DYNAMICS OF OBSERVED POPULATIONS

人口统计学的最新进展有力地表明， 所有种群的行为都有显著的特征， 了解这些过程可以在健康方面发挥重要作用， 规划 这项研究将探索与癌症相关的 有两个主要主题：人口与环境之间的动态关系， 率和规模和结构的观察人口， 将任何观察到的种群与其稳定种群联系起来的分析联系 对应物。 关于第一个主题，拟议的工作将使用差异化， 随着时间的推移进行差异，以检查人口规模的边际变化， 结构 在单一生活状态的人群中， 用于分析几个时间间隔内的变化，并提供 短期到中期的显式数学表达式 当前人口行为的影响。 在那些 一个以上的生活状态是公认的，努力将集中在模式， 在一个时间间隔内变化。 关于第二个主题，观察到的人口与 他们的稳定！将审查对应方。 第一联动件可 由“交叉点”表示， 观察到的人口和稳定人口的人口事件相互交叉。 的 第二个联系是人口势头， 人口在实现更替后继续增加 生育率和死亡率。 第三个链接由 Kullback距离，一种测量观察到的种群距离 稳定 这项工作将强调直接相关的联系 一个观察到的种群和它的稳定种群之间的关系。

Recent advances in mathematical demography strongly suggest that significant regularities characterize the behavior of all populations, and understanding those processes can play an important part in health planning. The proposed research will explore regularities associated with two major themes: the dynamic relationships between demographic rates and the size and structure of observed populations, and the analytical linkages that connect any observed population to its stable counterpart. On the first theme, the proposed work will use differentiation and differencing over time to examine marginal change in population size and structure. In populations with a single living state, efforts will be made to analyze change over several intervals of time, and to provide explicit mathematical expressions for the short to intermediate term implications of present demographic behavior. In populations where more than one living state is recognized, efforts will focus on patterns of change over a single time interval. On the second theme, three linkages between observed populations and their stable !counterparts will be examined. The first linkage is represented by "crossover points" where proportional distributions of demographic events from observed and stable populations intersect. The second linkage is population momentum, the tendency for a growing population to continue to increase in size after achieving replacement level fertility and mortality. The third linkage is represented by the Kullback distance, a measure of how far an observed population is from stability. The work will emphasize the immediately relevant connections between an observed population and its stable counterpart.