Lifetime reproductive performance is quantified here by the LRS (lifetime reproductive success), the random number of offspring an individual produces over its lifetime. Many field studies find that distributions of LRS among individuals are non-normal, zero-inflated and highly skewed. These results beg the question, what is the distribution of LRS predicted by demographic models when the only source of randomness is demographic stochasticity? Here we present the first exact analysis of the probability distribution of LRS for species described by age + stage models; our analysis starts with estimated vital rates. We illustrate with three examples: the Hadza, human hunter-foragers (age-only), the evergreen tree Tsuga canadensis (stage-only) and Roe deer, Capreolus capreolus (age + stage). For each we obtain the exact distribution of LRS, but also calculate and discuss the first three moments. Our results point to important questions about how such LRS distributions affect natural selection, and life history evolution.

中文翻译：

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终生生殖成功的偏差分布：超出均值和方差。

终生生殖能力在这里通过LRS（终生生殖成功）来量化，LRS是个体一生中产生的后代的随机数。许多现场研究发现，个体中LRS的分布是非正态的，零膨胀的和高度偏斜的。这些结果引出了一个问题，当唯一的随机性来源是人口随机性时，人口模型预测的LRS分布是什么？在这里，我们对年龄+阶段模型描述的物种的LRS概率分布进行首次精确分析。我们的分析从估计的生命率开始。我们用三个例子来说明：Hadza，人类猎人-觅食者（仅年龄），常绿树Tsuga canadensis（仅阶段）和Ro，Capreolus capreolus（年龄+阶段）。对于每一个，我们获得LRS的确切分布，而且还要计算和讨论前三个时刻。我们的结果指出了有关LRS分布如何影响自然选择和生活史演变的重要问题。