Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and regressions. Population genetic equations depend on genetic variances. How can we read those statistical expressions with respect to the meaning of natural selection? One possibility is to relate the statistical expressions to the amount of information that populations accumulate by selection. However, the connection between selection and information theory has never been compelling. Here, I show the correct relations between statistical expressions for selection and information theory expressions for selection. Those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics and communication. We can now read the equations of selection in terms of their natural meaning. Selection causes populations to accumulate information about the environment.     

Surrogate marker evaluation from an information theory perspective

The last 20 years have seen lots of work in the area of surrogate marker validation, partly devoted to frame the evaluation in a multitrial framework, leading to definitions in terms of the quality of trial- and individual-level association between a potential surrogate and a true endpoint (Buyse et al., 2000, Biostatistics 1, 49-67). A drawback is that different settings have led to different measures at the individual level. Here, we use information theory to create a unified framework, leading to a definition of surrogacy with an intuitive interpretation, offering interpretational advantages, and applicable in a wide range of situations. Our method provides a better insight into the chances of finding a good surrogate endpoint in a given situation. We further show that some of the previous proposals follow as special cases of our method. We illustrate our methodology using data from a clinical study in psychiatry.     

合成微生物体系研究进展

合成微生物体系作为自下而上构建的人工合成微生物群落,相比于自然微生物群落具有复杂度低及可控性、可操作性强等特点。其作为新兴的生物技术,综合借鉴了合成生物学、系统生物学、生物进化等知识,通过合理的设计、规划与调控,成为研究微生物生态学理论的实验平台,以及验证已知理论的微生物系统。本文首先简单介绍了合成微生物体系的概念及其由来,阐述了其基本构建原则,随后介绍了其生态学理论基础,并总结概括了近年来的实际应用,最后提出合成微生物体系的发展前景,包括需要设计构建更为复杂的人工合成微生物群落,以及优化生态模型。     

Autonomy: an information theoretic perspective

We present a tentative proposal for a quantitative measure of autonomy. This is something that, surprisingly, is rarely found in the literature, even though autonomy is considered to be a basic concept in many disciplines, including artificial life. We work in an information theoretic setting for which the distinction between system and environment is the starting point. As a first measure for autonomy, we propose the conditional mutual information between consecutive states of the system conditioned on the history of the environment. This works well when the system cannot influence the environment at all and the environment does not interact synergetically with the system. When, in contrast, the system has full control over its environment, we should instead neglect the environment history and simply take the mutual information between consecutive system states as a measure of autonomy. In the case of mutual interaction between system and environment there remains an ambiguity regarding whether system or environment has caused observed correlations. If the interaction structure of the system is known, we define a "causal" autonomy measure which allows this ambiguity to be resolved. Synergetic interactions still pose a problem since in this case causation cannot be attributed to the system or the environment alone. Moreover, our analysis reveals some subtle facets of the concept of autonomy, in particular with respect to the seemingly innocent system-environment distinction we took for granted, and raises the issue of the attribution of control, i.e. the responsibility for observed effects. To further explore these issues, we evaluate our autonomy measure for simple automata, an agent moving in space, gliders in the game of life, and the tessellation automaton for autopoiesis of Varela et al. [Varela, F.J., Maturana, H.R., Uribe, R., 1974. Autopoiesis: the organization of living systems, its characterization and a model. BioSystems 5, 187-196].     

The expansion of information in ecological systems: Emergence as a quantifiable state

Although the term ‘emergence’ has received wide attention in the literature, most of this attention has been focused on epistemological discussions about the nature of what might be considered emergent behavior in self-organizing systems. For the concept of emergence to have any great utility for biologists, it must (1) be perceptible as a physical, quantitative property rather than just a philosophical one; (2) have a quantitative definition applicable to all levels of biological organization; and (3) be an essential component of biological system performance or evolution. Using an independent, cellular population model (running in the StarLogo system), we have developed a mutual information calculation to measure the information expansion when considering the interactions between a population of herbivores and an environment in comparison to the interactions between the individual herbivores and that environment. In self-organizing biological systems, the collective action of massively parallel units generates a greater potential complexity in the information processing capacity of the ‘whole’ system relative to the ‘individual’ parts, and as such, there is a demonstrable increase in mutual information content. From this perspective, we consider emergence to exist as a simple information expansion that is a default behavior of any system with multiple, component parts governed by a simple, probabilistic rule set. It is not a first principle of self-organizing biological systems, but rather a collective behavior that can be quantitatively described in practical terms for experimental biologists. With a quantitative formulation, the concept of emergence may become a useful information statistic in assessing the structure of biological systems.     

