Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2603.27140 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914429166157824 |
|---|---|
| author | Blanchet, Jose Zhang, Zhenyuan |
| author_facet | Blanchet, Jose Zhang, Zhenyuan |
| contents | We study a continuous-time nearest-neighbor branching random walk on the $d$-dimensional $b$-ary hypercube $\{0,1,\dots,b-1\}^d$ as a model for viral quasispecies evolution under mutation and replication. Motivated by mutagenic antiviral treatments and evolutionary-safety questions, we analyze the first passage time to a fixed target genotype at Hamming distance $m$, corresponding to the first appearance of a prescribed collection of mutations. We derive sharp asymptotics for these first passage times, uniformly for $m\le d/L$ as $d\to\infty$ (where $L>0$ is a large constant), and identify a phase transition in first-passage scaling at $ρ=e$, where $ρ$ denotes the effective growth parameter. In the slow-branching regime $ρ\in(1,e)$ relevant to mutagenic treatment scenarios, the first passage time is asymptotically affine in the genome length $d$ and the target distance $m$. In particular, when replication is fixed and mutation exceeds branching, increasing the mutation rate can delay the first appearance of a prescribed genotype by order $d$, providing a quantitative perspective on evolutionary safety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_27140 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Viral Quasispecies Evolution as a Branching Random Walk on the Hypercube Blanchet, Jose Zhang, Zhenyuan Probability We study a continuous-time nearest-neighbor branching random walk on the $d$-dimensional $b$-ary hypercube $\{0,1,\dots,b-1\}^d$ as a model for viral quasispecies evolution under mutation and replication. Motivated by mutagenic antiviral treatments and evolutionary-safety questions, we analyze the first passage time to a fixed target genotype at Hamming distance $m$, corresponding to the first appearance of a prescribed collection of mutations. We derive sharp asymptotics for these first passage times, uniformly for $m\le d/L$ as $d\to\infty$ (where $L>0$ is a large constant), and identify a phase transition in first-passage scaling at $ρ=e$, where $ρ$ denotes the effective growth parameter. In the slow-branching regime $ρ\in(1,e)$ relevant to mutagenic treatment scenarios, the first passage time is asymptotically affine in the genome length $d$ and the target distance $m$. In particular, when replication is fixed and mutation exceeds branching, increasing the mutation rate can delay the first appearance of a prescribed genotype by order $d$, providing a quantitative perspective on evolutionary safety. |
| title | Viral Quasispecies Evolution as a Branching Random Walk on the Hypercube |
| topic | Probability |
| url | https://arxiv.org/abs/2603.27140 |