A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations.
A Hierarchical Kinetic Theory of Birth, Death and Fission in Age-Structured Interacting Populations.
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DOI：
10.1007/s10955-016-1524-x
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发表时间：
2016
影响因子：
1.6
通讯作者：
Greenman CD
中科院分区：
文献类型：
--
作者：
Chou T;Greenman CD
我们开发了描述随机年龄结构种群进化的数学模型。在回顾了现有的方法之后，我们制定了一个完整的动力学框架，用于在空间依赖环境中经历出生、死亡和裂变过程的年龄结构相互作用的种群。我们定义了人口规模年龄图的全概率密度，并在特定条件下找到结果。还明确地推导了与更经典模型的联系。特别是，我们表明非相互作用过程的阶乘矩是由描述平均场确定性行为的McKendrick-von Foerster方程的自然推广来描述的。我们的方法利用混合型多维概率分布，类似于气体动力学研究中使用的分布，并且具有满足bbgky类方程层次的术语。
We develop mathematical models describing the evolution of stochastic age-structured populations. After reviewing existing approaches, we formulate a complete kinetic framework for age-structured interacting populations undergoing birth, death and fission processes in spatially dependent environments. We define the full probability density for the population-size age chart and find results under specific conditions. Connections with more classical models are also explicitly derived. In particular, we show that factorial moments for non-interacting processes are described by a natural generalization of the McKendrick-von Foerster equation, which describes mean-field deterministic behavior. Our approach utilizes mixed-type, multidimensional probability distributions similar to those employed in the study of gas kinetics and with terms that satisfy BBGKY-like equation hierarchies.