This sharpens the result in the paper Jagers and Zuyev (J Math Biol 81:845–851, 2020): consider a population changing at discrete (but arbitrary and possibly random) time points, the conditional expected change, given the complete past population history being negative, whenever population size exceeds a carrying capacity. Further assume that there is an \(\epsilon > 0\) such that the conditional probability of a population decrease at the next step, given the past, always exceeds \(\epsilon \) if the population is not extinct but smaller than the carrying capacity. Then the population must die out.

中文翻译：

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修正：软承载环境中的种群最终灭绝

这增强了 Jagers 和 Zuyev (J Math Biol 81:845–851, 2020) 论文中的结果：考虑在离散（但任意且可能随机）时间点变化的种群，考虑到完整的过去种群历史，条件预期变化为负，当人口规模超过承载能力时。进一步假设有一个\（\小量> 0 \） ，使得给定的过去在下一步骤群体减少的条件概率，总是超过\（\小量\）如果人口不灭绝但比小承载能力。那么人口必须灭绝。