Evolution of Robustness and Plasticity under Environmental Fluctuation: Formulation in Terms of Phenotypic Variances

The characterization of plasticity, robustness, and evolvability, an important issue in biology, is studied in terms of phenotypic fluctuations. By numerically evolving gene regulatory networks, the proportionality between the phenotypic variances of epigenetic and genetic origins is confirmed. The former is given by the variance of the phenotypic fluctuation due to noise in the developmental process; and the latter, by the variance of the phenotypic fluctuation due to genetic mutation. The relationship suggests a link between robustness to noise and to mutation, since robustness can be defined by the sharpness of the distribution of the phenotype. Next, the proportionality between the variances is demonstrated to also hold over expressions of different genes (phenotypic traits) when the system acquires robustness through the evolution. Then, evolution under environmental variation is numerically investigated and it is found that both the adaptability to a novel environment and the robustness are made compatible when a certain degree of phenotypic fluctuations exists due to noise. The highest adaptability is achieved at a certain noise level at which the gene expression dynamics are near the critical state to lose the robustness. Based on our results, we revisit Waddington’s canalization and genetic assimilation with regard to the two types of phenotypic fluctuations.     

Evolution of canalizing Boolean networks

Boolean networks with canalizing functions are used to model gene regulatory networks. In order to learn how such networks may behave under evolutionary forces, we simulate the evolution of a single Boolean network by means of an adaptive walk, which allows us to explore the fitness landscape. Mutations change the connections and the functions of the nodes. Our fitness criterion is the robustness of the dynamical attractors against small perturbations. We find that with this fitness criterion the global maximum is always reached and that there is a huge neutral space of 100% fitness. Furthermore, in spite of having such a high degree of robustness, the evolved networks still share many features with “chaotic” networks.     

Evolution of a population of random Boolean networks

We investigate the evolution of populations of random Boolean networks under selection for robustness of the dynamics with respect to the perturbation of the state of a node. The fitness landscape contains a huge plateau of maximum fitness that spans the entire network space. When selection is so strong that it dominates over drift, the evolutionary process is accompanied by a slow increase in the mean connectivity and a slow decrease in the mean fitness. Populations evolved with higher mutation rates show a higher robustness under mutations. This means that even though all the evolved populations exist close to the plateau of maximum fitness, they end up in different regions of network space.     

Comparing the evolution of canalyzing and threshold networks

We study the influence of the type of update functions on the evolution of Boolean networks under selection for dynamical robustness. The chosen types of functions are canalyzing functions and threshold functions. Starting from a random initial network, we evolve the network by an adaptive walk. During the first time period, where the networks evolve to the plateau of 100 percent fitness, we find that both type of update functions give the same behavior, albeit for different network sizes and connectedness. However, on the long run, as the networks continue to evolve on the fitness plateau, the different types of update functions give rise to different network structure, due to their different mutational robustness. When both types of update functions occur together, none of them is preferred under long-term evolution.     

Mean-field effects on the aging transitions in the damaged networks

We investigate the dynamical robustness property of the damaged network of active and inactive oscillators under the influence of the mean-field diffusion. The tolerance of dynamical activity of the entire coupled network has realized through the aging transition in the coupled dynamical network. We analytically derived the critical threshold of mean-field density and coupling values for the appearance of the aging transition in the damaged network. By using the critical values as a quantifiable measure of dynamical robustness of the damaged network, we showed that higher mean-field value is favorable to increase the dynamical robustness of the entire network. We also perform the numerical experiment on the network of Stuart-Landau oscillators and the obtained numerical results have an excellent agreement with the analytical findings. Finally, we extend our investigation into the coupled time-delayed network and discussed the affirmative influence of the mean-field parameter on the dynamical robustness of the network.     

Scale-free properties of information flux networks in genetic algorithms

In this study, we present empirical analysis of statistical properties of mating networks in genetic algorithms (GAs). Under the framework of GAs, we study a class of interaction network model—information flux network (IFN), which describes the information flow among generations during evolution process. The IFNs are found to be scale-free when the selection operator uses a preferential strategy rather than a random. The topology structure of IFN is remarkably affected by operations used in genetic algorithms. The experimental results suggest that the scaling exponent of the power-law degree distribution is shown to decrease when crossover rate increases, but increase when mutation rate increases, and the reason may be that high crossover rate leads to more edges that are shared between nodes and high mutation rate leads to many individuals in a generation possessing low fitness. The magnitude of the out-degree exponent is always more than the in-degree exponent for the systems tested. These results may provide a new viewpoint with which to view GAs and guide the dissemination process of genetic information throughout a population.     

