The formal demography of kinship: A matrix formulation
The formal demography of kinship: A matrix formulation
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DOI：
10.4054/demres.2019.41.24
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发表时间：
2019-09-10
影响因子：
2.1
通讯作者：
Caswell, Hal
中科院分区：
文献类型：
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作者：
Caswell, Hal
背景技术任何人的一生都会被一个不断发展的亲属网络所包围。在一篇相当著名的论文中，Goodman、Keyfitz 和 Pullum (1974) 提出了死亡率和生育率表所隐含的（女性、母系）亲属平均数量的正式计算。 目的 本文的目的是提出一种新的亲属人口学理论，它提供年龄分布和预期数量，允许计算亲属的属性（例如，依赖性），易于计算，并且不需要模拟。方法分析依赖于一种新颖的方法。应用队列组成人口预测的矩阵公式来描述亲属关系网络的动态。该方法源于对焦点个体的亲属形成群体的观察，并且可以将其建模为一个。结果亲属动态由非自治矩阵方程的耦合系统描述。我展示了如何计算年龄分布、总数、患病率、依赖性和亲属死亡经历。作为一个例子，我比较了 1947 年和 2014 年日本女性的经期生命率所隐含的亲属关系网络。在此期间，生育率下降了 70%，而预期寿命增加了 60%。这些变化对亲属关系结构的影响是深远的。根据 1947 年的比率，人们的一生主要是经历亲人的死亡，而现在，亲人的死亡是一件罕见的事情。另一方面，与 2014 年的比率相比，受抚养的老年亲属（包括患有痴呆症的亲属）的负担要高出许多倍。结论这一新理论为迄今为止无法触及的亲属关系方面的研究打开了大门，并有可能应用于解决家庭人口学中的许多问题。
BACKGROUNDAny individual is surrounded by a network of kin that develops over her lifetime. In a justly famous paper, Goodman, Keyfitz, and Pullum (1974) presented formal calculations of the mean numbers of (female, matrilineal) kin implied by a mortality and fertility schedule.OBJECTIVEThe aim of this paper is a new theory of kinship demography that provides age distributions as well as expected numbers, permits calculation of properties (e.g., dependency) of kin, is easily computable, and does not require simulation.METHODSThe analysis relies on a novel application of the matrix formulation of cohort component population projection to describe the dynamics of a kinship network. The approach arises from the observation that the kin of a focal individual form a population, and can be modelled as one.RESULTSKinship dynamics are described by a coupled system of non-autonomous matrix equations. I show how to calculate age distributions, total numbers, prevalence, dependency, and the experience of the death of relatives. As an example, I compare the kinship networks implied by the period vital rates of Japanese women in 1947 and 2014. Over this interval, fertility declined by 70% while life expectancy increased by 60%. The implications of these changes for kinship structure are profound; a lifetime dominated, under 1947 rates, by the experience of the death of kin has changed to one in which the death of kin is a rare event. On the other hand, the burden of dependent aged kin, including those suffering from dementia, is many-fold larger under 2014 rates.CONCLUSIONSThis new theory opens to investigation hitherto inaccessible aspects of kinship, with potential applications to many problems in family demography.