Pickens G T, Mode C J
Department of Mathematics and Computer Science, Drexel University, Philadelphia, PA 19104.
IMA J Math Appl Med Biol. 1986;3(1):1-22. doi: 10.1093/imammb/3.1.1.
This paper provides algorithms for projection of mean and covariance functions for stochastic population processes governed by time-homogeneous laws of fertility and mortality. The theoretical foundation of the algorithms is general age-dependent branching processes in discrete time. The algorithms are employed in several illustrative projections, based on 1982 Chinese data, of a population experiencing an abrupt transition to below replacement fertility. Methods of constructing confidence limits for total population size are illustrated. Also developed are procedures for projecting mean and variance functions for populations which may be heterogeneous with respect to mortality or fertility. The projections performed yield two observations. First, the coefficient of variation in population size appears to be inversely related to the Malthusian parameter of population growth. Second, the coefficient of variation for population size is negligible for large homogeneous initial populations. But when the initial population is heterogeneous with respect to fertility or mortality, then substantial coefficients of variation, exceeding 0.4, are observed in some of the projections performed.
本文提供了用于对由生育和死亡的时间齐次规律所支配的随机种群过程的均值和协方差函数进行投影的算法。这些算法的理论基础是离散时间中的一般年龄依赖分支过程。基于1982年中国数据，将这些算法应用于对经历向低于更替生育率突然转变的种群的几个说明性投影中。阐述了构建总人口规模置信区间的方法。还开发了针对在死亡率或生育率方面可能存在异质性的种群的均值和方差函数投影程序。所进行的投影得出了两个观察结果。第一，种群规模的变异系数似乎与种群增长的马尔萨斯参数呈负相关。第二，对于大型同质初始种群，种群规模的变异系数可以忽略不计。但是当初始种群在生育率或死亡率方面存在异质性时，在一些所进行的投影中会观察到超过0.4的显著变异系数。
