigated in an eco-evolutionary framework. In our model, we study a finite population in continuous time, where each individual is characterized by a trait under selection and a completely linked neutral marker. Population dynamics are driven by births and deaths, mutations at birth, and competition between individuals. Trait values influence ecological processes (demographic events, competition), and competition generates selection on trait variation, thus closing the eco-evolutionary feedback loop. The demographic effec…
Ecological and evolutionary processes show various population dynamics depending on internal interactions and environmental changes. While crucial in predicting biological processes, discovering general relations for such nonlinear dynamics has remained a challenge. Here, we derive a universal information-theoretical constraint on a broad class of nonlinear dynamical systems represented as population dynamics. The constraint is interpreted as a generalization of Fisher's fundamental theorem of natural selection. Furthermore, the constraint indicates nontrivial bounds for the speed of critical …
The cryptocurrency market surpassed the barrier of \$100 billion market capitalization in June 2017, after months of steady growth. Despite its increasing relevance in the financial world, however, a comprehensive analysis of the whole system is still lacking, as most studies have focused exclusively on the behaviour of one (Bitcoin) or few cryptocurrencies. Here, we consider the history of the entire market and analyse the behaviour of 1,469 cryptocurrencies introduced between April 2013 and June 2017. We reveal that, while new cryptocurrencies appear and disappear continuously and their mark…
The purpose of this roadmap article is to draw attention to a paradigm shift in our understanding of evolution towards a perspective of ecological-evolutionary feedback, highlighted through two recent highly simplified examples of rapid evolution. The first example focuses primarily on population dynamics: anomalies in population cycles can reflect the influence of strong selection and the interplay with mutations. The second focuses primarily on the way in which ecological structure can potentially be influenced by what is arguably the most powerful source of genetic novelty: horizontal gene …
Deterministic continuum models formulated in terms of non-local partial differential equations for the evolutionary dynamics of populations structured by phenotypic traits have been used recently to address open questions concerning the adaptation of asexual species to periodically fluctuating environmental conditions. These deterministic continuum models are usually defined on the basis of population-scale phenomenological assumptions and cannot capture adaptive phenomena that are driven by stochastic variability in the evolutionary paths of single individuals. In this paper, we develop a sto…
The basic mechanics of evolution have been understood since Darwin. But debate continues over whether macroevolutionary phenomena are driven primary by the fitness structure of genotype space or by ecological interaction. In this paper we propose a simple, abstract model capturing some key features of fitness-landscape and ecological models of evolution. Our model describes evolutionary dynamics in a high-dimensional, structured genotype space with a significant role for interspecific interaction. We find some promising qualitative similarity with the empirical facts about macroevolution, incl…
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…
The dynamics of species' densities depend both on internal and external variables. Internal variables include frequencies of individuals exhibiting different phenotypes or living in different spatial locations. External variables include abiotic factors or non-focal species. These internal or external variables may fluctuate due to stochastic fluctuations in environmental conditions. We prove theorems for stochastic persistence and exclusion for stochastic ecological difference equations accounting for internal and external variables. Specifically, we use a stochastic analog of average Lyapuno…
When studying the dynamics of trait distribution of populations in a heterogeneous environment, classical models from quantitative genetics choose to look at its system of moments, specifically the first two ones. Additionally, in order to close the resulting system of equations, they often assume that the trait distribution is Gaussian (see for instance Ronce and Kirkpatrick 2001). The aim of this paper is to introduce a mathematical framework that follows the whole trait distribution (without prior assumption) to study evolutionary dynamics of sexually reproducing populations. Specifically, …
In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes…
The theory of life history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens in both epidemic and endemic situations. This framework, however, relies on the assumption that pathogen populations are very large and that one can neglect the effects of demographic stochasticity. Here we expand the theory of life history evolution to account for the effects of finite population size on the evolution of pathogen virulence. We show that demographic stochasticity introduces additional evolutionary forces that can qualitatively affect the dynamics and the evol…
