Speaker
Description
How does spatial structure influence the fate of novel mutations in a population? Fixation dynamics and mutation-selection balance are known to depend sensitively on the interaction network underlying spatial structure \cite{lieberman:nature:2005,sharma:NatComm:2025, sharma:biorxiv:2025}. However, analyzing these processes on large heterogeneous graphs quickly becomes analytically intractable. In this talk, we develop a continuum framework for evolutionary dynamics using graph function (graphon) limits \cite{glasscock:arxiv:2016}, which can be understood as limits of sequences of large graphs. In the first part, we consider a Moran-type birth-death process and analyze the asymptotic fixation probabilities of rare beneficial mutations via a branching process approximation. In the second part, we study a Moran-type birth-death process with selection and mutation on a graphon and describe the nonlocal integro-differential equation governing the spatial distribution of mutant density. Within this framework, we characterize how fixation probabilities depend on network structure and analyze mutation-selection balance, examining how structural features of the graphon shape equilibrium configurations. Our results suggest that graphons provide a flexible and tractable approach for studying evolutionary dynamics in large structured populations.
Bibliography
@article{lieberman:nature:2005,
title = {Evolutionary dynamics on graphs},
volume = {433},
copyright = {http://www.springer.com/tdm},
issn = {0028-0836, 1476-4687},
url = {https://www.nature.com/articles/nature03204},
doi = {10.1038/nature03204},
language = {en},
number = {7023},
urldate = {2026-03-13},
journal = {Nature},
author = {Lieberman, Erez and Hauert, Christoph and Nowak, Martin A.},
month = jan,
year = {2005},
pages = {312--316},
}
@article{sharma:biorxiv:2025,
title={Population structure amplifies mutation load},
author={Sharma, Nikhil and Das, Suman G and Traulsen, Arne and Krug, Joachim},
journal={bioRxiv},
pages={2025--09},
year={2025},
publisher={Cold Spring Harbor Laboratory}
}
@misc{glasscock:arxiv:2016,
title = {What is a graphon?},
url = {http://arxiv.org/abs/1611.00718},
doi = {10.48550/arXiv.1611.00718},
urldate = {2026-03-13},
publisher = {arXiv},
author = {Glasscock, Daniel},
month = nov,
year = {2016},
note = {arXiv:1611.00718},
keywords = {Mathematics - Combinatorics},
}
@article{sharma:NatComm:2025,
title = {Graph-structured populations elucidate the role of deleterious mutations in long-term evolution},
volume = {16},
issn = {2041-1723},
url = {https://www.nature.com/articles/s41467-025-57552-9},
doi = {10.1038/s41467-025-57552-9},
language = {en},
number = {1},
urldate = {2026-03-13},
journal = {Nature Communications},
author = {Sharma, Nikhil and Das, Suman G. and Krug, Joachim and Traulsen, Arne},
month = mar,
year = {2025},
pages = {2355},
}
