Demography is at the core of ecology, evolution, and conservation biology. The simple recognition that individuals in a given population contribute to its dynamics in different ways revolutionised the ways in which demographers approach data collection, analyses, and interpretation of their study populations, from bacteria to humans. Matrix population models, discrete-time, discrete-state (i.e. individuals are categorised into discrete categories based on traits such as age or stage), were first introduced to the scientific community by Patrick Leslie 75 years ago. Since then, the applications of matrix population models to ecology, evolution, and conservation biology have strongly been running strong and in parallel with its robust mathematical development. This special feature contains 14 novel contributions that represent some the cutting-edge mathematical formulations and applications of this powerful demographic tool. In addition to highlighting the key contributions of this manuscripts, we provide suggestions to some of the challenges that researchers using matrix population models must overcome in the coming decades to truly unlock the potential of this analytical demographic tool.

人口统计学是生态学，进化论和保护生物学的核心。对给定种群中的个体以不同方式对其动态做出贡献的简单认识，彻底改变了人口统计学家从细菌到人类的数据收集，分析和解释研究种群的方式。矩阵总体模型，离散时间，离散状态（即根据年龄或阶段等特征将个人分为不同的类别），是75年前帕特里克·莱斯利（Patrick Leslie）首次将其引入科学界的。从那时起，矩阵种群模型在生态学，进化论和保护生物学中的应用一直在强劲发展，并与其稳健的数学发展并行。此特殊功能包含14项新颖的著作，代表了这一强大的人口统计工具的一些前沿数学公式和应用。除了强调该手稿的关键作用外，我们还为使用矩阵人口模型的研究人员在未来几十年中必须克服的一些挑战提供建议，以真正释放这种分析人口统计工具的潜力。