AMC-SS Spatial models for populations with variable offspring laws

具有可变后代规律的种群的 AMC-SS 空间模型

• 批准号: 0706713
• 负责人: Wenbo Li
• 金额: $ 13.18万
• 依托单位: University of Delaware
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-08-01 至 2011-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0706713&HistoricalAwards=false
• 关键词: AMC; SS; Spatial; models; populations

This project is concerned with the analysis of spatial stochastic particle models for which the offspring distribution is state dependent or relatively singular. For the former, the study is focused on offspring distributions that give small populations (of a particular type) an advantage. Various (non-linear) self-regulation mechanisms as well as spatial distributions of the particle population will be investigated, including versions of voter models with selection, multi-type models with fixed local population size and branching particle models alongside their large population diffusion limits. One of the central questions will be to determine parameter regimes for long-term survival without explosion of the population size and -if multiple types of particles are present initially- of long-term coexistence of various or all types. Another part of this project is concerned with the description of spatially distributed particle populations with singular offspring distributions that model populations with potentially large individual families. These have attracted much recent attention as several deep connections between different classes of stochastic processes have been discovered and exploited - albeit in a non-spatial setting. The focus of this work will be on the forward evolution of particle mass as well as the backward evolution of genealogies and their diffusion limits as described by measure-valued processes, stochastic differential equations and spatial coalescent processes. Multi-type models for genes with mutation, selection and recombination that have ties to both lines of research will also be considered. Understanding the behavior of large particle systems is of importance for deducing macroscopic properties from microscopic rules in a wide variety of fields such as Physics, Chemistry, Biology and Computer Science. In this research, spatial stochastic processes that model self-regulation phenomena are constructed and analyzed. Such phenomena are observed in many physical systems of particle populations. The aim is to identify the underlying mechanisms and conditions for various macroscopic behaviors such as survival and coexistence of different types to occur. These questions are in particular of interest for biological populations in epidemiology, ecology and genetics. Spatial stochastic models for reproducing populations in which the offspring of single individuals may on occasion replace a significant proportion or the population are also considered. This kind of behavior is thought to occur, for example, in populations in which certain genes carry a selective advantage. These models are therefore of particular relevance in genetics. The analysis of realistic models for the evolution of genes and the description of genealogies is of importance for the correct quantitative analysis and interpretation of the now ubiquitous gene sequence data. Applications range from reconstructing the origin and history of humans to locating and identifying genes on the genome that are causative factors for diseases.

该项目涉及空间随机粒子模型的分析，其后代分布是状态相关的或相对单一的。对于前者，该研究的重点是赋予小种群（特定类型）优势的后代分布。将研究各种（非线性）自我调节机制以及粒子种群的空间分布，包括具有选择的选民模型版本、具有固定局部种群大小的多类型模型以及具有大种群扩散限制的分支粒子模型。核心问题之一是确定长期生存的参数制度，而不会导致种群规模爆炸，以及（如果最初存在多种类型的粒子）各种或所有类型的长期共存。该项目的另一部分涉及对具有单一后代分布的空间分布粒子种群的描述，该种群对具有潜在大个体家族的种群进行建模。这些最近引起了人们的广泛关注，因为不同类别的随机过程之间的一些深层联系已经被发现和利用——尽管是在非空间环境中。这项工作的重点将是粒子质量的前向演化以及谱系的后向演化及其扩散极限，如测值过程、随机微分方程和空间聚结过程所描述的。还将考虑与这两个研究方向相关的具有突变、选择和重组的基因的多类型模型。了解大粒子系统的行为对于从物理、化学、生物学和计算机科学等众多领域的微观规则推断宏观特性非常重要。 在这项研究中，构建并分析了模拟自我调节现象的空间随机过程。这种现象在许多粒子群物理系统中都可以观察到。目的是确定各种宏观行为（例如不同类型的生存和共存）发生的潜在机制和条件。这些问题对于流行病学、生态学和遗传学领域的生物群体尤其感兴趣。用于繁殖种群的空间随机模型，其中单个个体的后代有时可能会取代很大一部分，或者也考虑种群。这种行为被认为会发生在某些基因具有选择优势的群体中。因此，这些模型在遗传学中具有特别的相关性。 基因进化的现实模型的分析和谱系的描述对于正确定量分析和解释现在无处不在的基因序列数据具有重要意义。 应用范围从重建人类的起源和历史到定位和识别基因组上作为疾病致病因素的基因。