Frequencies of pedigrees of consanguineous marriages and mating structure of the population
Authors: BARRAI I. , CAVALLI‐SFORZA L. L. , MORONI A. 
Published: September 2007

1. A sample of consanguinity dispensations obtained from the bishoprics of Parma and Piacenza referring to the period 1851–1957, and from the bishoprics of Reggio Emilia for the period 1927‐57, was analysed. Only dispensations for uncomplicated consanguinity of the following types were recorded: uncle‐niece and aunt‐nephew, first cousins, first cousins once removed (also called 1 ½ cousins), second cousins, second cousins once removed (2½ cousins) and third cousins. Dispensations not giving the complete pedigree were discarded. Altogether, there remained 15,647 dispensations which were analysed for the frequency of pedigree structure. There is highly significant heterogeneity of the frequencies of pedigrees within each of the above six major types (degrees) of consanguineous marriages. This is presumed to be the consequence of the mating system of the population under examination; therefore, the analysis of such heterogeneity can offer some insight into the mating structure of the population.

Further analysis, to be summarized briefly below, showed that three major factors may account for practically all the observed variation, namely: sex‐differential migration, age difference between mates, and sex of the mates' parents.

2. The number of intermediate ancestors of the male sex accounts for most of the observed variation, especially in even cousins pedigrees where it is by far the most important effect (first, second, third cousins). However, there is a reversal of sex effect between first cousins on one hand, second and third on the other; with first cousins, pedigrees with more female intermediate ancestors are more common, while for second and third cousins the frequency of pedigrees increases regularly with the number of males among intermediate ancestors. The mode of increase can be predicted by a simple formula.

The interpretation offered is the following. Migration has almost no effect when the intermediate ancestors are only the parents of the consanguineous mates, i.e. in first cousins, or it is counterbalanced by other phenomena, to be considered later. When, however, the relationship is more remote, as in second and third cousins, migration can be effective in removing potential consanguineous mates sufficiently far apart to decrease the probability of their marriage. In fact, it is known that isolation by distance is very strict in this area. If migration is differential for sex, the female sex migrating more often than the male, the pattern of pedigree frequencies should be precisely as the observed one. Moreover, estimates of the ratio between male and female emigration can be derived from pedigree frequencies. In the area under analysis it is probable that most of the migration takes place at marriage, and when two mates are from different villages, it is usually the bride who moves to the husband's village. The effect will accumulate over generations, and make pedigrees containing females among intermediate ancestors less frequent, the more so, the more females are present.

A complete verification of the hypothesis will demand a comparison of the estimates of male/female migration as obtained from the analysis of consanguineous marriages, with direct demographic estimates of the same values. Such an analysis could also explain some of the variations encountered in the estimates of male/female migration from pedigree analysis.

3. The difference of age between mates also plays an important role in determining the probability of consanguineous marriage. This effect is, as expected, stronger in uneven cousins pedigrees (1½ and 2½ and uncle‐niece or aunt‐nephew).

One can calculate the expected age difference between husband and wife as a function of pedigree structure. The age difference most favourable to marriage is taken to be the mean age difference between husband and wife in the general population. It has been shown that the frequency of pedigrees varies, other factors being equal, being smaller when the expected age difference between the mates deviates more from the difference which is optimal for marriage. The variations can be described by a simple formula.

4. It has also been found that the pedigrees containing two females are more frequent tha‐comparable pedigrees with male and female, or two males as nearest intermediate ancestors, i.e. parents of the mates. The explanation may be that the consanguineous mothers of the mates are more instrumental in arranging marriages, than consanguineous fathers. This phenomenon is clearly observed in second and third cousins.

5. The aberrant behaviour of first cousins, as regards sex of intermediate ancestors, can be explained through the latter effect, the peculiarities of sex‐differential migration, a reduced effect of the latter on marriages of the first generation, and in other ways as discussed more fully in the text.

6. One can predict accurately the frequencies expected for all the thirty‐two types of pedigrees of 1½ and second cousins, or all the 128 types of pedigrees of 2½ and third cousins, by making use of information from expected age difference and sex of intermediate ancestors, fed into simple formulae. Maximum likelihood estimates have been obtained giving a substantially satisfactory fit.

Practically the only variation left after fitting the theoretical model is that due to the effect described in point 4.

Further refinements, and direct knowledge of quantities which can be obtained by demographic investigation (sex differential migration, age distributions at marriage and childbirth) can provide a safe basis for these conclusions, and a more complete synthesis than has been so far achieved.

Thus, factors for ‘non‐randomness’ of consanguineous marriages can be isolated and measured in a sample of consanguineous marriages of adequate size, provided full pedigrees are given for each marriage.

This work has been supported by grants from the U.S. Atomic Energy Commission, The Comitato Nazionale per l'Energia Nucleare and The Rockefeller Foundation. We are also grateful to Olivetti Elettronica for their help in numerical maximum likelihood analysis.

Criticism of the text of the paper by Dr K. R. Dronamraju and by Prof. J. B. S. Haldane is gratefully acknowledged.