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Dynamics of Advantageous Mutant Spread in Spatial Death-Birth and Birth-Death Moran Models

Communications on Applied Mathematics and Computation 2024年第1期6卷 576-604页

作者： Jasmine Foo Einar Bjarki Gunnarsson Kevin Leder David Sivakoff School of Mathematics University of MinnesotaTwin CitiesMN55455USA Department of Industrial and Systems Engineering University of MinnesotaTwin CitiesMN55455USA Departments of Statistics and Mathematics The Ohio State UniversityColumbusOH43210USA

The spread of an advantageous mutation through a population is of fundamental interest in population genetics. While the classical Moran model is formulated for a well-mixed population, it has long been recognized that in real-world applications, the population usually has an explicit spatial structure which can significantly influence the dynamics. In the context of cancer initiation in epithelial tissue, several recent works have analyzed the dynamics of advantageous mutant spread on integer lattices, using the biased voter model from particle systems theory. In this spatial version of the Moran model, individuals first reproduce according to their fitness and then replace a neighboring individual. From a biological standpoint, the opposite dynamics, where individuals first die and are then replaced by a neighboring individual according to its fitness, are equally relevant. Here, we investigate this death-birth analogue of the biased voter model. We construct the process mathematically, derive the associated dual process, establish bounds on the survival probability of a single mutant, and prove that the process has an asymptotic shape. We also briefly discuss alternative birth-death and death-birth dynamics, depending on how the mutant fitness advantage affects the dynamics. We show that birth-death and death-birth formulations of the biased voter model are equivalent when fitness affects the former event of each update of the model, whereas the birth-death model is fundamentally different from the death-birth model when fitness affects the latter event.

关键词： Spatial death-birth models Spatial birth-death models Spatial evolutionary models Spatial cancer models Evolutionary graph theory Stochastic processes Biased voter model Dual process fixation probability Shape theorem

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Characterizing the Effect of Network Structure on Evolutionary Dynamics via a Novel Measure of Structural Heterogeneity

Characterizing the Effect of Network Structure on Evolutiona...

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第25届中国控制与决策会议

作者： Shaolin Tan Jinhu Lü Xinghuo Yu David Hill Institute of Systems Science Academy of Mathematics and Systems Science Chinese Academy of Sciences School of Electrical and Computer Engineering RMIT University Academy of Mathematics and Systems Science The University of Sydney

ISBN: (纸本)9781467355339

Recently, the study of evolutionary dynamics on structured population has attracted an increasing attention in various fields. This paper aims at investigating the effect of network structure on evolutionary dynamics. In detail, a novel measure of structural heterogeneity is introduced to characterize the network structure effect on evolutionary dynamics. By simulating the evolutionary dynamics of invasion process on a massive amount of randomly sampled networks, we find that structural heterogeneity amplifies the selective effect on fixation probability of invader in birthdeath process, however, it weakens the selective effect in death-birth process. These findings provide a fundamental principle for designing selection amplifier, which benefits advantageous invaders while inhibits unadvantageous ones. Moreover, an effective algorithm is proposed to generate selection amplifiers with specified size and average degree.

关键词： Evolutionary dynamics fixation probability population structure heterogeneity

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Efficiency and stability on multi-level structures

Efficiency and stability on multi-level structures

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2010 Chinese Control and Decision Conference

作者： Pei-ai Zhang~1 1.Department of Mathematics,Jinan University,Guangzhou,510632,P.R.China

＜正＞Multi-level structures are extremely popular in many organizations and social *** game theory, this paper shows that two-level structures are more efficient than three-level structures,while with evolutionary graph technique we find that three-level structures are more stable than two-level *** results are correspondingly extended to more general *** summary,the multi-level structures with different numbers of levels are compared in this ***,evolutionary graph theory is extended to social field in this paper.

关键词： organizational issues operations strategy multi-level structures fixation probability hierarchy fitness game theory

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基于Moran过程的消费者众筹策略演化动态

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管理科学 2018年第2期 105-110页

作者：王先甲何奇龙全吉顾翠伶

考虑混合均匀的N个消费者众筹策略演化动态，每个消费者可选择参与众筹或者不参与众筹两个策略。基于Moran过程的扎根概率，计算出有限消费者群体中，参与众筹策略和不参与众筹策略成功入侵的概率。比较个体扎根的概率和中性入侵的概率... 详细信息

考虑混合均匀的N个消费者众筹策略演化动态，每个消费者可选择参与众筹或者不参与众筹两个策略。基于Moran过程的扎根概率，计算出有限消费者群体中，参与众筹策略和不参与众筹策略成功入侵的概率。比较个体扎根的概率和中性入侵的概率大小，分别得到两策略在强选择性和弱选择性强度下占优的条件。研究发现，强选择性条件下，消费者数量小于某个数值时，不参与众筹策略演化稳定侵占整个种群，众筹融资失败。弱选择性条件下，消费者依据净收益和支出成本两因素决定是否参与众筹，净收益大于支出成本三倍，演化稳定于众筹成功，净收益小于支出成本二分之三倍，演化稳定于众筹失败。

关键词：演化博弈众筹 Moran过程扎根概率 crowdfunding evolutionary game moran process fixation probability

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