Estimate the variance of realized relatedness around pedigree kinship
Source:R/markerRealizedRelatednessVariance.R
markerRealizedRelatednessVariance.RdPedigree-expected relatedness (this package's existing kinship
output, doubled) is only an average – the actual proportion of
genome shared identical-by-descent (IBD) between two relatives varies
around that expectation because of Mendelian sampling and linkage (finite
chromosome number/map length creates covariance in IBD status among
nearby loci). This function estimates that variance for
Parent-Offspring, Full-Siblings, and Half-Siblings pairs (issue #153,
D3a) – the closed-form solution of Hill & Weir (2011), extending the
pedigree kinship this package already computes rather than requiring a
new population-genetics framework. Every other pedigree-relationship
category (grandparent, cousin, avuncular, more distant, unrelated, self)
returns NA for the variance, not an error – a pedigree-wide call
will legitimately include many such pairs as a matter of course.
Arguments
- kmat
square kinship matrix, as produced by
kinship.- ped
dataframe with (at least)
id,sire, anddamcolumns, as used byconvertRelationships.- nChr
chromosome count (e.g. autosome count for the species), meant to be a whole number. Only a single positive numeric value is enforced, so a non-integer such as
20.5is accepted.- mapLength
numeric; total autosomal genetic map length in Morgans. Must be a single positive value.
- ids
character vector of IDs or
NULLto which the analysis should be restricted, as inconvertRelationships.
Value
A dataframe with columns id1, id2, kinship,
relation, R (pedigree relationship, 2 * kinship),
varR (the realized-relatedness variance estimate), and
sdR (its square root). varR/sdR are NA for
every relation other than "Parent-Offspring",
"Full-Siblings", or "Half-Siblings".
Details
Relationship pairs are classified from the pedigree structure via the
existing convertRelationships (not re-derived). The
variance combines nChr chromosomes, each approximated as the
average length mapLength / nChr – Hill & Weir (2011) give an
exact weighted-sum combination rule (their equation 5) only for lineal
descendants; for Full-Sib/Half-Sib pairs they state in prose that this
equal-length approximation closely matches a real heterogeneous-length
genome, which this package's own PRE-RED research verified numerically
against their published human-genome Table 2 (within ~2%; see the test
file header for the full derivation).
References
Hill WG, Weir BS. 2011. Variation in actual relationship as a consequence of Mendelian sampling and linkage. Genetics Research 93(1):47-64.
Examples
library(nprcgenekeepr)
ped <- nprcgenekeepr::smallPed
kmat <- kinship(ped$id, ped$sire, ped$dam, ped$gen, sparse = FALSE)
## Rhesus macaque autosome count/map length are used only as an example
## scale -- callers should supply values appropriate to their own species.
markerRealizedRelatednessVariance(kmat, ped, nChr = 20L, mapLength = 28)
#> id1 id2 kinship relation R varR sdR
#> 1 A A 0.50000 Self 1.0000 NA NA
#> 2 A B 0.00000 No Relation 0.0000 NA NA
#> 3 A C 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 4 A D 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 5 A E 0.00000 No Relation 0.0000 NA NA
#> 6 A F 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 7 A G 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 8 A H 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 9 A I 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 10 A J 0.00000 No Relation 0.0000 NA NA
