Recurrence in Sequence Space: How Epistasis Mimics Shared Ancestry
Abstract
Sequences in a protein family do not explore the sequence space freely: folding, packing, and binding couple residues, so the set of viable sequences is irreducibly correlated, a phenomenon referred to as epistasis. We show that such correlations lower the \emph{intrinsic dimension} dIN of sequence space, counteracting the concentration of measure and broadening the distribution of pairwise distances. Consequentially, they make it likely that independently evolving lineages \emph{recur}, approaching one another by chance long after they last shared an ancestor. Using Kac's lemma we show that the logarithmic mean recurrence time grows linearly with the intrinsic dimension, log τrec ∝ dIN for typical sequences, so strongly constrained (low-dimensional) families recur often and generate sequence similarity that carries no genealogical signal. We establish this first in a solvable Ising-like model with tunable correlation, then in a real protein family using Potts models and Markov chain Monte Carlo, where dIN remains predictive of recurrence even in multi-basins landscapes. Because recurrence is a property of the evolutionary process rather than of any estimator, it bounds the recoverability of deep history for distance-based and likelihood methods alike.
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BibTeX
@misc{chiarantoni2026recurrence,
title = {{Recurrence in Sequence Space: How Epistasis Mimics Shared Ancestry}},
author = {Pietro Chiarantoni and Mina Mahboubi and Jason Lamanna and Vincenzo Carnevale},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00360},
eprint = {2611.00360},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00360},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Recurrence in Sequence Space: How Epistasis Mimics Shared Ancestry
AU - Pietro Chiarantoni
AU - Mina Mahboubi
AU - Jason Lamanna
AU - Vincenzo Carnevale
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00360
UR - https://arxiv.org/abs/2611.00360
AB - Sequences in a protein family do not explore the sequence space freely: folding, packing, and binding couple residues, so the set of viable sequences is irreducibly correlated, a phenomenon referred to as epistasis. We show that such correlations lower the \emph{intrinsic dimension} d_IN of sequence space, counteracting the concentration of measure and broadening the distribution of pairwise distances. Consequentially, they make it likely that independently evolving lineages \emph{recur}, approaching one another by chance long after they last shared an ancestor. Using Kac's lemma we show that the logarithmic mean recurrence time grows linearly with the intrinsic dimension, log τ_rec ∝ d_IN for typical sequences, so strongly constrained (low-dimensional) families recur often and generate sequence similarity that carries no genealogical signal. We establish this first in a solvable Ising-like model with tunable correlation, then in a real protein family using Potts models and Markov chain Monte Carlo, where d_IN remains predictive of recurrence even in multi-basins landscapes. Because recurrence is a property of the evolutionary process rather than of any estimator, it bounds the recoverability of deep history for distance-based and likelihood methods alike.
ER -