基于信息网络模型的生态风险评价

人类开发活动造成剧烈的生态系统自然条件变化,生态风险评价可以对受到人为干扰下生态系统(包括物种和群落等)的潜在影响进行模拟和量化。通过对信息流量的概念和网络控制分析,综合考虑生态系统组分间的直接和间接作用,提出一种能实现全局风险模拟的生态网络模型,即信息网络模型。在该模型基础上,建立了面向整体生态系统的生态风险评价框架,同时实现兼容多胁迫因子统一模拟和多风险受体间的风险追踪。以澜沧江漫湾水库为例,在估算重金属Hg、Pb和Cd初始环境风险后,利用信息网络模型追踪分析生态系统中不同生态功能组分之间的风险传递路径,评估各生态组分和整体系统的危险程度。结果表明,在累积效应作用下,对于生态系统和部分群落,整合网络风险值与初始环境风险值之间有着显著差别;在发生环境胁迫时,虽然处于食物网底层的生物类群可能最先受险,但在控制信息作用下食物网上层类群也会受险,甚至其最终受到的潜在威胁比前者更大。信息网络模型可识别出复杂的风险流动路径和群落间的风险累积,从而为生态系统风险评价和管理提供更为系统综合的理论依据。     

福建省生态足迹和生态承载力的动态变化

利用生态足迹理论,计算分析了福建省1999～2003年5年间的生态足迹变化过程.结果表明,福建省人均生态足迹由1999年的1.428 hm²上升至2003年的1.658 hm²,人均生态承载力由1999年的0.683 hm²减少到2003年的0.607 hm²,生态赤字逐年提高,生态足迹与生态承载力之间的矛盾加剧,生态环境处于不安全状态.生态足迹供需结构分析表明,福建省人均生态足迹供需存在严重的不平衡,其需求以草地和化石燃料为主,两者占总量的55.74%～63.43%,而供给以耕地为主,草地仅占人均生态承载力的0.77%～0.82%,化石燃料的供给几乎为零.5年间万元GDP生态足迹总体上呈下降趋势,表明福建省的资源利用率不断提高.与此同时,结合福建省经济发展现状和资源分布特点,提出了减少区域生态赤字的对策.     

Sustainable ecosystem management using optimal control theory: part 1 (deterministic systems)

The concept of sustainability, an abstract one by its nature, has been given a mathematical representation through the use of Fisher information as a measure. It is used to propose the sustainability hypotheses for dynamical systems, which has paved the way to achieve sustainable development through externally enforced control schemes. For natural systems, this refers to the task of ecosystem management, which is complicated due the lack of clear objectives. This work attempts to incorporate the idea of sustainability in ecosystem management. The natural regulation of ecosystems suggests two possible control options, top-down control and bottom-up control. A comparison of these two control philosophies is made on generic food chain models using the objectives derived from the sustainability hypotheses. Optimal control theory is used to derive the control profiles to handle the complex nature of the models and the objectives. The results indicate a strong relationship between the hypotheses and the dynamic behavior of the models, supporting the use of Fisher information as a measure. As regards to ecosystem management, it has been observed that top-down control is more aggressive but can result in instability, while bottom-up control is guaranteed to give a stable and improved dynamic response. The results also indicate that bottom-up control is a better option to affect shifts in the dynamic regimes of a system, which may be required to recover the system from a natural disaster like the hurricane Katrina.     

Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations

We investigate the emergence of spatio-temporal patterns in ecological systems. In particular, we study a generalized predator-prey system on a spatial domain. On this domain diffusion is considered as the principal process of motion. We derive the conditions for Hopf and Turing instabilities without specifying the predator-prey functional responses and discuss their biological implications. Furthermore, we identify the codimension-2 Turing-Hopf bifurcation and the codimension-3 Turing-Takens-Bogdanov bifurcation. These bifurcations give rise to complex pattern formation processes in their neighborhood. Our theoretical findings are illustrated with a specific model. In simulations a large variety of different types of long-term behavior, including homogenous distributions, stationary spatial patterns and complex spatio-temporal patterns, are observed.     

