Mathematical Sciences: Interacting Particle Systems with Applications to Population Biology

点击翻译按钮获取中文摘要

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.