Stochastic evolutionary public goods game with first and second order costly punishments in finite populations

We study the stochastic evolutionary public goods game with punishment in a finite size population. Two kinds of costly punishments are considered, i.e., first-order punishment in which only the defectors are punished, and second-order punishment in which both the defectors and the cooperators who do not punish the defective behaviors are punished. We focus on the stochastic stable equilibrium of the system. In the population, the evolutionary process of strategies is described as a finite state Markov process. The evolutionary equilibrium of the system and its stochastic stability are analyzed by the limit distribution of the Markov process. By numerical experiments, our findings are as follows.（i） The first-order costly punishment can change the evolutionary dynamics and equilibrium of the public goods game, and it can promote cooperation only when both the intensity of punishment and the return on investment parameters are large enough.（ii）Under the first-order punishment, the further imposition of the second-order punishment cannot change the evolutionary dynamics of the system dramatically, but can only change the probability of the system to select the equilibrium points in the ＂C＋P＂ states, which refer to the co-existence states of cooperation and punishment. The second-order punishment has limited roles in promoting cooperation, except for some critical combinations of parameters.（iii） When the system chooses＂C＋P＂ states with probability one, the increase of the punishment probability under second-order punishment will further increase the proportion of the ＂P＂ strategy in the ＂C＋P＂ states.

The Origin of Population Diversity: Stochastic Interactions between a Modifier Variant and the Individual Genetic Background

Stochastic epistasis that is one of the characteristics of epistatic gene modules can have an important role in the maintenance of intraspecific population diversity. The effect of an epistatic modifier variant can vary in size and direction among the modifier careers on the basis of stochastic genetic individuality and the entire module effect can be also individually stochastic. This stochastic genetic contribution under a genetic background may be conditional upon the presence of a monomorphic switch locus in the gene module. The genetic background includes multiple modifier variants and the gene module is composed of the switch and the modifiers. The bell-shaped distribution of quantitative traits can be well simulated by the involvement of multiple stochastic epistatic modules. The phenotypic stochasticity makes the presence of switch and modifiers cryptic or missing in the research field and this cryptic gene networks can maintain and innovate in the phenotypic diversity under selection as a process of the evolution of complexity.

Bayesian analysis for mixed-effects model defined by stochastic differential equations

The nonlinear mixed-effects model with stochastic differential equations （SDEs） is used to model the population pharmacokinetic （PPK） data that are extended from ordinary differential equations （ODEs） by adding a stochastic term to the state equation. Compared with the ODEs, the SDEs can model correlated residuals which are ubiquitous in actual pharmacokinetic problems. The Bayesian estimation is provided for nonlinear mixed-effects models based on stochastic differential equations. Combining the Gibbs and the Metropolis-Hastings algorithms, the population and individual parameter values are given through the parameter posterior predictive distributions. The analysis and simulation results show that the performance of the Bayesian estimation for mixed-effects SDEs model and analysis of population pharmacokinetic data is reliable. The results suggest that the proposed method is feasible for population pharmacokinetic data.

Higher-order approximate solutions of fractional stochastic point kinetics equations in nuclear reactor dynamics

Stochastic point kinetics equations(SPKEs) are a system of Ito? stochastic differential equations whose solution has been obtained by higher-order approximation.In this study, a fractional model of SPKEs has been analyzed. The efficiency of the proposed higher-order approximation scheme has been discussed in the results section. The solutions of SPKEs in the presence of Newtonian temperature feedback have also been provided to further discuss the physical behavior of the fractional model.

EXTINCTION OF POPULATION-SIZE-DEPENDENT BRANCHING CHAINS IN RANDOM ENVIRONMENTS

We consider a population-size-dependent branching chain in a general random environment.We give suffcident conditions for certain extinction and for non-certain extinction.The chain exhibits different asymptotic according to supk,θmk,θ1, mk,θn→1 as k →∞, n→∞, infk,θmk,θ1.

