Immigrants can mix with the population of a receiving country in various ways. We consider demographic mixing by which we mean cross-mating, and more particularly the bearing of children where one parent is of immigrant descent and the other is not - cross-parenting as we term it. We consider a hypothetical country with an initial stable population and introduce immigration. The results of cross-parenting are taken into account by identifying three separate populations within the overall total: non-immigrant population, immigrant population (immigrants and their descendants), and mixed population. We develop a stylized model to track the three populations, with interest focusing in particular on how the proportion of mixed population changes through time as it moves toward a steady state. The model has a stable projection (Leslie) matrix that holds for all three populations and moves them forward from generation to generation as each evolves in its own way. As cross-parenting occurs the resulting progeny are transferred from the other populations to the mixed population. The pattern of cross-parenting is determined in the first instance by a matrix representing preferences among the three populations and alternative preferential patterns are experimented with, ranging from complete isolation to indifference as to cross-parenting choices. However the matrix must be modified to recognize supply constraints imposed by the sizes of the available populations and a restricted least-squares procedure is employed to effect the modification while remaining as close as possible to the original preference pattern. Alternative rates of immigration are experimented with also.
immigration population mixing cross-parenting demographic modeling parenting preferences