Article,
The estimation of pairwise relationships
Annals of Human Genetics, 39 (2): 173-188 (1975)
DOI: 10.1111/j.1469-1809.1975.tb00120.x
Abstract
Pairwise relationships between individuals have been extensively studied from the point of
view of conditional prediction or genetic counselling. Cotterman ( 1940) first introduced the
‘ k-coegicients ’ which are a sufficient specification of the relationship between any two non-inbred
individuals;
k = ( k o , k l , k 2 ) , k i 3 0 , k , + 2 k l + k , = 1,
(1)
where k,, 2k1 and k, are (respectively) the probabilities that the two individuals have 0, 1 and 2
genes in common (see, for example, Crow & Kimura (1970)). I n this paper it will be more
convenient to use the coefficients
x = ( K ~ K ,
~ K , ~ ) ,
where
K, =
k,,
K~
=
2k1 and
K,
= k,,
(1’)
being the probability of i genes in common.
Cotterman’s work has been extended by, amongst many others, Malbcot (1948) and Li & Sacks
( 1954), who first gave the pairwise genotype distributions for two related non-inbred individuals.
The specification of relationships and the derivation of joint genotype distributions has been
extended by Jacquard (1972) to cases of two possibly inbred individuals, and by Thompson
( 1 9 7 4 ~ t o ) cases of several individuals.
Edwards (1967) suggested that the relationships between the members of a population should
be studied from the point of view of inference rather than of prediction. Given sufficient data on
individual genotypes, and perhaps also the ages and sexes of individuals, it should be possible to
reconstruct the detailed genealogy of any population. It may be shown that in practice sufficient
data may well be available to enable useful inferences regarding population structure to be made.
Turnbull (1972) has detailed some of the problems of anthropologists in obtaining accurate
information of relationships in some small-scale societies, and it has been estimated that often
only 80% may be correct. With currently obtainable data it is possible to reconstruct the
genealogy of a small population with at least this accuracy (Thompson, 1974b). Methods of
genealogy reconstruction may also be of practical use in animal populations, but human popula-
tions provide a useful starting point, particularly since the most suitable genetic data as yet
available are those on the human blood-group polymorphisms.
However, a study of structure or relationship inferences has a further purpose. Even where
inference as to detailed population structure is not yet a practical proposition, a study of relation-
ships from the point of view of inference rather than prediction can greatly clarify the relation
between genealogical and genetic structure.
