title: Two-time-scale population evolution on a singular landscape.
abstract: Under the effect of strong genetic drift, it is highly probable to observe gene fixation or gene loss in a population, shown by singular peaks on a potential landscape. The genetic drift-induced noise gives rise to two-time-scale diffusion dynamics on the bipeaked landscape. We find that the logarithmically divergent (singular) peaks do not necessarily imply infinite escape times or biological fixations by iterating the Wright-Fisher model and approximating the average escape time. Our analytical results under weak mutation and weak selection extend Kramers's escape time formula to models with B (Beta) function-like equilibrium distributions and overcome constraints in previous methods. The constructed landscape provides a coherent description for the bistable system, supports the quantitative analysis of bipeaked dynamics, and generates mathematical insights for understanding the boundary behaviors of the diffusion model.
authors.affiliation: Department of Biomathematics, University of California at Los Angeles, Los Angeles, California 90095-1766, USA.
authors.forename: Song
authors.initials: S
authors.lastname: Xu
authors.affiliation: Shanghai Center for Systems Biomedicine, Key Laboratory of Systems Biomedicine of Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China and Department of Mathematics, Xinyang Normal University, Xinyang 464000, Henan, China.
authors.forename: Shuyun
authors.initials: S
authors.lastname: Jiao
authors.affiliation: Department of Ecology and Evolution, University of Chicago, 1101 E. 57th Street, Chicago, Illinois 60637, USA.
authors.forename: Pengyao
authors.initials: P
authors.lastname: Jiang
authors.affiliation: Shanghai Center for Systems Biomedicine, Key Laboratory of Systems Biomedicine of Ministry of Education, Shanghai Jiao Tong University, Shanghai 200240, China and Department of Physics, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Ping
authors.initials: P
authors.lastname: Ao
mesh_terms: D000818:Animals; D003198:Computer Simulation; D017753:Ecosystem; D040961:Genetic Drift; D005828:Genetics, Population; D006801:Humans; D008957:Models, Genetic; D015233:Models, Statistical; D009154:Mutation / Q000235:genetics*; D012641:Selection, Genetic / Q000235:genetics*