History matters when individual prior conditions contain important information about the fate of individuals. We present a general framework for demographic models which incorporates the effects of history on population dynamics. The framework incorporates prior condition into the i-state variable and includes an algorithm for constructing the population projection matrix from information on current state dynamics as a function of prior condition. Three biologically motivated classes of prior condition are included: prior stages, linear functions of current and prior stages, and equivalence classes of prior stages. Taking advantage of the matrix formulation of the model, we show how to calculate sensitivity and elasticity of any demographic outcome. Prior condition effects are a source of inter-individual variation in vital rates, i.e., individual heterogeneity. As an example, we construct and analyze a second-order model of Lathyrus vernus, a long-lived herb. We present population growth rate, the stable population distribution, the reproductive value vector, and the elasticity of λ to changes in the second-order transition rates. We quantify the contribution of prior conditions to the total heterogeneity in the stable population of Lathyrus using the entropy of the stable distribution.

中文翻译：

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历史重要的人口统计学：二阶矩阵人口模型的构建和分析。

当个人的先决条件包含有关个人命运的重要信息时，历史就很重要。我们为人口模型提供了一个总体框架，其中纳入了历史对人口动态的影响。该框架结合了之前状态到我状态变量，并包括一种算法，用于根据当前状态动态的信息根据先验条件构造总体投影矩阵。包括三个生物动力类别的先决条件：先验阶段，当前阶段和先验阶段的线性函数以及先验阶段的等价类。利用模型的矩阵公式，我们展示了如何计算任何人口统计结果的敏感性和弹性。先前状况的影响是生命率（即个体异质性）个体间差异的来源。例如，我们构建并分析了长寿命山La豆山thy豆的二阶模型。我们给出了人口增长率，稳定的人口分布，生殖价值向量以及种群的弹性。λ表示二阶跃迁速率的变化。我们使用稳定分布的熵来量化先前条件对稳定山thy豆种群总体异质性的贡献。