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-selection perturbation expansion of a mutant's fixation probability, from an arbitrary initial configuration of mutant and resident types. Our results apply to a broad class of stochastic evolutionary models, in which the size and spatial structure are arbitrary (but fixed). The problem of whether selection favors a given trait is thereby reduced from exponential to polynomial complexity in the population size, when selection is weak. We conclude by applying these methods to obtain new results for evolutionary dynamics on graphs.

Alex McAvoy

Benjamin Allen

Journal of mathematical biology

数学生物学杂志专注于数学生物学 - 使用数学方法获得生物学理解或解释生物学现象的工作。涵盖的生物学领域包括但不限于细胞生物学、生理学、发育、神经生物学、遗传学和种群遗传学，人口生物学、生态学、行为生物学、进化论、流行病学、免疫学、分子生物学、生物流体、DNA和蛋白质结构和功能。包括计算和可视化方法在内的所有数学方法都是合适的。

The Journal of Mathematical Biology focuses on mathematical biology, aiming to understand and explain biological phenomena through mathematical methods. The fields of biology covered include, but are not limited to, cell biology, physiology, development, neurobiology, genetics, population genetics, demography, ecology, behavioral biology, evolution, epidemiology, immunology, molecular biology, biophysics, and the structure and function of DNA and proteins. All mathematical methods, including computational and visualization techniques, are welcome.

《Journal of Mathematical Biology》是一本专注于数学生物学的期刊，致力于通过数学方法来理解和解释生物现象。该期刊涵盖的生物学领域包括但不限于细胞生物学、生理学、发育、生物神经学、遗传学、种群遗传学、人口生物学、生态学、行为生物学、进化论、流行病学、免疫学、分子生物学、生物流体以及DNA和蛋白质的结构与功能。所有涉及计算和可视化方法的数学研究均被接受。

Journal of Mathematical Biology

J Math Biol

Fixation probabilities in evolutionary dynamics under weak selection.

This study obtains a weak-selection perturbation expansion of a mutant’s fixation probability, from an arbitrary initial configuration of mutant and resident types, in which the size and spatial structure are arbitrary (but fixed).

Category	Quartile
数学	4
数学, 数学与计算生物学	3
数学, 生物学	4

Fixation probabilities in evolutionary dynamics under weak selection.

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Category	Quartile
MATHEMATICAL & COMPUTATIONAL BIOLOGY	2