Kim Y J
Theor Popul Biol. 1987 Apr;31(2):306-22. doi: 10.1016/0040-5809(87)90031-1.
A general and complete exposition of the dynamics of populations with changing vital rates is given in the discrete time formulation. Results obtained are stronger than Lopez's or Hajnal's. In addition to the proof of existence of limits, an explicit expression for the age distribution is obtained by considering forward products of population projection matrices, while an explicit expression for the generalized reproductive values is obtained by considering backward products. The forward and backward characteristic equations respectively determine the forward and backward growth rates. The relative age distribution is compared to the alternative expression of Y.J. Kim (1986, Demography 23 (3), 451-461), which is the discrete version of S.H. Preston and A.J. Coale (1982, Pop. Index 48 (2), 217-259).
离散时间公式给出了具有变化生命率的种群动态的全面且完整的阐述。所得到的结果比洛佩兹或哈伊纳尔的结果更强。除了极限存在性的证明外，通过考虑种群投影矩阵的前向乘积得到年龄分布的显式表达式，而通过考虑后向乘积得到广义繁殖值的显式表达式。前向和后向特征方程分别确定前向和后向增长率。将相对年龄分布与Y.J. 金（1986年，《人口统计学》23(3)，451 - 461）的替代表达式进行比较，后者是S.H. 普雷斯顿和A.J. 科尔（1982年，《人口索引》48(2)，217 - 259）的离散版本。