Uncertainty in a Measurement of Density Dependence on Population Fluctuations

This article discusses the question of how elasticity of the system is intertwined with external stochastic disturbances. The speed at which a displaced system returns to its equilibrium is a measure of density dependence in population dynamics. Population dynamics in random environments, linearized around the equilibrium point, can be represented by a Langevin equation, where populations fluctuate under locally stable (not periodic or chaotic) dynamics. I consider a Langevin model in discrete time, driven by time-correlated random forces, and examine uncertainty in locating the population equilibrium. There exists a time scale such that for times shorter than this scale the dynamics can be approximately described by a random walk;it is difficult to know whether the system is heading toward the equilibrium point. Density dependence is a concept that emerges from a proper coarse-graining procedure applied for time-series analysis of population data. The analysis is illustrated using time-series data from fisheries in the North Atlantic, where fish populations are buffeted by stochastic harvesting in a random environment.

Convergence Towards the Population Cross-Diffusion System from Stochastic Many-Particle System

In this paper,we derive rigorously a non-local cross-diffusion system from an interacting stochastic many-particle system in the whole space.The convergence is proved in the sense of probability by introducing an intermediate particle system with a mollified interaction potential,where the mollification is of algebraic scaling.The main idea of the proof is to study the time evolution of a stopped process and obtain a Gronwall type estimate by using Taylor's expansion around the limiting stochastic process.

Some Analytical Properties of the Model for Stochastic Evolutionary Games in Finite Populations with Non-uniform Interaction Rate

Traditional evolutionary games assume uniform interaction rate, which means that the rate at which individuals meet and interact is independent of their strategies. But in some systems, especially biological systems, the players interact with each other discriminately. Taylor and Nowak (2006) were the first to establish the corresponding non-uniform interaction rate model by allowing the interaction rates to depend on strategies. Their model is based on replicator dynamics which assumes an infinite size population. But in reality, the number of individuals in the population is always finite, and there will be some random interference in the individuals' strategy selection process. Therefore, it is more practical to establish the corresponding stochastic evolutionary model in finite populations. In fact, the analysis of evolutionary games in a finite size population is more difficult. Just as Taylor and Nowak said in the outlook section of their paper, 'The analysis of non-uniform interaction rates should be extended to stochastic game dynamics of finite populations.' In this paper, we are exactly doing this work. We extend Taylor and Nowak's model from infinite to finite case, especially focusing on the influence of non-uniform connection characteristics on the evolutionary stable state of the system. We model the strategy evolutionary process of the population by a continuous ergodic Markov process. Based on the limit distribution of the process, we can give the evolutionary stable state of the system. We make a complete classification of the symmetric 2×2 games. For each case game, the corresponding limit distribution of the Markov-based process is given when noise intensity is small enough. In contrast with most literatures in evolutionary games using the simulation method, all our results obtained are analytical. Especially, in the dominant-case game, coexistence of the two strategies may become evolutionary stable states in our model. This result can be used to explain the emergence of cooperation in the Prisoner is Dilemma Games to some extent. Some specific examples are given to illustrate our results.

AN INVARIANCE PRINCIPLE IN LARGE POPULATION STOCHASTIC DYNAMIC GAMES

We study large population stochastic dynamic games where the so-called Nash certainty equivalence based control laws are implemented by the individual players. We first show a martingale property for the limiting control problem of a single agent and then perform averaging across the population; this procedure leads to a constant value for the martingale which shows an invariance property of the population behavior induced by the Nash strategies.

Mean-square Stability of Stochastic Age-dependent Delay Population Systems with Jumps

In this paper, we present the compensated stochastic θ method for stochastic age-dependent delay population systems（SADDPSs） with Poisson jumps. The definition of mean-square stability of the numerical solution is given and a sufficient condition for mean-square stability of the numerical solution is derived. It is shown that the compensated stochastic θ method inherits stability property of the numerical solutions. Finally,the theoretical results are also confirmed by a numerical experiment.

