Symbols used for relative pair types

Relationship class symbolϒ0ϒ1ϒ2ΦSexRelative types
t1Embedded ImageEmbedded Image0Embedded ImageMale–maleFull-sib, half-sib (through female parent), grandfather–grandson (through female)
t2Embedded ImageEmbedded Image0Embedded ImageMale–maleUncle–nephew (through female)
v1010Embedded ImageFemale–femaleParent–offspring, half-sib (through male parent), grandmother–granddaughter (through male)
v20Embedded ImageEmbedded ImageEmbedded ImageFemale–femaleFull-sib
v3Embedded ImageEmbedded Image0Embedded ImageFemale–femaleHalf-sib (through female parent), aunt–niece (through male), grandmother–granddaughter (through female)
v4Embedded ImageEmbedded Image0Embedded ImageFemale–femaleAunt–niece (through female)
u1010Embedded ImageMale–femaleParent–offspring
u2Embedded ImageEmbedded Image0Embedded ImageMale–femaleFull-sib, half-sib (through female parent), uncle–niece (through male), grandfather–granddaughter (through female), grandmother–grandson (through female)
u3Embedded ImageEmbedded Image0Embedded ImageMale–femaleUncle–niece (through female)
u4Embedded ImageEmbedded Image0Embedded ImageMale–femaleAunt–nephew (through female)
t3Embedded ImageMale–maleUncertain second-degree relative
v5Embedded ImageFemale–femaleUncertain second-degree relative
u5Embedded ImageMale–femaleUncertain second-degree relative
  • ϒ0, ϒ1, and ϒ2 designate the probabilities that individuals share 0, 1, and 2 alleles IBD at an X-linked locus, respectively. All types of relative pairs denoted by the same symbol have the same kinship coefficient, sexes, and probabilities of sharing 0, 1, and 2 alleles IBD. Φ can be calculated from ϒ1 and ϒ2 using Φij = ϒ1 if i and j are both male, Embedded Imageϒ1+Embedded Image if i and j are both female, and Embedded Image if i is male and j is female. For each possible pair of sexes (male–male, female–female, and male–female), the kinship coefficient for second-degree relatives of an uncertain type was found by averaging the kinship coefficients for all second-degree relationships in Table 1 with that pair of sexes, assuming that all were equally likely. Second-degree relationships include half-sib, grandparent–grandchild, and avuncular pairs. For male–male pairs, Embedded Image. For female–female pairs, Embedded Image. For male–female pairs, Embedded Image. The divisor in each of the previous equations describes the total number of possible second-degree relatives for that sex pair (e.g., grandmother–grandson, aunt–nephew, etc., for the male–female case). This number includes second-degree relatives that are not related on the X chromosome, because the assignment of relationships in the data set was based on autosomal data. The kinship coefficients for t3, v5, and u5 were used only for analysis of population data, and they were not used in our investigations of the effects on the estimators of varying the parameters.