Explore a mathematical lecture on Lambda-coalescents arising in populations with dormancy. Delve into a model of population evolution through spring, summer, and winter seasons, examining how dormant individuals wake and reproduce. Discover how early-waking individuals can lead to Lambda-coalescent genealogies, allowing multiple ancestral lines to merge simultaneously. Learn about the characterization of Lambda-coalescents in this framework, including the beta coalescent's role when wake-up rates increase exponentially. Investigate topics such as the Wright-Fisher Model, Kingman's Coalescent, Cannings models, and heavy-tailed offspring distributions. Gain insights into the genealogy of populations with dormancy and the classification of possible limits in this mathematical exploration of population dynamics.
Lambda-Coalescents Arising in a Population With Dormancy
Hausdorff Center for Mathematics via YouTube
Overview
Syllabus
A-coalescents arising in a population with dormancy
The Wright-Fisher Model
Kingman's Coalescent (Kingman, 1982)
A Limit Theorem
Coalescents with multiple mergers (A-coalescents)
Definition and construction of the A-coalescent
Cannings models (Cannings, 1974)
Convergence of the genealogy in Cannings models
Heavy-tailed offspring distributions
Idea of the proof (1 2)
Idea of Wright and Vestigian (2019)
A model involving dormancy
A two-point distribution
Genealogy of the population
Exponentially increasing rate of exit from dormancy
Classifying the possible limits
The effect of summer
Summary and conclusions
Taught by
Hausdorff Center for Mathematics