A stochastic population pharmacodynamic model of QAP14 in the treatment of lung metastases of 4T1 breast cancer

Cancer metastasis is a process with multi-step complexity and apparent randomness. In this study, we aimed to establish a stochastic mathematical model to describe the random process of cancer metastasis and predict the drug effect of QAP14 on metastasis in a mouse model. The data of lung metastases on the 22^(nd) day after cancer cell implantation with or without the treatment of QAP14, a new chemical compound, were collected in 4T1 breast cancer BALB/c mice. Based on the exponential growth of the primary tumor and metastatic loci, a joint distribution model of metastasis size and number was developed. Disease progression of metastasis and preclinical efficacy of QAP14 were modeled. Parameters M and m representing maximum and minimum of metastasis volume were 3.24 and 0.0184 mm^(3), respectively. The metastasis growth rate γ and metastasis promotion time ρ were estimated and fixed to be 0.0216 d^(-1) and 7.8 d, respectively. The efficacy of QAP14 acted on metastasis promotion time and metastasis growth rate constant in an exponential term, and the effect parameter Effectρ and Effectγ were 16.6 and 0.327 g/mg, respectively. In the present study, we comprehensively characterized the random process of lung metastasis and efficacy of QAP14 in 4T1 breast cancer mice, which might provide a useful reference for the establishment of a clinical population model of cancer metastasis.

An Algorithm for the Stochastic Simulation of Gene Expression and Heterogeneous Population Dynamics

We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics.The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte Carlo method to simulate time-dependent statistical characteristics of growing cell populations.To benchmark performance,we compare simulation results with steadystate and time-dependent analytical solutions for several scenarios,including steadystate and time-dependent gene expression,and the effects on population heterogeneity of cell growth,division,and DNA replication.This comparison demonstrates that the algorithm provides an efficient and accurate approach to simulate how complex biological features influence gene expression.We also use the algorithm to model gene expression dynamics within"bet-hedging"cell populations during their adaption to environmental stress.These simulations indicate that the algorithm provides a framework suitable for simulating and analyzing realistic models of heterogeneous population dynamics combining molecular-level stochastic reaction kinetics,relevant physiological details and phenotypic variability.

东北三省碳排放影响因素分析和趋势预测——基于STIRPAT模型和情景分析法

东北三省是“双碳”目标下碳减排工作的重点区域。利用STIRPAT(可拓展的随机性环境影响评估)模型对2000—2021年东北三省各省的碳排放影响因素进行分析,并利用情景分析法预测截止到2040年以前、均衡情景下东北三省各省的碳排放趋势。模型分析结果表明:各省只存在导致碳排放量增加的影响因素;能源消费总量、碳排放强度、人均GDP是各省的共同影响因素;各省的影响因素是不同的组合;各省影响因素的促进作用存在省份差异性。预测结果表明:碳排放量同期数值由高到低依次为辽宁省、黑龙江省、吉林省;各省的碳排放量曲线都呈现出倒“U”形并能够看出明显的峰值;黑龙江省和吉林省碳达峰的时间都为2012年,而辽宁省碳达峰的时间为2025年。针对分析和预测结果,提出能源、社会经济、区域协调3个方面的建议。

面向城市能源系统的碳达峰评估方法研究

能源系统脱碳化是实现“双碳”战略目标的关键。由于城市之间存在区域不平衡性,跟踪与评估面向城市能源系统的碳排放达峰水平具有重要意义。提出一种考虑加速化脱碳进程的城市能源系统碳达峰评估方法。首先,确定影响城市能源碳排放的七种主要驱动因素,建立基于对人口、经济水平和技术的随机影响回归(STIRPAT)分析的碳排放预测模型,即可拓展的随机性和环境影响评估模型。其次,通过偏最小二乘(PLS)求解模型,采用情景分析法预测未来六种情景下各城市碳排放量。最后,构建基于Mann-Kendall方法的城市能源碳达峰趋势判断模型,对所预测的碳排放结果进行趋势检验,并据此评估城市能源碳达峰状态。算例分析基于我国上海、天津和重庆的2001—2020年城市面板数据的仿真测算。仿真结果表明:上海于2030年前基本实现碳达峰;天津、重庆实现碳达峰则面临较大压力。所提方法能够实现对不同情景下城市能源系统碳达峰水平的量化评估。

