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Quantitative Biology > Populations and Evolution

arXiv:2306.11609 (q-bio)
[Submitted on 20 Jun 2023 (v1), last revised 5 Jul 2024 (this version, v2)]

Title:Error-induced extinction in a multi-type critical birth-death process

Authors:Meritxell Brunet Guasch, P. L. Krapivsky, Tibor Antal
View a PDF of the paper titled Error-induced extinction in a multi-type critical birth-death process, by Meritxell Brunet Guasch and 1 other authors
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Abstract:Extreme mutation rates in microbes and cancer cells can result in error-induced extinction (EEX), where every descendant cell eventually acquires a lethal mutation. In this work, we investigate critical birth-death processes with $n$ distinct types as a birth-death model of EEX in a growing population. Each type-$i$ cell divides independently $(i)\to(i)+(i)$ or mutates $(i)\to(i+1)$ at the same rate. The total number of cells grows exponentially as a Yule process until a cell of type-$n$ appears, which cell type can only die at rate one. This makes the whole process critical and hence after the exponentially growing phase eventually all cells die with probability one. We present large-time asymptotic results for the general $n$-type critical birth-death process. We find that the mass function of the number of cells of type-$k$ has algebraic and stationary tail $(\text{size})^{-1-\chi_k}$, with $\chi_k=2^{1-k}$, for $k=2,\dots,n$, in sharp contrast to the exponential tail of the first type. The same exponents describe the tail of the asymptotic survival probability $(\text{time})^{-\chi_n}$. We present applications of the results for studying extinction due to intolerable mutation rates in biological populations.
Comments: 34 pages, 7 figures
Subjects: Populations and Evolution (q-bio.PE); Probability (math.PR)
Cite as: arXiv:2306.11609 [q-bio.PE]
  (or arXiv:2306.11609v2 [q-bio.PE] for this version)
  https://doi.org/10.48550/arXiv.2306.11609
arXiv-issued DOI via DataCite

Submission history

From: Xell Brunet Guasch [view email]
[v1] Tue, 20 Jun 2023 15:37:52 UTC (1,042 KB)
[v2] Fri, 5 Jul 2024 14:42:36 UTC (1,485 KB)
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