A cell-centered approach to developmental biology

Explaining embryonic development of multicellular organisms requires insight into complex interactions between genetic regulation and physical, generic mechanisms at multiple scales. As more physicists move into developmental biology, we need to be aware of the “cultural” differences between the two fields, whose concepts of “explanations” and “models” traditionally differ: biologists aiming to identify genetic pathways and expression patterns, physicists tending to look for generic underlying principles.Here we discuss how we can combine such biological and physical approaches into a cell-centered approach to developmental biology. Genetic information can only indirectly influence the morphology and physiology of multicellular organisms. DNA translates into proteins and regulatory RNA sequences, which steer the biophysical properties of cells, their response to signals from neighboring cells, and the production and properties of extracellular matrix (ECM). We argue that in many aspects of biological development, cells’ inner workings are irrelevant: what matter are the cell's biophysical properties, the signals it emits and its responses to extracellular signals. Thus we can separate questions about genetic regulation from questions about development. First, we ask what effects a gene network has on cell phenomenology, and how it operates. We then ask through which mechanisms such single-cell phenomenology directs multicellular morphogenesis and physiology. This approach treats the cell as the fundamental module of development.We discuss how this cell-centered approach—which requires significant input from computational biophysics—can assist and supplement experimental research in developmental biology. We review cell-centered approaches, focusing in particular on the Cellular Potts Model (CPM), and present the Tissue Simulation Toolkit which implements the CPM.     

Adaptive synchronization of weighted complex dynamical networks with coupling time-varying delays

This Letter considers the problem of controlling a weighted complex dynamical network with coupling time-varying delay toward an assigned evolution. Adaptive controllers have been designed for nodes of the controlled network. Analytical results show that the states of the weighted dynamical network can globally asymptotically synchronize onto a desired orbit under the designed controllers. In comparison with the common linear feedback controllers, the adaptive controllers have strong robustness against asymmetric coupling matrix, time-varying weights, delays, and noise. Numerical simulations illustrated by a nearest-neighbor coupling network verify the effectiveness of the proposed controllers.     

Phase diagrams of quasispecies theory with recombination and horizontal gene transfer

We consider how transfer of genetic information between individuals influences the phase diagram and mean fitness of both the Eigen and the parallel, or Crow-Kimura, models of evolution. In the absence of genetic transfer, these physical models of evolution consider the replication and point mutation of the genomes of independent individuals in a large population. A phase transition occurs, such that below a critical mutation rate an identifiable quasispecies forms. We show how transfer of genetic information changes the phase diagram and mean fitness and introduces metastability in quasispecies theory, via an analytic field theoretic mapping.     

Adaptation dynamics of the quasispecies model

We study the adaptation dynamics of an initially maladapted population evolving via the elementary processes of mutation and selection. The evolution occurs on rugged fitness landscapes which are defined on the multi-dimensional genotypic space and have many local peaks separated by low fitness valleys. We mainly focus on the Eigen’s model that describes the deterministic dynamics of an infinite number of self-replicating molecules. In the stationary state, for small mutation rates such a population forms a quasispecies which consists of the fittest genotype and its closely related mutants. The quasispecies dynamics on rugged fitness landscape follow a punctuated (or steplike) pattern in which a population jumps from a low fitness peak to a higher one, stays there for a considerable time before shifting the peak again and eventually reaches the global maximum of the fitness landscape. We calculate exactly several properties of this dynamical process within a simplified version of the quasispecies model.      

Evolutionary design of oscillatory genetic networks

The present study is devoted to the design and statistical investigations of dynamical gene expression networks. In our model problem, we aim to design genetic networks which would exhibit stable periodic oscillations with a prescribed temporal period. While no rational solution of this problem is available, we show that it can be effectively solved by running a computer evolution of the network models. In this process, structural rewiring mutations are applied to the networks with inhibitory interactions between genes and the evolving networks are selected depending on whether, after a mutation, they closer approach the targeted dynamics. We show that, by using this method, networks with required oscillation periods, varying by up to three orders of magnitude, can be constructed by changing the architecture of regulatory connections between the genes. Statistical properties of designed networks, including motif distributions and Laplacian spectra, are considered.     

