微生物和癌细胞的极端突变率可能会导致错误诱发的灭绝（EEX），其中每个后代细胞最终都会获得致命的突变。在这项工作中，我们研究了 n 种不同类型的关键出生-死亡过程，作为不断增长的人口中 EEX 的出生-死亡模型。每个 i 型细胞以相同的速率独立分裂 ( i ) → ( i ) ( i ) 或突变 ( i ) → ( i 1 ) 。细胞总数以 Yule 过程呈指数增长，直到出现 n 型细胞，该细胞类型只能以速率 1 分裂或死亡。这使得整个过程变得至关重要，因此在指数增长阶段之后，最终所有细胞都会以概率 1 死亡。我们提出了一般 n 型临界生灭过程的大时间渐近结果。我们发现，k 型细胞数量的质量函数具有代数平稳尾部 ( size ) - 1 - χ k ，其中 χ k = 2 1 - k ，对于 k = 2 , ⋯ , n ，形成鲜明对比到第一种类型的指数尾。相同的指数描述了渐近生存概率 ( time ) - xi k 的尾部。我们将这些结果应用于研究由于生物种群中无法忍受的突变率而导致的灭绝。© 2024。作者。

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 ) → ( i ) + ( i ) or mutates ( i ) → ( 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 divide or 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 ( size ) - 1 - χ k , with χ k = 2 1 - k , for k = 2 , ⋯ , n , in sharp contrast to the exponential tail of the first type. The same exponents describe the tail of the asymptotic survival probability ( time ) - ξ k . We present applications of the results for studying extinction due to intolerable mutation rates in biological populations.© 2024. The Author(s).