Abstract The need to follow structured populations, as opposed to unstructured ones, is well-recognized. The most detailed category of population models are the individual-based population models (IBMs), also called agent-based population models (ABMs). Their analysis is generally by simulation in time followed by statistical analysis of the numerical results. A less detailed method is the physiologically structured population model approach (PSPMs) leading originally to continuous-time partial differential equations ( pde s) for the p(opulation)-states such as number(-density) with respect to time and i(ndividual)-state such as age and/or size and later to a delay equation formulation. Their mathematical analysis and computational methods are generally complex. Discrete-time matrix population models (MPMs) are much simpler to analyse in all respects, but the applicability is limited due to stringent modelling assumptions made. We discuss here a class of models we call the Cohort Projection Models (CPMs), which were formerly introduced as a special case of PSPMs with pulsed reproduction. CPMs follow cohorts of identical individuals in a Lagrangian way of which the changes of their i-states such as, size, energy reserves and maturity, are described by age dependent ordinary differential equations ( ode )s from DEB theory. Simultaneously the p-states, such as number of individuals are described by time dependent ode s obeying conservation laws. The population is subdivided in generations on the assumption that seasonal cycles synchronize reproduction events among cohorts and all eggs that are produced by different generations are the same. Feedback from the environment can be included via specification of food dynamics that accommodates competition. Temperature follows a specified periodic trajectory in time. This allows for the definition of a projection map of i-states and p-states, from one reproduction event to the next. The projection interval is typically one year for seasonal variability. The properties of the map can be studied using nonlinear dynamical system theory, such as existence and stability of fixed points and, thereby, the long-term dynamics of the food-population system. We demonstrate this using deb parameter values from the Add-my-Pet (AmP) collection for over 2000 animal species, which were estimated from empirical data. CPMs are meant to match the relative simplicity of the analysis of MPMs with the realism of the deb models for the dynamics of the population individuals.

中文翻译：

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一种跟踪具有周期性、同步和迭代繁殖的结构化种群的队列投影方法

摘要 与非结构化人群相反，需要遵循结构化人群，这是众所周知的。人口模型最详细的类别是基于个体的人口模型 (IBM)，也称为基于代理的人口模型 (ABM)。他们的分析通常是通过及时模拟，然后对数值结果进行统计分析。一个不太详细的方法是生理结构的人口模型方法 (PSPMs)，最初导致 p(opulation) 状态的连续时间偏微分方程 (pde s)，例如数量(-密度) 相对于时间和 i(ndividual )-状态，例如年龄和/或大小，然后是延迟方程公式。他们的数学分析和计算方法通常很复杂。离散时间矩阵总体模型 (MPM) 在所有方面都更易于分析，但由于进行了严格的建模假设，因此其适用性受到限制。我们在这里讨论一类我们称为群组投影模型 (CPM) 的模型，它以前是作为具有脉冲再现的 PSPM 的一个特例引入的。CPM 以拉格朗日的方式跟踪相同个体的队列，其中它们的 i 状态的变化，例如大小、能量储备和成熟度，由 DEB 理论中的年龄相关常微分方程 (ode) 描述。同时，p 状态，例如个体数量，由遵守守恒定律的时间相关 ode 描述。假设季节性周期使队列之间的繁殖事件同步，并且不同代产生的所有卵都相同，则种群被细分为几代。可以通过适应竞争的食物动态规范来包括来自环境的反馈。温度在时间上遵循指定的周期性轨迹。这允许定义从一个再现事件到下一个再现事件的 i 状态和 p 状态的投影图。对于季节性变化，预测间隔通常为一年。可以使用非线性动力系统理论研究地图的属性，例如不动点的存在性和稳定性，从而研究食物人口系统的长期动态。我们使用来自 Add-my-Pet (AmP) 集合的 2000 多种动物物种的 deb 参数值证明了这一点，这些值是根据经验数据估计的。CPM 旨在将 MPM 分析的相对简单性与 deb 模型对种群个体动态的真实性相匹配。