#> 11 A K 0.00000 No Relation 0.0000 NA NA
#> 12 A L 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 13 A M 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 14 A N 0.00000 No Relation 0.0000 NA NA
#> 15 A O 0.00000 No Relation 0.0000 NA NA
#> 16 A P 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 17 A Q 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 19 B B 0.50000 Self 1.0000 NA NA
#> 20 B C 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 21 B D 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 22 B E 0.00000 No Relation 0.0000 NA NA
#> 23 B F 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 24 B G 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 25 B H 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 26 B I 0.00000 No Relation 0.0000 NA NA
#> 27 B J 0.00000 No Relation 0.0000 NA NA
#> 28 B K 0.00000 No Relation 0.0000 NA NA
#> 29 B L 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 30 B M 0.00000 No Relation 0.0000 NA NA
#> 31 B N 0.00000 No Relation 0.0000 NA NA
#> 32 B O 0.00000 No Relation 0.0000 NA NA
#> 33 B P 0.00000 No Relation 0.0000 NA NA
#> 34 B Q 0.00000 No Relation 0.0000 NA NA
#> 37 C C 0.50000 Self 1.0000 NA NA
#> 38 C D 0.25000 Full-Siblings 0.5000 0.0018350199 0.04283713
#> 39 C E 0.00000 No Relation 0.0000 NA NA
#> 40 C F 0.12500 Full-Avuncular 0.2500 NA NA
#> 41 C G 0.12500 Full-Avuncular 0.2500 NA NA
#> 42 C H 0.25000 Full-Siblings 0.5000 0.0018350199 0.04283713
#> 43 C I 0.12500 Half-Siblings 0.2500 0.0009175099 0.03029043
#> 44 C J 0.00000 No Relation 0.0000 NA NA
#> 45 C K 0.00000 No Relation 0.0000 NA NA
#> 46 C L 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 47 C M 0.12500 Half-Siblings 0.2500 0.0009175099 0.03029043
#> 48 C N 0.00000 No Relation 0.0000 NA NA
#> 49 C O 0.00000 No Relation 0.0000 NA NA
#> 50 C P 0.06250 Avuncular - Other 0.1250 NA NA
#> 51 C Q 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 55 D D 0.50000 Self 1.0000 NA NA
#> 56 D E 0.00000 No Relation 0.0000 NA NA
#> 57 D F 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 58 D G 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 59 D H 0.25000 Full-Siblings 0.5000 0.0018350199 0.04283713
#> 60 D I 0.12500 Half-Siblings 0.2500 0.0009175099 0.03029043
#> 61 D J 0.00000 No Relation 0.0000 NA NA
#> 62 D K 0.00000 No Relation 0.0000 NA NA
#> 63 D L 0.12500 Full-Avuncular 0.2500 NA NA
#> 64 D M 0.12500 Half-Siblings 0.2500 0.0009175099 0.03029043
#> 65 D N 0.00000 No Relation 0.0000 NA NA
#> 66 D O 0.00000 No Relation 0.0000 NA NA
#> 67 D P 0.06250 Avuncular - Other 0.1250 NA NA
#> 68 D Q 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 73 E E 0.50000 Self 1.0000 NA NA
#> 74 E F 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 75 E G 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 76 E H 0.00000 No Relation 0.0000 NA NA
#> 77 E I 0.00000 No Relation 0.0000 NA NA
#> 78 E J 0.00000 No Relation 0.0000 NA NA
#> 79 E K 0.00000 No Relation 0.0000 NA NA
#> 80 E L 0.00000 No Relation 0.0000 NA NA
#> 81 E M 0.00000 No Relation 0.0000 NA NA
#> 82 E N 0.00000 No Relation 0.0000 NA NA
#> 83 E O 0.00000 No Relation 0.0000 NA NA
#> 84 E P 0.00000 No Relation 0.0000 NA NA
#> 85 E Q 0.00000 No Relation 0.0000 NA NA
#> 91 F F 0.50000 Self 1.0000 NA NA
#> 92 F G 0.25000 Full-Siblings 0.5000 0.0018350199 0.04283713
#> 93 F H 0.12500 Full-Avuncular 0.2500 NA NA