Towards a sounder interpretation of entropy-based indicators in ecological network analysis

Various indicators rooted in the concepts of information and entropy have been proposed to be used for ecological network analysis. They are theoretically well grounded and widely used in the literature, but have always been difficult to interpret due to an apparent lack of strict relations with node and link weight. We generated several sets of 10,000 networks in order to explore such relations and work towards a sounder interpretation. The indices we explored are based on network composition (i.e., type and importance of network compartments), or network flows (i.e., type and importance of flows among compartments), including Structural Information (SI), Total System Throughput (TST), Average Mutual Information (AMI), Flow Diversity (H), and Ascendency (ASC). A correlation analysis revealed a lack of strict relationships among the responses of the investigated indicators within the simulated space of variability of the networks. However, fairly coherent patterns of response were revealed when networks were sorted by following a “bottom-up” criterion, i.e. by increasing the dominance of the large-sized top predator in the network. This ranking is reminiscent of ecosystem succession, along which the prominence of higher trophic level organisms progressively increases. In particular, the results show that a simple increase in organisms having large size and low consumption rates is potentially able to simultaneously lead to an increase of different types of information (as SI, H and AMI), thus also emphasizing the importance of bionomic traits related to body size in affecting information-related properties in a trophically connected community. The observed trends suffer from a certain dispersion of data, which was diminished by imposing specific and ecologically meaningful constraints, such as mass balancing and restriction to certain range of the ratio A/C, an index related to the viability of ecological networks. These results suggest that the identification of a set of effective constraints may help to identify improved conditions for applicability of the investigated flow-based indicators, and also provide indication on how to normalise them with respect to meaningful network properties or reference states. Thus, in order to increase confidence in the derived network metrics describing a particular ecosystem state, and thus increase their applicability, it is advisable to construct replicate networks by taking the variability of input data into account, and by applying uncertainty and sensitivity analyses.     

Measuring complexity to infer changes in the dynamics of ecological systems under stress

Despite advances in our mechanistic understanding of ecological processes, the inherent complexity of real-world ecosystems still limits our ability in predicting ecological dynamics especially in the face of on-going environmental stress. Developing a model is frequently challenged by structure uncertainty, unknown parameters, and limited data for exploring out-of-sample predictions. One way to address this challenge is to look for patterns in the data themselves in order to infer the underlying processes of an ecological system rather than to build system-specific models. For example, it has been recently suggested that statistical changes in ecological dynamics can be used to infer changes in the stability of ecosystems as they approach tipping points. For computer scientists such inference is similar to the notion of a Turing machine: a computational device that could execute a program (the process) to produce the observed data (the pattern). Here, we make use of such basic computational ideas introduced by Alan Turing to recognize changing patterns in ecological dynamics in ecosystems under stress. To do this, we use the concept of Kolmogorov algorithmic complexity that is a measure of randomness. In particular, we estimate an approximation to Kolmogorov complexity based on the Block Decomposition Method (BDM). We apply BDM to identify changes in complexity in simulated time-series and spatial datasets from ecosystems that experience different types of ecological transitions. We find that in all cases, K_BDM complexity decreased before all ecological transitions both in time-series and spatial datasets. These trends indicate that loss of stability in the ecological models we explored is characterized by loss of complexity and the emergence of a regular and computable underlying structure. Our results suggest that Kolmogorov complexity may serve as tool for revealing changes in the dynamics of ecosystems close to ecological transitions.     

Invasive advance of an advantageous mutation: nucleation theory

For sedentary organisms with localized reproduction, spatially clustered growth drives the invasive advance of a favorable mutation. We model competition between two alleles where recurrent mutation introduces a genotype with a rate of local propagation exceeding the resident's rate. We capture ecologically important properties of the rare invader's stochastic dynamics by assuming discrete individuals and local neighborhood interactions. To understand how individual-level processes may govern population patterns, we invoke the physical theory for nucleation of spatial systems. Nucleation theory discriminates between single-cluster and multi-cluster dynamics. A sufficiently low mutation rate, or a sufficiently small environment, generates single-cluster dynamics, an inherently stochastic process; a favorable mutation advances only if the invader cluster reaches a critical radius. For this mode of invasion, we identify the probability distribution of waiting times until the favored allele advances to competitive dominance, and we ask how the critical cluster size varies as propagation or mortality rates vary. Increasing the mutation rate or system size generates multi-cluster invasion, where spatial averaging produces nearly deterministic global dynamics. For this process, an analytical approximation from nucleation theory, called Avrami's Law, describes the time-dependent behavior of the genotype densities with remarkable accuracy.     

Persistence of predator-prey systems in an uncertain environment

Summary The time derivatives of prey and predator populations are assumed to satisfy a set of inequalities, instead of a precise differential equation, reflecting an uncertain environmental and/or lack of knowledge by the modeler. A system of differential equations is found whose solution gives the boundary of a persistent set, which is positive flow invariant for any system satisfying the inequalities. Conditions are given for the persistent set to be bounded away from both axes, which show that resonance effects cannot drive either predator or prey to extinction if that does not happen for an autonomous system satisfying the inequalities. In general predator-prey systems are more persistent when there is strong asymptotic stability, when there is correlation between prey and predator dynamics, when the effect of perturbations is density dependent, and are more persistent under perturbations of the prey than of the predator.     

