Mathematical Sciences: Interacting Particle Systems with Applications to Population Biology

9403644：诺伊豪泽摘要。 前两部分的研究涉及到生态学和种群生物学的几个多种群模型的调查。 这些模型被制定为复杂的空间系统的整数格，其中每个网站是在一个有限数量的状态，表明是否存在某个物种在该网站之一。 这些系统随着时间的推移，根据非确定性的本地规则，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。 要考虑的模型包括寄主-寄生蜂协会和一个模型，用于研究一个物种的遗传多样性在一个细分的栖息地，其中当地的preception是频繁的。 这些调查是理论和实验（计算机模拟）。 主要目标是研究空间成分如何影响所涉物种的生存/共存。 第三部分讨论了DNA序列比较中存在的问题。 一个项目是构建一个统计检验，将所有类型的突变考虑在内，以评估此类比较的统计学意义。 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，研究者将从生态学和种群生物学的角度研究几个多物种模型。 这些模型被公式化为复杂的空间系统，根据非确定性的本地规则随时间演变。 例子包括寄主-寄生蜂协会和模型的遗传多样性的一个物种在一个细分的栖息地，其中当地的栖息地是频繁的研究。 一些拟议的工作是与来自威斯康星州-麦迪逊大学生物系和美国农业部林务局的研究人员合作完成的。 主要目标是研究空间成分如何影响生存/共存。第三部分讨论了DNA序列比对中存在的问题。这样的比较已经揭示了一些意想不到的序列相似性，并且需要统计学检验来评估这样的比较的统计学显著性。 目前，还没有一种测试方法可以将DNA序列中发生的所有类型的突变都考虑在内。 此外，所有可用的测试都需要序列的组成（即，序列中字母出现的频率）不要太不同。 拟议的研究解决了这两个问题。

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.