By quantifying key life history parameters in populations, such as growth rate, longevity, and generation time, researchers and administrators can obtain valuable insights into its dynamics. Although point estimates of demographic parameters have been available since the inception of demography as a scientific discipline, the construction of confidence intervals has typically relied on approximations through series expansions or computationally intensive techniques. This study introduces the first mathematical expression for calculating confidence intervals for the aforementioned life history traits when individuals are unidentifiable and data are presented as a life table. The key finding is the accurate estimation of the confidence interval for $r$, the instantaneous growth rate, which is tested using Monte Carlo simulations with four arbitrary discrete distributions. In comparison to the bootstrap method, the proposed interval construction method proves more efficient, particularly for experiments with a total offspring size below 400. We discuss handling cases where data are organized in extended life tables or as a matrix of vital rates. We have developed and provided accompanying code to facilitate these computations.

通过量化种群中的关键生命史参数，例如增长率、寿命和世代时间，研究人员和管理人员可以获得对其动态的宝贵见解。尽管自人口统计学作为一门科学学科诞生以来就可以对人口参数进行点估计，但置信区间的构建通常依赖于通过级数展开或计算密集型技术进行近似。本研究引入了第一个数学表达式，用于计算当个体无法识别且数据以生命表形式呈现时上述生活史特征的置信区间。关键发现是准确估计置信区间$r$，瞬时增长率，使用蒙特卡罗模拟和四个任意离散分布进行测试。与 bootstrap 方法相比，所提出的区间构建方法被证明更有效，特别是对于后代总大小低于 400 的实验。我们讨论处理数据在延长寿命表中或作为生命率矩阵组织的情况。我们开发并提供了随附的代码来促进这些计算。