Abstract We discuss lifetimes for a family of population-dependent branching processes. The attenuation factor (due to environment or competition, for example) is of Ricker type, i.e., the probability of an individual having offspring at all is of the form if the total population is n. Equivalently we can write the probability as where the carrying capacity K is the inverse of the attenuating factor. It is well known that the expected lifetime of such a process is exponential in K. If the carrying capacities vary much over time, for instance, if they are i.i.d. with a heavy-tailed distribution, the extinction scenario may change to a growth-catastrophe one with expected lifetimes much shorter. In addition to Ricker’s model, production functions of the Beverton–Holt and Hassell types are also discussed.

中文翻译：

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关于大小相关分支过程的生命周期

摘要 我们讨论了一个依赖种群的分支过程家族的生命周期。衰减因子（例如由于环境或竞争）是 Ricker 类型的，即一个个体有后代的概率是总人口数为 n 的形式。等效地，我们可以将概率写为其中承载能力 K 是衰减因子的倒数。众所周知，这种过程的预期寿命是 K 的指数。如果承载能力随时间变化很大，例如，如果它们具有重尾分布，则灭绝情景可能会变成增长灾难一种预期寿命要短得多。除了 Ricker 模型之外，还讨论了 Beverton-Holt 和 Hassell 类型的生产函数。