The Growth and Stabilization of Populations
The Growth and Stabilization of Populations
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人口的增长和稳定
DOI：
10.1214/ss/1177011694
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发表时间：
1991
影响因子：
5.7
通讯作者：
P. Jagers
中科院分区：
文献类型：
--
作者：
P. Jagers
生死式传统中的人口模型有一个令人不快的（通常不做广告的）暗示，即个体不会衰老：根据整个人口的马尔可夫特性，寿命必须呈指数分布，并且繁殖以分裂或泊松过程的形式发生。这只能通过实时假设更复杂的马尔可夫属性（例如年龄和胎次相关的人口学模型）来部分地解决（并且审美成本很高）。相反，如果人口增长存在合理的马尔可夫结构，那么它就存在于谱系中，女儿从母亲那里继承基因型，并独立于她们的祖先（考虑到这些类型）。这个想法被用来定义一般的分支过程并分析它们的性质：灭绝、增长和渐近组成。结果用于解释生物进化中突变分子钟的假设。
Population models in the birth-and-death style tradition have the unpleasant (and usually not advertised) implication that individuals do not age: It follows from the Markov properties of the whole population that life spans must be exponentially distributed and reproduction occur as splitting or in a Poisson process. This can be remedied only in parts (and at a high esthetical cost) by assuming more complicated Markovian properties in real time, like the age and parity dependent models of demography. Instead, if there is a sensible Markov structure in population growth, it resides in the pedigree, daughters inheriting genotypes from their mothers and being independent of their ancestors, given these types. This idea is used to define general branching processes and to analyze their properties: extinction, growth and asymptotic composition. The results are used to interpret the hypothesis of a molecular clock of mutations in biological evolution.