Evolutionary Accessibility in Tunably Rugged Fitness Landscapes

The adaptive evolution of a population under the influence of mutation and selection is strongly influenced by the structure of the underlying fitness landscape, which encodes the interactions between mutations at different genetic loci. Theoretical studies of such landscapes have been carried out for several decades, but only recently experimental fitness measurements encompassing all possible combinations of small sets of mutations have become available. The empirical studies have spawned new questions about the accessibility of optimal genotypes under natural selection. Depending on population dynamic parameters such as mutation rate and population size, evolutionary accessibility can be quantified through the statistics of accessible mutational pathways (along which fitness increases monotonically), or through the study of the basin of attraction of the optimal genotype under greedy (steepest ascent) dynamics. Here we investigate these two measures of accessibility in the framework of Kauffman’s LK-model, a paradigmatic family of random fitness landscapes with tunable ruggedness. The key parameter governing the strength of genetic interactions is the number K of interaction partners of each of the L sites in the genotype sequence. In general, accessibility increases with increasing genotype dimensionality L and decreases with increasing number of interactions K. Remarkably, however, we find that some measures of accessibility behave non-monotonically as a function of K, indicating a special role of the most sparsely connected, non-trivial cases K=1 and 2. The relation between models for fitness landscapes and spin glasses is also addressed.     

Emergent criticality through adaptive information processing in boolean networks

We study information processing in populations of boolean networks with evolving connectivity and systematically explore the interplay between the learning capability, robustness, the network topology, and the task complexity. We solve a long-standing open question and find computationally that, for large system sizes N, adaptive information processing drives the networks to a critical connectivity K(c)=2. For finite size networks, the connectivity approaches the critical value with a power law of the system size N. We show that network learning and generalization are optimized near criticality, given that the task complexity and the amount of information provided surpass threshold values. Both random and evolved networks exhibit maximal topological diversity near K(c). We hypothesize that this diversity supports efficient exploration and robustness of solutions. Also reflected in our observation is that the variance of the fitness values is maximal in critical network populations. Finally, we discuss implications of our results for determining the optimal topology of adaptive dynamical networks that solve computational tasks.     

Spatiotemporal chaos and noise

Low-dimensional chaotic dynamical systems can exhibit many characteristic properties of stochastic systems, such as broad Fourier spectra. They are distinguishable from stochastic processes through finite values for their dimension, Lyapunov exponents, and Kolmogorov-Sinai entropy. We discuss how these characteristic observables are modified in spatiotemporal chaotic systems like. coupled map lattices. We analyze with the help of Lyapunov concepts how the stochastic limit is approached and how these properties can be observed directly through local dimension measurements from reconstructed time series. Finally, we discuss the interaction of spatiotemporal attractors with external noise and possible connections to problems of pattern selection and stability.     

基于自归一化神经网络的脉冲星候选体选择

脉冲星候选体选择是脉冲星搜寻任务中的重要步骤.为了提高脉冲星候选体选择的准确率,提出了一种基于自归一化神经网络的候选体选择方法.该方法采用自归一化神经网络、遗传算法、合成少数类过采样这三种技术提升对脉冲星候选体的筛选能力.利用自归一化神经网络的自归一化性质克服了深层神经网络训练中梯度消失和爆炸的问题,大大加快了训练速度.为了消除样本数据的冗余性,利用遗传算法对脉冲星候选体的样本特征进行选择,得到了最优特征子集.针对数据中真实脉冲星样本数极少带来的严重类不平衡性,采用合成少数类过采样技术生成脉冲星候选体样本,降低了类不平衡率.以分类精度为评价指标,在3个脉冲星候选体数据集上的实验结果表明,本文提出的方法能有效提升脉冲星候选体选择的性能.     

A self-organized model for network evolution

Here we provide a detailed analysis, along with some extensions and additonal investigations, of a recently proposed [1] self-organized model for the evolution of complex networks. Vertices of the network are characterized by a fitness variable evolving through an extremal dynamics process, as in the Bak-Sneppen [2] model representing a prototype of Self-Organized Criticality. The network topology is in turn shaped by the fitness variable itself, as in the fitness network model [3]. The system self-organizes to a nontrivial state, characterized by a power-law decay of dynamical and topological quantities above a critical threshold. The interplay between topology and dynamics in the system is the key ingredient leading to an unexpected behaviour of these quantities.     

一种用于玉米品种鉴别的近红外光谱频率选择方法

提出了一种近红外光谱的频率选择方法用于玉米品种鉴别。首先确定一种衡量特征鉴别能力的准则函数,然后根据该准则函数逐步选出适合于分类的特征频率,并通过去除各频率特征之间的相关性使得优选出的频率特征包含尽可能多的品种类间差异信息,优先选择方差较大的频率特征以减弱噪声的影响。实验结果表明,频率选择大幅度地改善了识别效果,仅使用30维频率特征即可达到94.16%的识别率。随机模拟实验显示,优选出的频率特征的识别效果对频率的小幅随机扰动不敏感,验证了本方法的鲁棒性。