Fixation probabilities in evolutionary dynamics under weak selection

McAvoy, Alex; Allen, Benjamin

doi:10.1007/s00285-021-01568-4

Cited by 48 publications

(64 citation statements)

References 76 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To calculate the zeroth-and first-order coefficients, ρ � and ρ 0 respectively, in the weak-selection expansion, Eq (3), we apply methods developed in previous works [14,33,45]. We address the zeroth-order (neutral drift) and first-order (weak selection) terms separately.…”

Section: Calculating Fixation Probabilitymentioning

confidence: 99%

“…Weak selection. To obtain the first-selection coefficient, ρ 0 , we turn to a method developed by McAvoy and Allen [33]. Consider an arbitrary initialization, characterized by a probability distribution {μ i } of initial mutant locations.…”

Section: Calculating Fixation Probabilitymentioning

confidence: 99%

“…However, most nonlethal biological mutations are either neutral (r = 1) or weakly selected (r � 1). Our previous work [12,14,33] has shown that, in these cases, fixation probabilities can be computed in polynomial time. For neutral mutations, the fixation probability determines the population's "molecular clock"-the rate at which neutral genetic substitutions accrue over time.…”

Section: Introductionmentioning

confidence: 99%

“…For weakly selected mutations, fixation probabilities can be computed by combining perturbative methods [33][34][35][36][37] with coalescing random walks [38][39][40][41]. Allen et al [12] applied this method to dB updating, and showed how it allows for the efficient identification of amplifiers and suppressors of weak selection.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Fixation probabilities in graph-structured populations under weak selection

et al. 2021

Self Cite

View full text Add to dashboard Cite

A population’s spatial structure affects the rate of genetic change and the outcome of natural selection. These effects can be modeled mathematically using the Birth-death process on graphs. Individuals occupy the vertices of a weighted graph, and reproduce into neighboring vertices based on fitness. A key quantity is the probability that a mutant type will sweep to fixation, as a function of the mutant’s fitness. Graphs that increase the fixation probability of beneficial mutations, and decrease that of deleterious mutations, are said to amplify selection. However, fixation probabilities are difficult to compute for an arbitrary graph. Here we derive an expression for the fixation probability, of a weakly-selected mutation, in terms of the time for two lineages to coalesce. This expression enables weak-selection fixation probabilities to be computed, for an arbitrary weighted graph, in polynomial time. Applying this method, we explore the range of possible effects of graph structure on natural selection, genetic drift, and the balance between the two. Using exhaustive analysis of small graphs and a genetic search algorithm, we identify families of graphs with striking effects on fixation probability, and we analyze these families mathematically. Our work reveals the nuanced effects of graph structure on natural selection and neutral drift. In particular, we show how these notions depend critically on the process by which mutations arise.

show abstract

Section: Calculating Fixation Probabilitymentioning

confidence: 99%

Section: Calculating Fixation Probabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Fixation probabilities in graph-structured populations under weak selection

et al. 2021

Self Cite

View full text Add to dashboard Cite

show abstract

“…The effects of population structure on cooperation have been studied theoretically, using computer simulations 18 , by approximation techniques 19 , and by direct analysis of special cases 20,21 ; and they have been observed empirically in laboratory experiments . The latest mathematical results allow for exhaustive analysis of large families of heterogeneous population structures [23][24][25] and arbitrary initial configurations of individuals 26 . A large portion of population structures favor antisocial traits, such as spite 27 , which is simultaneously intriguing and concerning.…”

mentioning

confidence: 99%

Evolution of prosocial behavior in multilayer populations

McAvoy

Mori

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

Human societies include many types of social relationships. Friends, family, business colleagues, online contacts, and religious groups, for example, can all contribute to an individual's social life. Individuals may behave differently in different domains, but their success in one domain may nonetheless engender success in another. The complexity caused by distinct, but coupled, arenas of social interaction may be a key driver of prosocial or selfish behavior in societies. Here, we study this problem using multilayer networks to model a population with multiple domains of social interactions. An individual can appear in multiple different layers, each with separate behaviors and environments. We provide mathematical results on the resulting behavioral dynamics, for any multilayer structure. Across a diverse space of structures, we find that coupling between layers tends to promote prosocial behavior. In fact, even if prosociality is disfavored in each layer alone, multilayer coupling can promote its proliferation in all layers simultaneously. We apply these techniques to six real-world multilayer social networks, ranging from the networks of socio-emotional and professional relationships in a Zambian community, to the networks of online and offline relationships within an academic University. Our results suggest that coupling between distinct domains of social interaction is critical for the spread of prosociality in human societies.

show abstract

Spectral dynamics of guided edge removals and identifying transient amplifiers for death–Birth updating

Richter

2023

J. Math. Biol.

View full text Add to dashboard Cite

The paper deals with two interrelated topics: (1) identifying transient amplifiers in an iterative process, and (2) analyzing the process by its spectral dynamics, which is the change in the graph spectra by edge manipulation. Transient amplifiers are networks representing population structures which shift the balance between natural selection and random drift. Thus, amplifiers are highly relevant for understanding the relationships between spatial structures and evolutionary dynamics. We study an iterative procedure to identify transient amplifiers for death–Birth updating. The algorithm starts with a regular input graph and iteratively removes edges until desired structures are achieved. Thus, a sequence of candidate graphs is obtained. The edge removals are guided by quantities derived from the sequence of candidate graphs. Moreover, we are interested in the Laplacian spectra of the candidate graphs and analyze the iterative process by its spectral dynamics. The results show that although transient amplifiers for death–Birth updating are generally rare, a substantial number of them can be obtained by the proposed procedure. The graphs identified share structural properties and have some similarity to dumbbell and barbell graphs. We analyze amplification properties of these graphs and also two more families of bell-like graphs and show that further transient amplifiers for death–Birth updating can be found. Finally, it is demonstrated that the spectral dynamics possesses characteristic features useful for deducing links between structural and spectral properties. These feature can also be taken for distinguishing transient amplifiers among evolutionary graphs in general.

show abstract

Fixation probabilities in evolutionary dynamics under weak selection

Cited by 48 publications

References 76 publications

Fixation probabilities in graph-structured populations under weak selection

Fixation probabilities in graph-structured populations under weak selection

Evolution of prosocial behavior in multilayer populations

Spectral dynamics of guided edge removals and identifying transient amplifiers for death–Birth updating

Contact Info

Product

Resources

About