Evolutionary dynamics of predator-prey systems: an ecological perspective

 Evolution takes place in an ecological setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals – the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the context of predator–prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator–prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species. Received 10 November 1993; received in revised form 25 July 1994     

An information theory based framework for the measurement of population health

This paper proposes a new framework for the measurement of population health and the ranking of the health of different geographies. Since population health is a latent variable, studies which measure and rank the health of different geographies must aggregate observable health attributes into one summary measure. We show that the methods used in nearly all the literature to date implicitly assume that all attributes are infinitely substitutable. Our method, based on the measurement of multidimensional welfare and inequality, minimizes the entropic distance between the summary measure of population health and the distribution of the underlying attributes. This summary function coincides with the constant elasticity of substitution and Cobb–Douglas production functions and naturally allows different assumptions regarding attribute substitutability or complementarity. To compare methodologies, we examine a well-known ranking of the population health of U.S. states, America's Health Rankings. We find that states’ rankings are somewhat sensitive to changes in the weight given to each attribute, but very sensitive to changes in aggregation methodology. Our results have broad implications for well-known health rankings such as the 2000 World Health Report, as well as other measurements of population and individual health levels and the measurement and decomposition of health inequality.     

Modelling the growth of Japanese eel Anguilla japonica in the lower reach of the Kao-Ping River, southern Taiwan: an information theory approach

Information theory was applied to select the best model fitting total length ( L _T)-at-age data and calculate the averaged model for Japanese eel Anguilla japonica compiled from published literature and the differences in growth between sexes were examined. Five candidate growth models were the von Bertalanffy, generalized von Bertalanffy, Gompertz, logistic and power models. The von Bertalanffy growth model with sex-specific coefficients was best supported by the data and nearly overlapped the averaged growth model based on Akaike weights, indicating a similar fit to the data. The Gompertz, generalized von Bertalanffy and power growth models were also substantially supported by the data. The L _T at age of A. japonica were larger in females than in males according to the averaged growth mode, suggesting a sexual dimorphism in growth. Model inferences based on information theory, which deal with uncertainty in model selection and robust parameter estimates, are recommended for modelling the growth of A. japonica .     

面向生态文明的超循环经济:理论、模型与实例

在全球气候变化背景下,研究适应生态文明要求的新的经济运行模式——超循环经济的基本原理、结构模型、运行机理和实际应用。首先,运用系统结构分析方法梳理不同时期经济运行模式的演进过程:由"从摇篮到产品"的粗放经济,到"从摇篮到坟墓"的末端治理经济,再到"从摇篮到摇篮"的循环经济。延续这一绿色发展趋势,根据文明演化的共生理论和艾根创立的超循环理论,提出超循环经济的理论构想,并描绘"从孕育到孕育"的超循环经济的概念结构。其次,将超循环经济思想应用于林纸拓展系统(EFPS)。在分析中国造纸工业的发展现状和瓶颈及其与林业和生态环境相互关系的基础上,按照资源链、生态链和价值链(简称"三链",或3C)逐层拓展的逻辑顺序,研究EFPS超循环经济的系列结构模型。具体来说,依次建立起各层次的超循环结构模型——制浆造纸系统的资源链核心层模型、供应链系统的资源链拓展层模型、生态环境系统的生态链拓展层模型,以及社会经济系统的价值链拓展层模型。然后将各层次的结构模型综合起来,形成EFPS超循环经济的多重拓展-嵌套整体模型。该模型既能展示EFPS超循环经济系统的全貌,又包含其各层次的系统结构。因此既能为各级政府在制定国家和地区的循环经济总体发展规划时提供参考,又能为制造企业、营林组织、供应链、行业协会等各类经济主体的绿色经营决策提供支撑。最后,在上述实证研究的基础上进行理论提升。一方面提出超循环经济的5R原则:减量化、再循环、再利用、再分配和再培育。另一方面基于5R原则和3C循环链,构建5R-3C理论模型,并研究其5R-3C共生运行机理。研究表明,在超循环经济模式下,产业与生态系统可以实现互利共生的良性循环。以上研究成果的主要创新之处在于:在原理上,揭示了面向生态文明的超循环经济的概念结构、本质属性和5R原则;在机理上,创立了超循环经济的5R-3C模型及其共生运行机理;在实施上,以林纸拓展系统为例,为超循环经济理论的"落地生根"和推广应用构建了具体的多重拓展-嵌套模型。