Monotonicity of fixation probability of evolutionary dynamics on complex networks

2012 ◽  
Author(s):  
Shaolin Tan ◽  
Jinhu Lu ◽  
Xinghuo Yu ◽  
David Hill
Keyword(s):  
Complex Networks ◽  
Evolutionary Dynamics ◽  
Fixation Probability

scholarly journals Evolutionary Dynamics of Stochastic SEIR Models with Migration and Human Awareness in Complex Networks

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Yue Zhang ◽  
Yuxuan Li
Keyword(s):  
Complex Networks ◽  
Numerical Experiments ◽  
Evolutionary Dynamics ◽  
Sufficient Conditions ◽  
Deterministic System ◽  
Stochastic Solution ◽  
Epidemic Dynamic ◽  
Theoretical Results ◽  
Disease Persistence ◽  
Human Awareness

In this paper, a stochastic SEIR (Susceptible-Exposed-Infected-Removed) epidemic dynamic model with migration and human awareness in complex networks is constructed. The awareness is described by an exponential function. The existence of global positive solutions for the stochastic system in complex networks is obtained. The sufficient conditions are presented for the extinction and persistence of the disease. Under the conditions of disease persistence, the distance between the stochastic solution and the local disease equilibrium of the corresponding deterministic system is estimated in the time sense. Some numerical experiments are also presented to illustrate the theoretical results. Although the awareness introduced in the model cannot affect the extinction of the disease, the scale of the disease will eventually decrease as human awareness increases.

Evolutionary dynamics of strategies for threshold snowdrift games on complex networks

2017 ◽  
Vol 130 ◽  
pp. 51-61 ◽  
Author(s):  
Yuying Zhu ◽  
Jianlei Zhang ◽  
Qinglin Sun ◽  
Zengqiang Chen
Keyword(s):  
Complex Networks ◽  
Evolutionary Dynamics

scholarly journals How life history can sway the fixation probability of mutants

2016 ◽  
Author(s):  
Xiang-Yi Li ◽  
Shun Kurokawa ◽  
Stefano Giaimo ◽  
Arne Traulsen
Keyword(s):  
Life History ◽  
Age Structure ◽  
Evolutionary Dynamics ◽  
Selective Advantage ◽  
Fixation Probability ◽  
Relative Importance ◽  
Demographic Structure ◽  
Frequency Dependent ◽  
Intermediate Fraction ◽  
Size And Structure

AbstractIn this work, we study the effects of demographic structure on evolutionary dynamics, when selection acts on reproduction, survival, or both. In contrast with the previously discovered pattern that the fixation probability of a neutral mutant decreases while population becomes younger, we show that a mutant with constant selective advantage may have a maximum or a minimum of the fixation probability in populations with an intermediate fraction of young individuals. This highlights the importance of life history and demographic structure in studying evolutionary dynamics. We also illustrate the fundamental differences between selection on reproduction and on survival when age structure is present. In addition, we evaluate the relative importance of size and structure of the population in determining the fixation probability of the mutant. Our work lays the foundation for studying also density and frequency dependent effects in populations when demographic structures cannot be neglected.

scholarly journals The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population

2021 ◽  
Vol 17 (10) ◽  
pp. e1009537
Author(s):  
Mohammad Ali Dehghani ◽  
Amir Hossein Darooneh ◽  
Mohammad Kohandel
Keyword(s):  
Network Structure ◽  
Evolutionary Dynamics ◽  
Finite Population ◽  
Small World ◽  
Fixation Time ◽  
Fixation Probability ◽  
Neutral Drift ◽  
Scale Free ◽  
Wide Range ◽  
And Mathematics

The study of evolutionary dynamics on graphs is an interesting topic for researchers in various fields of science and mathematics. In systems with finite population, different model dynamics are distinguished by their effects on two important quantities: fixation probability and fixation time. The isothermal theorem declares that the fixation probability is the same for a wide range of graphs and it only depends on the population size. This has also been proved for more complex graphs that are called complex networks. In this work, we propose a model that couples the population dynamics to the network structure and show that in this case, the isothermal theorem is being violated. In our model the death rate of a mutant depends on its number of neighbors, and neutral drift holds only in the average. We investigate the fixation probability behavior in terms of the complexity parameter, such as the scale-free exponent for the scale-free network and the rewiring probability for the small-world network.

scholarly journals Fixation Probabilities of Evolutionary Graphs Based on the Positions of New Appearing Mutants

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Pei-ai Zhang
Keyword(s):  
Markov Chain ◽  
Graph Theory ◽  
Evolutionary Dynamics ◽  
Chain Process ◽  
Fixation Probability ◽  
Spatial Structures ◽  
Single Level ◽  
Fixation Probabilities ◽  
Evolutionary Graph Theory

Evolutionary graph theory is a nice measure to implement evolutionary dynamics on spatial structures of populations. To calculate the fixation probability is usually regarded as a Markov chain process, which is affected by the number of the individuals, the fitness of the mutant, the game strategy, and the structure of the population. However the position of the new mutant is important to its fixation probability. Here the position of the new mutant is laid emphasis on. The method is put forward to calculate the fixation probability of an evolutionary graph (EG) of single level. Then for a class of bilevel EGs, their fixation probabilities are calculated and some propositions are discussed. The conclusion is obtained showing that the bilevel EG is more stable than the corresponding one-rooted EG.

scholarly journals On the fixation probability of superstars

2013 ◽  
Vol 469 (2156) ◽  
pp. 20130193 ◽  
Author(s):  
Josep Díaz ◽  
Leslie Ann Goldberg ◽  
George B. Mertzios ◽  
David Richerby ◽  
Maria Serna ◽  
...  
Keyword(s):  
Computer Algebra ◽  
Evolutionary Dynamics ◽  
Process Models ◽  
Relative Fitness ◽  
Genetic Mutations ◽  
Fixation Probability ◽  
Mutant Population ◽  
Moran Process ◽  
Limiting Behaviour ◽  
Symbolic Matrix

The Moran process models the spread of genetic mutations through populations. A mutant with relative fitness r is introduced and the system evolves, either reaching fixation (an all-mutant population) or extinction (no mutants). In a widely cited paper, Lieberman et al. (2005 Evolutionary dynamics on graphs. Nature 433 , 312–316) generalize the model to populations on the vertices of graphs. They describe a class of graphs (‘superstars’), with a parameter k and state that the fixation probability tends to 1− r − k as the graphs get larger: we show that this is untrue as stated. Specifically, for k =5, we show that the fixation probability (in the limit, as graphs get larger) cannot exceed 1−1/ j ( r ), where j ( r )= Θ ( r 4 ), contrary to the claimed result. Our proof is fully rigorous, though we use a computer algebra package to invert a 31×31 symbolic matrix. We do believe the qualitative claim of Lieberman et al. —that superstar fixation probability tends to 1 as k increases—and that it can probably be proved similarly to their sketch. We were able to run larger simulations than the ones they presented. Simulations on graphs of around 40 000 vertices do not support their claim but these graphs might be too small to exhibit the limiting behaviour.

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