title: Populations with constant immigration.
abstract: "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)
mesh_terms: D003710:Demography; D004641:Emigration and Immigration; D005006:Ethnicity; D005190:Family; D005191:Family Characteristics; D005298:Fertility; D005789:Genealogy and Heraldry; D008018:Life Cycle Stages; D008390:Markov Chains; D008962:Models, Theoretical; D009026:Mortality; D011153:Population; D011154:Population Characteristics; D011157:Population Dynamics; D011336:Probability; D012106:Research; D013223:Statistics as Topic; D014171:Transients and Migrants
keywords: Demographic Factors; Family And Household; Family Research; Fertility; Genealogies; Immigrants; International Migration; Life Cycle; Markov Chain; Migrants; Migration; Models, Theoretical; Mortality; Nationality; Native-born; Population; Population Characteristics; Population Dynamics; Probability; Research Methodology; Statistical Studies; Studies; World