Mathematical Sciences: Interacting Particle Systems with Applications to Population Biology

数学科学：粒子系统的相互作用及其在群体生物学中的应用

• 批准号: 9403644
• 负责人: Claudia Neuhauser
• 金额: $ 6.5万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-05-15 至 1998-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9403644&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Interacting; Particle; Systems

9403644: Neuhauser Abstract. The first two parts of the research concern the investigation of several multispecies models from ecology and population biology. These models are formulated as complex spatial systems on the integer lattice in which each site is in one of a finite number of states indicating whether a certain species is present on that site. These systems evolve over time according to non-deterministic local rules which describe the dynamics of each species and how they interact with each other in this spatial environment. Models to be considered include host-parasitoid associations and a model for the study of genetic diversity of a species in a subdivided habitat in which local extinctions are frequent. These investigations are theoretical and experimental (computer simulations). The main goal is to study how the spatial component affects survival/coexistence of the species involved. In the third part, problems concerning DNA sequence comparisons are addressed. One project is to construct a statistical test that takes all types of mutations into account in order to assess the statistical significance of such comparisons. The other project is to investigate what happens when the sequences involved in the comparisons are very different. Current tests always assume that the frequencies with which letters in the sequences appear, are not too different. In the first two parts, the investigator will study several multispecies models from ecology and population biology. These models are formulated as complex spatial systems that evolve in time according to non-deterministic local rules. Examples include host-parasitoid associations and models for the study of genetic diversity of a species in a subdivided habitat in which local extinctions are frequent. Some of the proposed work is done in collaboration with researchers from the biology department at the University of Wisconsin - Madison and the USDA Forest Service. The main goal is to st udy ho w the spatial component affects survival/coexistence. In the third part, problems arising in DNA sequence comparisons are addressed. Such comparisons have revealed some unexpected sequence similarities and there is the need for statistical tests to assess statistical significance to such comparisons. Currently, there is no test available that takes all types of mutations into account that occur in DNA sequences. Furthermore, all available tests require the composition of the sequences (i.e., the frequencies with which the letters in the sequences appear) not to be too different. The proposed research addresses both problems.

9403644：《纽豪瑟摘要》。研究的前两部分从生态学和种群生物学的角度对几个多物种模型进行了研究。这些模型被表述为整数格上的复杂空间系统，其中每个站点处于指示该站点上是否存在特定物种的有限数量的状态之一。这些系统随着时间的推移根据非确定性的当地规则进化，这些规则描述了每个物种的动态以及它们如何在这个空间环境中相互作用。要考虑的模式包括寄主-寄生蜂联合和在局部灭绝频繁的细分生境中研究物种遗传多样性的模式。这些研究是理论和实验(计算机模拟)。主要目的是研究空间成分如何影响所涉及物种的生存/共存。第三部分讨论了DNA序列比对中存在的问题。一个项目是建立一个统计测试，考虑到所有类型的突变，以便评估这种比较的统计意义。另一个项目是研究当比较中涉及的序列非常不同时会发生什么。目前的测试总是假设字母在序列中出现的频率没有太大的不同。在前两部分中，调查者将从生态学和种群生物学的角度研究几个多物种模型。这些模型被表述为复杂的空间系统，根据非确定性的本地规则随时间演变。例子包括寄主-寄生蜂联合和模型，用于研究在局部灭绝频繁的细分生境中物种的遗传多样性。一些拟议的工作是与威斯康星大学麦迪逊分校生物系和美国农业部林业局的研究人员合作完成的。主要目的是研究影响生存/共存的空间因素。第三部分对DNA序列比对中存在的问题进行了分析。这种比较揭示了一些意想不到的序列相似之处，需要进行统计测试来评估这种比较的统计意义。目前，还没有一种测试可以将DNA序列中发生的所有类型的突变都考虑在内。此外，所有可用的测试都要求序列的组成(即序列中字母出现的频率)不能太不同。拟议的研究解决了这两个问题。