# Fixation probabilities in evolutionary dynamics under weak selection.

@article{McAvoy2021FixationPI, title={Fixation probabilities in evolutionary dynamics under weak selection.}, author={Alex McAvoy and Benjamin Allen}, journal={Journal of mathematical biology}, year={2021}, volume={82 3}, pages={ 14 } }

In evolutionary dynamics, a key measure of a mutant trait's success is the probability that it takes over the population given some initial mutant-appearance distribution. This "fixation probability" is difficult to compute in general, as it depends on the mutation's effect on the organism as well as the population's spatial structure, mating patterns, and other factors. In this study, we consider weak selection, which means that the mutation's effect on the organism is small. We obtain a weak…

## 18 Citations

### Fixation probabilities in graph-structured populations under weak selection

- MathematicsPLoS Comput. Biol.
- 2021

This work derives an expression for the fixation probability, of a weakly-selected mutation, in terms of the time for two lineages to coalesce, and enables weak-selection fixation probabilities to be computed, for an arbitrary weighted graph, in polynomial time.

### Natural selection of mutants that modify population structure

- Biology
- 2021

It is shown that enhanced motility tends to increase an invader’s fixation probability, but there are interesting exceptions, and that for low-dimensional lattices, the effect of altered motility is comparable to that of altered fitness.

### Suppressors of fixation can increase average fitness beyond amplifiers of selection.

- BiologyProceedings of the National Academy of Sciences of the United States of America
- 2022

It is shown that another set of graphs, called suppressors of fixation, can attain the highest population mean fitness, the key reason behind this is their ability to efficiently reject deleterious mutants.

### Fixation Maximization in the Positional Moran Process

- Computer ScienceAAAI
- 2022

The positional Moran process is introduced, a natural generalization in which the mutant fitness advantage is only realized on specific nodes called active nodes, and the problem of fixation maximization is studied: given a budget k, choose a set of k active nodes that maximize the fixation probability of the invading mutant.

### The arrow of evolution when the offspring variance is large

- Mathematics, Biology
- 2022

A model for the evolution of two types reproducing in a population of non-constant size shows that large offspring variance can reverse the direction of evolution and favor cooperation.

### A theory of evolutionary dynamics on any complex spatial structure

- BiologybioRxiv
- 2021

This work builds 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, and shows that both a network’s degree distribution and its node mixing pattern shape the evolutionary dynamics of new mutations.

### Evaluating the structure-coefficient theorem of evolutionary game theory.

- EconomicsProceedings of the National Academy of Sciences of the United States of America
- 2022

It is shown that the outcome of selection varies dramatically depending on how goods are produced and distributed, on the details of population structure, and on the rate of mutation.

### Invasion Dynamics in the Biased Voter Process

- Computer ScienceIJCAI
- 2022

The problem of fixation probability maximization under the voter process is studied, showing that the problem is NP-hard for both regimes r>1 and r<1, while the latter case is also inapproximable within any multiplicative factor that is independent of r.

### Intriguing effects of selection intensity on the evolution of prosocial behaviors

- BiologybioRxiv
- 2021

It is shown that there can be a “sweet spot” for the balance of these two forces, with sufficient noise for rare mutants to become established and sufficient selection to spread, and suggested that intermediate selection intensities can elicit novel and rich dynamics in the evolution of prosocial behaviors.

### The coalescent with arbitrary spatial and genetic structure

- Biology
- 2022

An abstract formulation of the coalescent that applies to a broad class of neutral drift models, allowing for arbitrary spatial structure and mating patterns is introduced, and biologically relevant quantities, including coalescence time, coalescence branch length, reproductive value, number of mutations prior to coalescence, and stationary probabilities of identity-by-descent and identity- by-state are defined and analyzed.

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