"We consider a Leslie-type model of a one-sex (female) population of natives with constant immigration. The fertility and mortality schedule of the natives may be below or above replacement level. Immigrants retain their fertility and mortality, their children adopt the fertility and mortality of the natives. It is shown how this model may be written in a homogeneous form (without additive term) with a Leslie-type matrix. Reproductive values of individuals in each age group are discussed in terms of a left eigenvector of this matrix. The homogeneous form of our projection model permits the transformation into a Markov chain with transient and recurrent states. The Markov chain is the basis for the definition of genealogies, which incorporate immigration. It is shown that genealogies describe the life histories of individuals in a population with immigration. We calculate absorption times of the Markov chain and relate them to genealogies. This extends the theory originally designed for closed populations to populations with immigration." (SUMMARY IN FRE)

中文翻译：

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不断移民的人口

结果表明，家谱描述了移民群体中个体的生活史。我们计算马尔可夫链的吸收时间并将它们与系谱联系起来。这将最初为封闭人群设计的理论扩展到有移民的人群。”（摘要信息）