Transient amplifiers of selection and reducers of fixation for death-Birth updating on graphs.
Benjamin Allen, Christine Sample, Robert Jencks, James Withers, Patricia Steinhagen, Lori Brizuela, Joshua Kolodny, Darren Parke, Gabor Lippner, Yulia A Dementieva
Author Information
Benjamin Allen: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America. ORCID
Christine Sample: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America. ORCID
Robert Jencks: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America.
James Withers: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America.
Patricia Steinhagen: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America.
Lori Brizuela: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America.
Joshua Kolodny: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America. ORCID
Darren Parke: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America.
Gabor Lippner: Department of Mathematics, Northeastern University, Boston, Massachusetts, United States of America.
Yulia A Dementieva: Department of Mathematics, Emmanuel College, Boston, Massachusetts, United States of America.
The spatial structure of an evolving population affects the balance of natural selection versus genetic drift. Some structures amplify selection, increasing the role that fitness differences play in determining which mutations become fixed. Other structures suppress selection, reducing the effect of fitness differences and increasing the role of random chance. This phenomenon can be modeled by representing spatial structure as a graph, with individuals occupying vertices. Births and deaths occur stochastically, according to a specified update rule. We study death-Birth updating: An individual is chosen to die and then its neighbors compete to reproduce into the vacant spot. Previous numerical experiments suggested that amplifiers of selection for this process are either rare or nonexistent. We introduce a perturbative method for this problem for weak selection regime, meaning that mutations have small fitness effects. We show that fixation probability under weak selection can be calculated in terms of the coalescence times of random walks. This result leads naturally to a new definition of effective population size. Using this and other methods, we uncover the first known examples of transient amplifiers of selection (graphs that amplify selection for a particular range of fitness values) for the death-Birth process. We also exhibit new families of "reducers of fixation", which decrease the fixation probability of all mutations, whether beneficial or deleterious.
