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Anomalous First Passage in Evolution: Edge-KPZ Theory

  • Tetsuhiro S. Hatakeyama
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Abstract

The pace of evolution depends on how rapidly new phenotypes arise. We show that neutral Wright-Fisher evolution exhibits anomalous first passage despite diffusive mutations. The mean time for the first individual to reach a prescribed phenotypic distance scales approximately as (σ2)−3/2 with mutation variance σ2. Two crossovers bound this regime, with inverse-variance scaling on either side. Combining coalescent theory with Kardar-Parisi-Zhang (KPZ) fluctuations at the dilute population edge, we develop an edge-KPZ theory of all three regimes. The anomaly persists under weak selection.

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Cite

BibTeXRIS
BibTeX
@misc{hatakeyama2026anomalous,
  title = {{Anomalous First Passage in Evolution: Edge-KPZ Theory}},
  author = {Tetsuhiro S. Hatakeyama},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.16499},
  eprint = {2609.16499},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.16499},
}
RIS
TY  - UNPB
TI  - Anomalous First Passage in Evolution: Edge-KPZ Theory
AU  - Tetsuhiro S. Hatakeyama
PY  - 2026
DA  - 2026/09/15
PB  - arXiv
DO  - 10.48550/arxiv.2609.16499
UR  - https://arxiv.org/abs/2609.16499
AB  - The pace of evolution depends on how rapidly new phenotypes arise. We show that neutral Wright-Fisher evolution exhibits anomalous first passage despite diffusive mutations. The mean time for the first individual to reach a prescribed phenotypic distance scales approximately as (σ^2)^−3/2 with mutation variance σ^2. Two crossovers bound this regime, with inverse-variance scaling on either side. Combining coalescent theory with Kardar-Parisi-Zhang (KPZ) fluctuations at the dilute population edge, we develop an edge-KPZ theory of all three regimes. The anomaly persists under weak selection.
ER  -