Applied Mathematical Demography

Author: Nathan Keyfitz (USA)
Editor: Cheng Duyuan
Publisher:
Publication Date: 2000-01-01
Features: This is a relatively professional book; it is one of the most influential works in the field of demography, known to all students of demography. It is widely regarded as the "bible" of population statistics abroad, and no population statistics book has yet surpassed its achievements. One of the translators, Zheng Zhenzhen from Peking University, praised this book. Those interested in sociology and demography should read it! Based on summarizing and standardizing the creative research results of predecessors and himself over decades, Professor Keyfitz systematically elaborated and argued the internal mechanisms and interrelationships of various population factors (death, fertility, marriage, migration), discussed life table methods, stable and unstable populations, multistate population models, population forecasting methods, family and kinship models, micro and macro population research, and various mathematical models and analytical methods of population analysis, such as the diversity and selectivity of population analysis.
Excerpt: The birth rate of relatively closed French Canadians may be higher than that of early immigrants. The earliest settlers numbered less than 10,000, with an average arrival time of 1700. By 1970, there were approximately 5,500,000 French Canadians, having multiplied 550 times, or 9 times over 270 years, meaning the doubling time was about 30 years. This population growth was almost entirely due to births exceeding deaths, with migration playing a negligible role. Even after the birth rate of the descendants of early immigrants declined significantly, the birth rate of French Canadians remained high. This confirms that the doubling time for early immigrants was 35 years, which is convenient for calculating our example. Tracing each early immigrant along the paternal line (with a few exceptions for females where the maternal line is followed), over 350 years from 1620 to 1970, they could have multiplied 10 times. (Patrilineal refers to the son of a son, and so on; matrilineal refers to the daughter of a daughter, and so on. This excludes the daughter of an old Brewster from being counted as a descendant.) It is said that about half of the early immigrants died during a difficult winter, so we only consider the survivors, about 50. Then each immigrant would have 2^10 = 1024 direct descendants, adding up to 50 × 1024, or about 50,000 male descendants of male immigrants and female descendants of female immigrants. If these early immigrants did not intermarry with outsiders, meaning their descendants did not mix with other groups and could always find partners within their own group, then the above number would approximate the current total. This would require an equal number of males and females at the beginning (or a specified number of women among the first-generation immigrants). What is more complicated is that these descendants were not isolated from the outside world. On the other hand, if they always sought partners from the descendants of other groups and included all their children, not just the patrilineal ones, then the population growth rate of the descendants of early immigrants would be twice the value mentioned earlier. Replacing the two descendants with four means the average doubling time is half of 35 years. Thus, each early immigrant would produce 220 or over a million descendants in the 350 years before 1970. The 50 survivors from that winter would collectively have over 50 million descendants. Therefore, those still alive and identifying themselves as descendants of the first batch of immigrants would number at least 50,000 (assuming they are a closed subpopulation and ignoring the fact that the initial sex ratio was unequal), or as many as 50 million (if they all intermarried with outsiders). Without intermarriage data, we cannot further narrow the estimate range. [What are the difficulties in collecting intermarriage data?] The purpose of the above calculation is only to illustrate the uncertainty of the sex ratio. I simplified the data. A more realistic analysis would involve identifying the 23 first-generation immigrants who maintained family continuity and then applying historical records to determine the size of their families. The Mayflower Descendants Society has about 15,000 registered members who can prove their descent from the first-generation immigrants, but the actual total number of true descendants is far greater. For our assumptions, the single-sex method provides a simple and unique answer: 50,000 people, while the corresponding two-sex method gives a range of 50,000 to 50 million. This is just one aspect of the problem. On the other hand, adding a certain number of females to the population has a greater effect on marriage and birth than adding males. Hunting does more harm to the reproduction of female rabbits than to male rabbits—the exact extent depends on the ability of the remaining males to overcome difficulties. It is difficult to find a satisfactory answer to such questions. Without facts or more detailed assumptions about individual behavior than general demography, this problem cannot be resolved. In the following chapters, it is generally assumed that there is no migration, and only females or only males are considered. How many people can trace their ancestors back to their starting point is not important; what we want to know is how fast a closed population grows and what determines the age distribution and other characteristics of the population. For this, we will consider each sex separately, avoiding the issue of whether partners are available. This section is intended to illustrate the difficulties of the problem. In fact, single-sex models simplify the complex problem while, to some extent, providing realistic answers, making this an undeniable achievement.