Search

As population ageing strains social insurance systems, cohorts whose own fertility was low will be reaching elderly status, leaving close biological kin in short supply. However, there is a countervailing trend, inasmuch as burgeoning divorce, remarriage and family blending have expanded the numbers and varieties of step-kin and other non-standard kinship ties. Methods of computer microsimulation in conjunction with richer sample surveys can help us to foresee the contours of kin numbers and kinship relations in the future. Prime areas include the likely frequency of kin-deprived elderly, the overlap with economic deprivation and the interaction between kin frequency and intensity of contact. Step-ties may be weaker but nonetheless critical in raising the probability of at least one compatible member with whom one can choose to maintain contact and rely on. Kinship networks extended through half- and step-links, by stretching across racial and economic lines, may promote social cohesion.

"Humans' protracted maturation before childbearing is an extreme example of a general characteristic of higher organisms: a positive lower bound on ages of procreation. The pre-procreative span, much discussed for its evolutionary and social ramifications, has consequences also for the mathematics of population renewal.... This paper proves the presence of a pre-procreative span sufficient, in and of itself, to guarantee the existence condition for bifurcation for all models in one important class. The class includes the best-studied examples of age-specific systems with and without homeostatic feedback in purely discrete and in purely continuous formulations.", (excerpt)

In the mathematical theory of stable populations, when the net maternity function is scaled by a constant divisor , changing its level without changing its shape, the rates of attrition of transient waves in the age structure of the population as it converges toward stability are altered. The attrition rates are specified by the real parts of the complex roots of Lotka 's equation. Conditions are given for the falsity of the longstanding claim that there always exists some rescaling that brings to zero the real part of the complex root governing the lowest frequency wave. A general account of scalable and unscalable roots follows for the discrete-age, Leslie formulation, elucidating and setting limits to the standard account of approach to stability.

Lee's (1974) formal demographic feedback models summarize the implications for births and age-structure of neo-Malthusian theories of baby booms such as those of Easterlin. For some parameter values, such models imply sustained cycles, so-called "limit cycles", in births. Frauenthal and Swick recently reestimated a continuous-age version of Lee's basic cohort model with U.S. series and, contrary to Lee's original findings, concluded that "limit cycles oscillations have been occurring in U.S. births." This article disputes their conclusion, ascribing it to an inconsistency in detrending procedures. Furthermore, it corrects Lee's original conclusion by showing that his alternative period labor-force feedback model, estimated from U.S. series, leads to cycles of implausibly long period. This article thus reopens the question of whether any feedback model could account for the observed cycles in U.S. births.

The performance of format demographic feedback models, like Ronald Lee's, provides a test of whether theories of endogenous fertility adjustment, like Richard Easterlin's, can explain the cyclic swings in U.S, and other births that they were designed to explain. This paper shows how the specification of a demographic feedback model determines its ability to sustain cycles of a given period and amplitude observed in data. Only a few of the many versions of Easterlinastyle theories imply formal models which do prove capable of matching U.S. targets, and then only by narrow margins. The general methods presented here are suitable for a broad investigation of the possible role of age- specific feedback in the diversity of more and less cyclic patterns in birth series in the developed world. [ABSTRACT FROM AUTHOR]