An extension of the Moran process using type-specific connection graphs

Melissourgos, Themistoklis; Nikoletseas, Sotiris; Raptopoulos, Christoforos; Spirakis, Paul G.

doi:10.1016/j.jcss.2021.07.007

Cited by 3 publications

(9 citation statements)

References 24 publications

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“…Here a Star graph , denoted S N , consists of a single node (called centre ) connected to all other nodes (called leaves ). It is known [44] that ρ ( S N ) ≤ 1/( N − 2)! and ρ⋆false(SNfalse)false→1 as N → ∞.…”

Section: Resultsmentioning

confidence: 99%

“…In one dimension, we consider circulation graphs CirNd (already studied in this context from a different point of view, see [44]). For a fixed even integer d , a d -Circulation graph, denoted CirNd, consists of N nodes arranged in a cycle, where each node is connected to d other nodes, namely the next d /2 nodes and the previous d /2 nodes in the cyclic order, see figure 6 a .…”

Section: Resultsmentioning

confidence: 99%

“…Second, following the game theory perspective, Melissourgos et al [44] asked what is the best mutant response to a given resident graph. That is, given a resident graph GNB on N nodes, which mutant graph GNA on N nodes maximizes the fixation probability ρfalse(GNA,GNBfalse)?…”

Section: Discussionmentioning

confidence: 99%

“…1=N holds for all resident graphs G B N = K N (we do know that it holds for G B N ¼ M N ). Second, following the game theory perspective, Melissourgos et al [44] asked what is the best mutant response to a given resident graph. That is, given a resident graph G B N on N nodes, which mutant graph G A N on N nodes maximizes the fixation probability rðG A N , G B N Þ?…”

Section: Discussionmentioning

confidence: 99%

“…By contrast, in this work we consider the two-graph setting from a biological perspective, and we present structural results concerning mutants with no reproductive advantage (r A = r B ) who, similarly to the residents, perceive the population structure either as an island model or as a low-dimensional lattice. On top of that, we answer a question stated in [44] related to the bestresponse dynamics in the space of all graphs. Namely, we show that while the Complete graph is locally optimal (see theorem A.1 in appendix A), it is not always the best response (figure 9).…”

Section: Related Workmentioning

confidence: 97%

See 4 more Smart Citations

Evolutionary dynamics of mutants that modify population structure

Tkadlec,

Kaveh,

Chatterjee

et al. 2023

J. R. Soc. Interface.

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Natural selection is usually studied between mutants that differ in reproductive rate, but are subject to the same population structure. Here we explore how natural selection acts on mutants that have the same reproductive rate, but different population structures. In our framework, population structure is given by a graph that specifies where offspring can disperse. The invading mutant disperses offspring on a different graph than the resident wild-type. We find that more densely connected dispersal graphs tend to increase the invader’s fixation probability, but the exact relationship between structure and fixation probability is subtle. We present three main results. First, we prove that if both invader and resident are on complete dispersal graphs, then removing a single edge in the invader’s dispersal graph reduces its fixation probability. Second, we show that for certain island models higher invader’s connectivity increases its fixation probability, but the magnitude of the effect depends on the exact layout of the connections. Third, we show that for lattices the effect of different connectivity is comparable to that of different fitness: for large population size, the invader’s fixation probability is either constant or exponentially small, depending on whether it is more or less connected than the resident.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 97%

See 3 more Smart Citations

Evolutionary dynamics of mutants that modify population structure

Tkadlec,

Kaveh,

Chatterjee

et al. 2023

J. R. Soc. Interface.

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Fixation probability in evolutionary dynamics on switching temporal networks

Bhaumik,

Masuda

2023

J. Math. Biol.

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Population structure has been known to substantially affect evolutionary dynamics. Networks that promote the spreading of fitter mutants are called amplifiers of selection, and those that suppress the spreading of fitter mutants are called suppressors of selection. Research in the past two decades has found various families of amplifiers while suppressors still remain somewhat elusive. It has also been discovered that most networks are amplifiers of selection under the birth-death updating combined with uniform initialization, which is a standard condition assumed widely in the literature. In the present study, we extend the birth-death processes to temporal (i.e., time-varying) networks. For the sake of tractability, we restrict ourselves to switching temporal networks, in which the network structure deterministically alternates between two static networks at constant time intervals or stochastically in a Markovian manner. We show that, in a majority of cases, switching networks are less amplifying than both of the two static networks constituting the switching networks. Furthermore, most small switching networks, i.e., networks on six nodes or less, are suppressors, which contrasts to the case of static networks.

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Fixation Dynamics on Multilayer Networks

Liu,

Masuda

2024

SIAM J. Appl. Math.

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An extension of the Moran process using type-specific connection graphs

Cited by 3 publications

References 24 publications

Evolutionary dynamics of mutants that modify population structure

Evolutionary dynamics of mutants that modify population structure

Fixation probability in evolutionary dynamics on switching temporal networks

Fixation Dynamics on Multilayer Networks

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