#> 94 F I 0.06250 Avuncular - Other 0.1250 NA NA
#> 95 F J 0.00000 No Relation 0.0000 NA NA
#> 96 F K 0.00000 No Relation 0.0000 NA NA
#> 97 F L 0.06250 Full-Cousins 0.1250 NA NA
#> 98 F M 0.06250 Avuncular - Other 0.1250 NA NA
#> 99 F N 0.00000 No Relation 0.0000 NA NA
#> 100 F O 0.00000 No Relation 0.0000 NA NA
#> 101 F P 0.03125 Cousin - Other 0.0625 NA NA
#> 102 F Q 0.06250 Other 0.1250 NA NA
#> 109 G G 0.50000 Self 1.0000 NA NA
#> 110 G H 0.12500 Full-Avuncular 0.2500 NA NA
#> 111 G I 0.06250 Avuncular - Other 0.1250 NA NA
#> 112 G J 0.00000 No Relation 0.0000 NA NA
#> 113 G K 0.00000 No Relation 0.0000 NA NA
#> 114 G L 0.06250 Full-Cousins 0.1250 NA NA
#> 115 G M 0.06250 Avuncular - Other 0.1250 NA NA
#> 116 G N 0.00000 No Relation 0.0000 NA NA
#> 117 G O 0.00000 No Relation 0.0000 NA NA
#> 118 G P 0.03125 Cousin - Other 0.0625 NA NA
#> 119 G Q 0.06250 Other 0.1250 NA NA
#> 127 H H 0.50000 Self 1.0000 NA NA
#> 128 H I 0.12500 Half-Siblings 0.2500 0.0009175099 0.03029043
#> 129 H J 0.00000 No Relation 0.0000 NA NA
#> 130 H K 0.00000 No Relation 0.0000 NA NA
#> 131 H L 0.12500 Full-Avuncular 0.2500 NA NA
#> 132 H M 0.12500 Half-Siblings 0.2500 0.0009175099 0.03029043
#> 133 H N 0.00000 No Relation 0.0000 NA NA
#> 134 H O 0.00000 No Relation 0.0000 NA NA
#> 135 H P 0.06250 Avuncular - Other 0.1250 NA NA
#> 136 H Q 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 145 I I 0.50000 Self 1.0000 NA NA
#> 146 I J 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 147 I K 0.00000 No Relation 0.0000 NA NA
#> 148 I L 0.06250 Avuncular - Other 0.1250 NA NA
#> 149 I M 0.12500 Half-Siblings 0.2500 0.0009175099 0.03029043
#> 150 I N 0.00000 No Relation 0.0000 NA NA
#> 151 I O 0.00000 No Relation 0.0000 NA NA
#> 152 I P 0.06250 Avuncular - Other 0.1250 NA NA
#> 153 I Q 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 163 J J 0.50000 Self 1.0000 NA NA
#> 164 J K 0.00000 No Relation 0.0000 NA NA
#> 165 J L 0.00000 No Relation 0.0000 NA NA
#> 166 J M 0.00000 No Relation 0.0000 NA NA
#> 167 J N 0.00000 No Relation 0.0000 NA NA
#> 168 J O 0.00000 No Relation 0.0000 NA NA
#> 169 J P 0.00000 No Relation 0.0000 NA NA
#> 170 J Q 0.00000 No Relation 0.0000 NA NA
#> 181 K K 0.50000 Self 1.0000 NA NA
#> 182 K L 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 183 K M 0.00000 No Relation 0.0000 NA NA
#> 184 K N 0.00000 No Relation 0.0000 NA NA
#> 185 K O 0.00000 No Relation 0.0000 NA NA
#> 186 K P 0.00000 No Relation 0.0000 NA NA
#> 187 K Q 0.00000 No Relation 0.0000 NA NA
#> 199 L L 0.50000 Self 1.0000 NA NA
#> 200 L M 0.06250 Avuncular - Other 0.1250 NA NA
#> 201 L N 0.00000 No Relation 0.0000 NA NA
#> 202 L O 0.00000 No Relation 0.0000 NA NA
#> 203 L P 0.03125 Cousin - Other 0.0625 NA NA
#> 204 L Q 0.06250 Other 0.1250 NA NA
#> 217 M M 0.50000 Self 1.0000 NA NA
#> 218 M N 0.00000 Parent-Offspring 0.0000 0.0000000000 0.00000000
#> 219 M O 0.00000 No Relation 0.0000 NA NA
#> 220 M P 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 221 M Q 0.12500 Grandparent-Grandchild 0.2500 NA NA
#> 235 N N 0.50000 Self 1.0000 NA NA
#> 236 N O 0.00000 No Relation 0.0000 NA NA
#> 237 N P 0.00000 Grandparent-Grandchild 0.0000 NA NA
#> 238 N Q 0.00000 No Relation 0.0000 NA NA
#> 253 O O 0.50000 Self 1.0000 NA NA
#> 254 O P 0.25000 Parent-Offspring 0.5000 0.0000000000 0.00000000
#> 255 O Q 0.00000 No Relation 0.0000 NA NA
#> 271 P P 0.50000 Self 1.0000 NA NA
#> 272 P Q 0.06250 Other 0.1250 NA NA
#> 289 Q Q 0.50000 Self 1.0000 NA NA