陕西省碳排放驱动因素分析及预测

采用碳排放系数法测算2000—2021年陕西省碳排放量并研究驱动因素,在此基础上进行预测并探索出5条减排路径。研究结果表明:陕西省碳排放量在2000—2021年呈上升趋势;驱动因素作用排序为经济发展、能源结构、能耗强度、产业结构、城镇化率以及人口数量;陕西省在高碳、基准、低碳3种情景下均可实现碳达峰,碳排放量分别为6.968 5×10^(8) t、6.636 6×10^(8) t、6.314 5×10^(8) t。因此,合理规划发展进程,注重技术进步,并严格控制产业和能源结构比例,对于陕西省顺利实现碳达峰目标任务具有现实意义。

污水流量与天气数据融合的贝叶斯服务人口预测

传统基于污水日均流量及人均用水量的人口预测模型缺乏对天气因素的考虑,存在人口数量测算偏大等问题。为了综合考虑天气因素对污水日均流量的影响,提出了一种基于污水监测数据与天气数据融合的贝叶斯服务人口预测模型。通过引入天气影响因子,同质化、异质化天气影响因子转化率,天气因素对污水日均流量的贡献量等,构建基于贝叶斯方法的污水日均流量生成模型。基于随机变分推理,获得生成模型参数的后验分布,进而实现各污水处理厂服务区域的服务人口预测模型。该模型能抵消区域天气因素的综合影响水平,能更合理地实现污水厂服务区域的人口数量预测。同时,通过统计分析对比了同质化、异质化天气影响因子转化率估计,天气因素对污水日均流量的影响等。该服务人口预测模型能进一步支撑城市人口的态势感知,对提升社会治理能力有重要意义。

北京市碳排放的影响因素分析

“十四五”时期是中国实现碳达峰的关键时期,也是推动经济高质量发展和生态环境质量持续改善的重要阶段。可拓展的随机性环境影响评估(Stochastic Impacts by Regression on Population,Affluence,and Technology,STIRPAT)模型可以根据研究需要增加自变量,更好地分析相关因素对因变量的影响。以北京市为研究区,通过构建扩展的STIRPAT模型,分析人均地区生产总值(Gross Domestic Product,GDP)、人均汽车保有量、城市化率、第三产业GDP占比、能源消费强度与人均碳排放量的关系,并采用对数平均迪氏指数(Logarithmic Mean Divisia Index,LMDI)分解法分解能源消费强度。结果表明,产业结构和能源消费强度对人均碳排放量均有显著的正向影响。总体来看,要平衡经济发展与碳排放的关系,提高能源利用效率,推广可再生能源,降低能源消耗,减少碳排放。

一类随机人口发展系统的指数稳定性

对人口系统的讨论 ,通常的数学模型没有考虑外界环境对系统的影响 .在假设随机的外界环境对迁移产生扰动的条件下 ,给出Hilbert空间中一类随机时变人口发展系统 .对随机时变人口发展系统的均方稳定性和指数稳定性进行了讨论 .利用Burkholder_Davis_Gundy不等式 ,Gronwall引理和Kolmogorov不等式得到了均方稳定和指数稳定的充分条件 .最后提出如果生育率选作控制变量 ,系统仍然是均方和指数稳定的 。

秦岭大熊猫(Ailuropoda melanoleuca)的种群存活力分析

以对秦岭野生大熊猫多年研究的资料 ,建立了一个机理性的随机模型 ,并用此模型对秦岭大熊猫种群进行了种群动态的模拟。分析了该种群的存活力 ,结果显示 :秦岭大熊猫种群具有正的增长潜力 ;在环境维持现状的情况下 ,秦岭大熊猫种群以小于 5 %的灭绝概率维持 2 0 0年所需的最小种群规模为 2 8～ 30只 ,低于此数值 ,由于种群统计学随机性 ,种群会有较高的灭绝概率 ;在密度制约因素的影响下 ,种群维持需要 5 0～ 6 0只个体 ;在非密度制约因素的影响下 ,每年由种群中减少的个体不应超过种群数量的 1%。结合秦岭目前大熊猫种群的实际数量 ,秦岭的大熊猫种群由于种群统计学随机性而发生灭绝的可能性很小 ,如果能够在保证现有的环境状况不恶化 ,并且能够逐步恢复的前提下 。

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内 ,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是 ,由于自然种群动态及其影响因子的复杂特征 ,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展 ,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状 ,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向 :更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用 ,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因 ,以期做出精确的预测。