| Summary: | Can the decline of a small and isolated population occur as a consequence of a random imbalance in the sex ratio at birth and/or in the male/female mortality rates in subsequent age groups? We should stress here the use of the term “random”. Indeed, the imbalance we refer to is what occurs in a small population as the ultimate result of pure chance. This hypothesis (of the imbalance of the sex ratio) was studied in particular by the Italian statistician Corrado Gini (1957), although it had previously been put forward by other authors (Livi 1941, 1944). More specifically, Gini explained the extinction of the medieval settlements in Greenland using this hypothesis.The recent publication of Lynnerup’s book (1998) concerning the demography of these settlements, based on the archaeological evidence of skeletal remains, prompted us to re-evaluate Gini’s treatise. We wanted to give a statistical contribution – using a Bayesian inference – to evaluate Gini’s hypothesis of that extinction. The extinction of the settlements in Greenland is widely regarded as “almost an enigma hinting at some inexplicable and dramatic event veiled by the passage of time” (Lynnerup1998, p. 8).The aim of this paper is therefore to check Gini’s hypothesis from a Bayesian point of view. In this scheme, the prior distribution is the probability of an imbalance in the sex ratio occurring in the history of a small and closed population as a result of random and unfavourable alterations of the sex-ratio at birth and at death. In order to evaluate such a probability, a Monte Carlo technique that uses historical, demographic and biometric constants (Livi Bacci 1998) will be outlined. The posterior probability is then updated in the light of some archaeological data.
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