The formal demography of kinship IV: Two-sex models and their approximations

Abstract

BACKGROUNDPrevious kinship models analyze female kin through female lines of descent, neglecting male kin and male lines of descent. Because males and females differ in mortality and fertility, including both sexes in kinship models is an important unsolved problem. OBJECTIVEThe objectives are to develop a kinship model including female and male kin through all lines of descent, to explore approximations when full sex-specific rates are unavailable, and to apply the model to several populations as an example. METHODSThe kin of a focal individual form an age×sex-classified population and are projected as Focal ages using matrix methods, providing expected age-sex structures for every type of kin at every age of Focal. Initial conditions are based on the distribution of ages at maternity and paternity. RESULTSThe equations for two-sex kinship dynamics are presented. As an example, the model is applied to populations with large (Senegal), medium (Haiti), and small (France) differences between female and male fertility. Results include numbers and sex ratios of kin as Focal ages. An approximation treating female and male rates as identical provides some insight into kin numbers, even when male and female rates are very different. CONTRIBUTIONMany demographic and sociological parameters (e.g., aspects of health, bereavement, labor force participation) differ markedly between the sexes. This model permits analysis of such parameters in the context of kinship networks. The matrix formulation makes it possible to extend the two-sex analysis to include kin loss, multistate kin demography, and time varying rates.

The formal demography of kinship V: Kin loss, bereavement, and causes of death

“…In this paper we have used the time-invariant one-sex (female) age-classified kinship model, relying on the androgynous approximation to calculate numbers of both male and female kin. But the matrix kinship theory exists in time-varying, multistate, and twosex models, and those extensions (Caswell 2019(Caswell , 2020(Caswell , 2022Caswell and Song 2021) could easily be used as the basis for a cause-of-death analysis. In particular, the use of a full two-sex model would permit analysis of causes of death that are sex-specific (e.g., complications of childbirth, prostate cancer) or nearly so (e.g., breast cancer); see Verdery et al (2023) for a first step.…”

“…The GKP factors for transformations from single-sex to two-sex kin A calculation in Caswell (2022) shows that the GKP factors give a close approximation to the full two-sex results, even in a case where there exists large male-female differences between both survival and fertility. Because the GKP factors treat the sexes as identical, the calculation cannot incorporate sex-specific causes of death.…”

“…We will refer to this approach as the 'matrix kinship model.' The model was first introduced in a one-sex, age-classified, time-invariant form (Caswell 2019), and then extended to include multistate models (Caswell 2020), time-variation (Caswell and Song 2021), and both sexes (Caswell 2022).…”

“…To compare deaths of different types of kin, it is essential to account for both sexes. The two-sex version of the matrix kinship model in Caswell (2022) does so, but requires sex-specific age schedules of mortality and fertility.…”

“…In the absence of complete male-and female-specific rates, an approximation due to Goodman, Keyfitz, and Pullum (1974) provides good two-sex results based on rates for just one sex, or both sexes combined. The approximation pretends that the sexes have identical rates and multiplies each type of kin by a scalar factor (called the GKP factors by Caswell (2022)) to obtain the numbers of combined male and female kin. The GKP factors are given in Table 2.…”