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

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 i...

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Autores principales:	Mohammad Ali Dehghani, Amir Hossein Darooneh, Mohammad Kohandel
Formato:	article
Lenguaje:	EN
Publicado:	Public Library of Science (PLoS) 2021
Materias:	Biology (General) QH301-705.5
Acceso en línea:	https://doaj.org/article/91bbe94677c44aaba92ac805ae7cb9b5
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spelling	oai:doaj.org-article:91bbe94677c44aaba92ac805ae7cb9b52021-11-11T05:51:55ZThe network structure affects the fixation probability when it couples to the birth-death dynamics in finite population1553-734X1553-7358https://doaj.org/article/91bbe94677c44aaba92ac805ae7cb9b52021-10-01T00:00:00Zhttps://www.ncbi.nlm.nih.gov/pmc/articles/PMC8575310/?tool=EBIhttps://doaj.org/toc/1553-734Xhttps://doaj.org/toc/1553-7358The 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. Author summary In this work, we examine an evolutionary model that considers the effect of competition between the mutated individuals for acquiring more resources. This competition has an effect on the death rate of mutants. The model purposes that the death rate of each mutant depends on the number of its neighbors, while the average death rate in the population is equal to one. The birth rate for all individuals is assumed to be the same and equal to one. This situation is called here the ‘neutral drift in average’. We study the dynamics of the model on complex networks to take into account the non-uniformity of the environment. The results show the fixation probability differs from the Moran model. For the construction of this model, we were biologically motivated by the avascular tumour, which consists of a population of normal and cancer cells. The cancer cells likely need more oxygen than normal cells. There is a competition between cells for consuming oxygen, and cancer cells are far more sensitive to the amount of oxygen in the environment than normal cells. This means the death rate of a cancer cell grows by increasing the number of its neighbors.Mohammad Ali DehghaniAmir Hossein DaroonehMohammad KohandelPublic Library of Science (PLoS)articleBiology (General)QH301-705.5ENPLoS Computational Biology, Vol 17, Iss 10 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Biology (General) QH301-705.5
spellingShingle	Biology (General) QH301-705.5 Mohammad Ali Dehghani Amir Hossein Darooneh Mohammad Kohandel The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population
description	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. Author summary In this work, we examine an evolutionary model that considers the effect of competition between the mutated individuals for acquiring more resources. This competition has an effect on the death rate of mutants. The model purposes that the death rate of each mutant depends on the number of its neighbors, while the average death rate in the population is equal to one. The birth rate for all individuals is assumed to be the same and equal to one. This situation is called here the ‘neutral drift in average’. We study the dynamics of the model on complex networks to take into account the non-uniformity of the environment. The results show the fixation probability differs from the Moran model. For the construction of this model, we were biologically motivated by the avascular tumour, which consists of a population of normal and cancer cells. The cancer cells likely need more oxygen than normal cells. There is a competition between cells for consuming oxygen, and cancer cells are far more sensitive to the amount of oxygen in the environment than normal cells. This means the death rate of a cancer cell grows by increasing the number of its neighbors.
format	article
author	Mohammad Ali Dehghani Amir Hossein Darooneh Mohammad Kohandel
author_facet	Mohammad Ali Dehghani Amir Hossein Darooneh Mohammad Kohandel
author_sort	Mohammad Ali Dehghani
title	The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population
title_short	The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population
title_full	The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population
title_fullStr	The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population
title_full_unstemmed	The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population
title_sort	network structure affects the fixation probability when it couples to the birth-death dynamics in finite population
publisher	Public Library of Science (PLoS)
publishDate	2021
url	https://doaj.org/article/91bbe94677c44aaba92ac805ae7cb9b5
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The network structure affects the fixation probability when it couples to the birth-death dynamics in finite population

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