Demographic dating of the Nukuoro society.

The techniques of mathematical demography are employed to determine the time of human settlement of an isolated coral atoll in the South Pacific. The ability to make this estimate is made possible by the unusual social customs practiced by the inhabitants of the atoll. The present inhabitants of Nukuoro, a small coral atoll in the Eastern Caroline Islands of the South Pacific, are the descendants of a party of drift voyagers who landed several centuries ago. Two unusual aspects of the social customs of these people make it possible to use demographic techniques to estimate the time of arrival of the original settlers. The first feature is that the oldest surviving member of the population was by social custom the religious ruler, i.e., the chief priest (Feeney, 1974). The second is that the only individuals whose names could be mentioned after their deaths were these religious rulers (Eilers, 1934). Consequently, although the history of the Nukuoro Society is very incomplete, the names of the past rulers have been preserved by oral tradition. The first major anthropological study of the Nukuoro Atoll (Eilers, 1934) lists the names (though not the tenure) of the 100 priests who had reigned between the time of arrival of the original settlers and the year 1871. In a brief survey of the history of the Nukuoro, Carroll (1975) observes that prior to about 1870, virtually no contacts had occurred between the Nukuoro Society and the Western World. A few early sightings from shipboard of natives in canoes and an estimate in 1875 by Robertson (1877), who actually visited the atoll, suggest that during the nineteenth century the Nukuoro population numbered around 150 to 200 people. Archaeological evidence (Davidson, 1971) shows no indication that the population was ever any larger, and the original party of drift voyagers is thought to have numbered just 24 (Carroll, 1975). This scant evidence will be taken to mean that over the several hundred years of human habitation, the population size of the Nukuoro remained virtually constant. There is good evidence, as well as a compelling argument (Thomas, 1971), that primitive humans are capable of maintaining their population at a strictly controlled, socially optimal size. In order to estimate the time of settlement of Nukuoro Atoll, the following questions are considered. What is the chance that a Nukuoro infant (henceforth referred to as Ego) just born will survive to become the ruler? Assuming that Ego does survive to become the ruler, what is the expected length and the variance of Ego's reign? Once the answers to these questions are known, it is straightforward to estimate the time of arrival of the original settlers on Nukuoro. To answer the above questions only two basic pieces of demographic information are needed: the age-specific death rate for members of the population, customarily called the force of mortality, and population age distribution at the instant of Ego's birth. An obvious but important observation is that to become ruler, Ego has only to outlive all the members of the tribe alive at the instant Ego is born, since all individuals born after Ego cannot be ruler while Ego is alive. The analysis is made formally tractable by assuming that no migration occurs and that the force of mortality does not change with time and applies to all individuals in the population. (Due to the extreme isolation of the Nukuoro Atoll and the primitive life-style of the inhabitants prior to 1871, these assumptions appear to be quite reasonable.) Begin by defining l(x), which is customarily called the survivorship, to be the probability that an individual is still alive at age x. The distribution function for the random lifetime of an individual is therefore given by 11(x), and is related to the force of mortality, ,i(x), by the expression