Exploring and mapping the universe of evolutionary graphs identifies structural properties affecting fixation probability and time

Möller, Marius; Hindersin, Laura; Traulsen, Arne

doi:10.1038/s42003-019-0374-x

Cited by 50 publications

(82 citation statements)

References 39 publications

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“…High (low) temperatures generally enhanced (suppressed) the strength of selection. This observation agrees with other results of evolutionary graph theory, see, for example, [21, 22,58] In particular, finding these temperatures provides a computationally efficient method of estimating the mutant fixation probabilities [79], and it may potentially lead to some general analytical insight. The mean temperature was also a good predictor of the fixation probabilities for a territorial raider model in [23].…”

Section: The Framework Of Broom and Rychtář: The Full Dynamic Modelsupporting

confidence: 89%

“…Hindersin and Traulsen [40] studied the effect of edge removal on the fixation time, which was robust to the removal even of a large number of edges. Möller et al [58] carried out a numerical study which also supported the robustness of evolutionary graph properties to structural change. We note that there will be some situations where changes to structure can have a big effect, for example specific graphs like the star that are subject to vertex or edge removal, as this will make the graph unconnected.…”

Section: Game and Dynamics Parametersmentioning

confidence: 89%

“…Thus on occasion, knowledge of a small number of graph properties (at least those we are currently aware of) is not always sufficient to predict the fixation probability, and this is true for evolutionary graph theory too. To this end, [58] investigate all small graphs considering fixation probabilities and fixation times. Rychtář and Stadler [74] showed that gradually changing the underlying graph from completely regular (a square lattice) to a completely random one increases the fixation probability with the randomness.…”

Section: Game and Dynamics Parametersmentioning

confidence: 99%

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Modelling Evolution in Structured Populations Involving Multiplayer Interactions

2020

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We consider models of evolution in structured populations involving multiplayer games. Whilst also discussing other models, we focus on the modelling framework developed by Broom and Rychtář (J Theor Biol 302:70-80, 2012) onwards. This includes key progress so far, the main gaps and limitations, the relationship and synergies with other models and a discussion of the direction of future work. In this regard as well as discussing existing work, there is some new research on the applicability and robustness of current models with respect to using them to model real populations. This is an important potential advance, as previously all of the work has been entirely theoretical. In particular, the most complex models will have many parameters, and we concentrate on considering simpler versions with a small number of parameters which still possess the key features which would make them applicable. We find that these models are generally robust, in particular issues that can arise related to small payoff changes at critical values and removal of pivotal vertices would have similar effects on other modelling system including evolutionary graph theory. These often occur where it can be argued that there is a lack of robustness in the real system that the model faithfully picks up, and so is not a problematic feature.

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Section: The Framework Of Broom and Rychtář: The Full Dynamic Modelsupporting

confidence: 89%

Section: Game and Dynamics Parametersmentioning

confidence: 89%

Section: Game and Dynamics Parametersmentioning

confidence: 99%

See 1 more Smart Citation

Modelling Evolution in Structured Populations Involving Multiplayer Interactions

2020

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“…There is a growing interest in the design of networks that optimize probabilities and times of spread of advantageous mutations in a population (for example in experimental evolution or for biotechnological applications), or the spread of cultural information (or misinformation) across social networks (Lieberman et al, 2005;Möller et al, 2019). Our results provide a general predictive theoretical framework for understanding the relevant network statistics for a population's future evolutionary dynamics.…”

Section: Introductionmentioning

confidence: 81%

A theory of evolutionary dynamics on any complex spatial structure

Nombela‐Arrieta

Carja

2021

Preprint

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Understanding how the spatial arrangement of a population shapes its evolutionary dynamics has been of long-standing interest in population genetics. Most previous studies assume a small number of demes connected by migration corridors, symmetrical structures that most often act as well-mixed populations. Other studies use networks to model the more complex topologies of natural populations and to study the structures that suppress or amplify selection. However, they usually assume very small, regular networks, with strong constraints on the strength of selection considered. Here we build network generation algorithms, evolutionary simulations and derive general analytic approximations for probabilities of fixation in populations with complex spatial structure. By tuning network parameters and properties independent of each other, we systematically span across network families and show that both a network's degree distribution, as well as its node mixing pattern shape the evolutionary dynamics of new mutations. We analytically write the relevant selective parameter, predictive of evolutionary dynamics, as a combination of network statistics. As one application, we use recent imaging datasets and build the cellular spatial networks of the stem cell niches of the bone marrow. Across a wide variety of parameters and regardless of the birth-death process used, we find these networks to be strong suppressors of selection, delaying mutation accumulation in this tissue. We also find that decreases in stem cell population size decrease the suppression strength of the tissue spatial structure, hinting at a potential diminishing spatial suppression in the bone marrow tissue as individuals age.

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“…The main findings are that generally fixation probability and fixation time is correlated such that a higher fixation probability comes with a higher fixation time. Within this general rule, it has further been shown that generalized stars maximize fixation probability while minimizing fixation time, while comet-kites minimize fixation probability while maximizing fixation time [18]. Furthermore, if we allow self loops and weighted links, we may construct arbitrarily strong amplifiers of selection [25].…”

Section: Introductionmentioning

confidence: 99%

Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N ≤ 14 Players

Richter

2020

Games

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We study the emergence of cooperation in structured populations with any arrangement of cooperators and defectors on the evolutionary graph. Using structure coefficients defined for configurations describing such arrangements of any number of mutants, we provide results for weak selection to favor cooperation over defection on any regular graph with N ≤ 14 vertices. Furthermore, the properties of graphs that particularly promote cooperation are analyzed. It is shown that the number of graph cycles of certain length is a good predictor for the values of the structure coefficient, and thus a tendency to favor cooperation. Another property of particularly cooperation-promoting regular graphs with a low degree is that they are structured to have blocks with clusters of mutants that are connected by cut vertices and/or hinge vertices.

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Exploring and mapping the universe of evolutionary graphs identifies structural properties affecting fixation probability and time

Cited by 50 publications

References 39 publications

Modelling Evolution in Structured Populations Involving Multiplayer Interactions

Modelling Evolution in Structured Populations Involving Multiplayer Interactions

A theory of evolutionary dynamics on any complex spatial structure

Evolution of Cooperation for Multiple Mutant Configurations on All Regular Graphs with N ≤ 14 Players

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