DYNAMICS OF OBSERVED POPULATIONS

数学人口学的最新进展有力地表明 所有人口的行为都有显著的规律性， 了解这些过程可以对健康起到重要作用 计划。拟议的研究将探索相关的规律性 有两个主要主题：人口统计之间的动态关系 比率以及观察到的种群的规模和结构，以及 将任何观察到的种群与其稳定性联系起来的分析联系 对应者。 关于第一个主题，拟议的工作将使用差异化和 随着时间的推移差异，以检查人口数量和边际变化 结构。在单一生活状态的人口中，将努力 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 当前人口统计行为的含义。在人口中有更多 不止一个生存状态被承认，努力将重点放在 在单个时间间隔内进行更改。 关于第二个主题，观察到的人口和 他们的马厩！将被检查。第一个联系是 由“交叉点”表示，其中按比例分布 来自观察到的和稳定的人群的人口统计事件相交。这个 第二个关联是人口动量，增长的趋势是 人口在实现更替后将继续增加规模 生育率和死亡率水平。第三个链接由 Kullback距离，用来衡量观察到的人口与 稳定性。这项工作将强调直接相关的联系 在观察到的种群和其稳定的对应种群之间。

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.