Limits on amplifiers of natural selection under death-Birth updating

Tkadlec, Josef; Pavlogiannis, Andreas; Chatterjee, Krishnendu; Nowak, Martin A.

doi:10.1371/journal.pcbi.1007494

Cited by 60 publications

(84 citation statements)

References 40 publications

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“…The differences between Birth-death and death-Birth dynamics are major for mutant fixation probabilities, but also in evolutionary game theory, where spatial structure can promote the evolution of cooperation in the latter case, but not in the former [27][28][29]. Previous efforts were made to generalize beyond these dynamics by allowing both types of update to occur in given proportions [30,31]. Interestingly, it was recently shown that no strong or universal amplification of selection can occur when even a small proportion of death-Birth events occurs [31], in contrast to the Birth-death case.…”

Section: Discussionmentioning

confidence: 99%

Toward a universal model for spatially structured populations

Marrec

Lamberti

Bitbol

2020

Preprint

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Microbial populations often have complex spatial structures, with homogeneous competition holding only at a local scale. Population structure can strongly impact evolution, in particular by affecting the fixation probability of mutants. Here, we propose a model of structured microbial populations on graphs, where each node of the graph contains a well-mixed deme whose size can fluctuate, and where migrations are independent from birth and death events. We study analytically and numerically the mutant fixation probabilities in different structures, in the rare migration regime. In particular, we demonstrate that the star graph continuously transitions between amplifying and suppressing natural selection as migration rate asymmetry is varied. This elucidates the apparent paradox in existing constant-size models on graphs, where the star is an amplifier or a suppressor depending on the details of the dynamics or update rule chosen, e.g. whether each birth event precedes or follows a death event. The celebrated amplification property of the star graph for large populations is preserved in our model, for specific migration asymmetry. We further demonstrate a general mapping between our model and constant-size models on graphs, under a constraint on migration rates, which directly stems from assuming constant size. By lifting this constraint, our model reconciles and generalizes previous results, showing that migration rate asymmetry is key to determining whether a given population structure amplifies or suppresses natural selection.SummaryA key question in evolution is how likely a mutant is to take over. This depends on natural selection and on stochastic fluctuations. Compared to a well-mixed population, some spatial structures have been predicted to amplify or suppress the impact of natural selection. This can have a major impact on evolution, as well as applications in biotechnology, e.g. by facilitating selection in directed evolution of biomolecules. We introduce a model for complex structured populations that generalizes over existing ones by allowing population size to fluctuate. We demonstrate that whether a given population structure amplifies or suppresses selection strongly depends on the asymmetry of migration rates. Our results are universal in the sense that they do not depend on update rules.

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Section: Discussionmentioning

confidence: 99%

Toward a universal model for spatially structured populations

Marrec

Lamberti

Bitbol

2020

Preprint

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“…As particles' kinetic energy form temperature, the persistence of opinion enhances the willingness for interaction and forms social temperature [34] , [35] . Supply abundance ensures low social temperature, with a tendency for cooperation and generosity [161] . When access to supplies reaches a critical level, competition for resources replaces cooperation [159] .…”

Section: Definitions Used In the Testmentioning

confidence: 99%

“…Our results suggest that positive environments occur encourage the generosity and cooperation by supporting mental energy growth. Desirable population structures promote cooperation [161] .…”

Section: Thermodynamic Considerations Of Brain Activitiesmentioning

confidence: 99%

The thermodynamics of cognition: A mathematical treatment

Deli¹,

Peters

Kisvárday

2021

Computational and Structural Biotechnology Journal

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Graphical abstract The thermodynamics consequences of intelligent computation. The neural system uses substantial resources to maintain the resting state; therefore, the Carnot cycle can model the evoked cycle. The synaptic complexity during neural computation changes in parallel with the ability to respond to future challenges. Positive emotions (top) trigger the reversed Carnot cycle, which accumulates energy and entropy (the entropy at the end of the cycle is A′ where S (A′) > S (A)). Negative emotions initiate an exothermic Carnot cycle, which accumulates information and wastes energy (entropy at the end of the cycle is A′ and S (A′) < S (A)).

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“…The six evolutionary dynamics differ in the order in which the birth and death events take place and the stage at which selection occurs. Several dynamics may also be combined into a single mixed dynamics, see, for example, [94,107]. Different updating mechanisms can yield different evolutionary outcomes, see, for example, [101].…”

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

confidence: 99%

“…Similarly, there are some very special directed graphs which act as amplifies (or suppressors) of selection [49] where the structure is critical and small structural changes would make big differences. Amplifying graphs and their properties are discussed in detail in [4,94].…”

Section: Game and Dynamics Parametersmentioning

confidence: 99%

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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Limits on amplifiers of natural selection under death-Birth updating

Cited by 60 publications

References 40 publications

Toward a universal model for spatially structured populations

Toward a universal model for spatially structured populations

The thermodynamics of cognition: A mathematical treatment

Modelling Evolution in Structured Populations Involving Multiplayer Interactions

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