Assessing the genealogical depth of an ancestry

Many studies in genetics and historical demography rely on family reconstitution, beginning with one individual and his or her ancestry. Information from such genealogies varies depending on the number of the individual's ancestors who can be identified. Traditional assessments of kinship or consanguinity ratios are often based on such reconstitutions. This reinforces the need for information from these genealogies to be quantified in order that individual situations may be compared. In this paper it is shown that an index which is supposed to provide information about the average length of an ancestry may lead to inconsistent results in some cases, and two new indices and their associated variances are introduced which eliminate inconsistencies and can be used to measure average genealogical lengths.