Mathematical Sciences: Interacting Particle Systems with Applications to Population Biology

[9403644] Neuhauser摘要。研究的前两部分涉及生态学和种群生物学的几个多物种模型的调查。这些模型被表述为整数晶格上的复杂空间系统，其中每个地点都处于有限数量的状态之一，表明该地点是否存在某种物种。随着时间的推移，这些系统根据不确定的局部规则进化，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。要考虑的模型包括寄主-拟寄生物的关联，以及在一个细分的栖息地中研究物种遗传多样性的模型，在这些栖息地中经常发生局部灭绝。这些研究是理论和实验（计算机模拟）。主要目标是研究空间成分如何影响相关物种的生存/共存。在第三部分中，讨论了有关DNA序列比较的问题。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序列中字母出现的频率没有太大的不同。在前两部分，研究者将研究来自生态学和种群生物学的几种多物种模型。这些模型被表述为复杂的空间系统，根据不确定的局部规则随时间进化。这方面的例子包括寄主-拟寄生物的联系，以及在一个细分的栖息地中研究物种遗传多样性的模型，在这些栖息地中经常发生局部灭绝。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。主要目标是研究空间成分如何影响生存/共存。在第三部分中，讨论了DNA序列比较中出现的问题。这种比较揭示了一些意想不到的序列相似性，需要进行统计检验来评估这种比较的统计意义。目前，还没有一种测试可以考虑到DNA序列中发生的所有类型的突变。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）不能相差太大。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.