Papers › Maintaining diversity in structured populations
Maintaining diversity in structured populations
David A. Brewster, Jakub Svoboda, Dylan Roscow, Krishnendu Chatterjee, Josef Tkadlec, Martin A. Nowak
We examine population structures for their ability to maintain diversity in neutral evolution. We use the general framework of evolutionary graph theory and consider birth-death (bd) and death-birth (db) updating. The population is of size N. Initially all individuals represent different types. The basic question is: what is the time T_N until one type takes over the population? This time is known as consensus time in computer science and as total coalescent time in evolutionary biology. For the complete graph, it is known that T_N is quadratic in N for db and bd. For the cycle, we prove that T_N is cubic in N for db and bd. For the star, we prove that T_N is cubic for bd and quasilinear (NlogN) for db. For the double star, we show that T_N is quartic for bd. We derive upper and lower bounds for all undirected graphs for bd and db. We also show the Pareto front of graphs (of size N=8) that maintain diversity the longest for bd and db. Further, we show that some graphs that quickly homogenize can maintain high levels of diversity longer than graphs that slowly homogenize. For directed graphs, we give simple contracting star-like structures that have superexponential time scales for maintaining diversity.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Tasks
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections