CKMRsim-pairwise-relationships

Eric C. Anderson

2026-07-26

CKMRsim is all about inference of pairwise relationships from genetic data. This vignette documents the named pairwise relationships that come “pre-loaded” with CKMRsim. By saying that they are “pre-loaded” we mean that each relationship’s IBD coefficients are included in the package’s kappa matrix and that the pedigree specifying the relationship (for simulating linked markers) is included in the pedigrees list. Both kappas and pedigrees are included as part of the built-in data for this package.

First, we shall print out a table of the identify coefficients for the different relationships.

library(CKMRsim)
library(tibble)
library(dplyr)
library(stringr)

long_names <- c(
  MZ = "Monozygotic (identical) twins",
  PO = "Parent-offspring",
  FS = "Full siblings",
  HS = "Half siblings",
  GP = "Grandparent-grandchild",
  AN = "Aunt-niece",
  DFC = "Double first cousins",
  HAN = "Half aunt-niece",
  FC = "First cousins",
  HFC = "Half first cousins",
  DHFC = "Double half first cousins",
  SC = "Second cousins",
  HSC = "Half second cousins",
  U = "Unrelated"
)

rtable <- as_tibble(kappas) %>%
  mutate(
    abbreviation = rownames(kappas),
    relationship = long_names
    ) %>%
  select(relationship, abbreviation, everything())

rtable
#> # A tibble: 14 × 5
#>    relationship                  abbreviation kappa0 kappa1 kappa2
#>    <chr>                         <chr>         <dbl>  <dbl>  <dbl>
#>  1 Monozygotic (identical) twins MZ            0     0      1     
#>  2 Parent-offspring              PO            0     1      0     
#>  3 Full siblings                 FS            0.25  0.5    0.25  
#>  4 Half siblings                 HS            0.5   0.5    0     
#>  5 Grandparent-grandchild        GP            0.5   0.5    0     
#>  6 Aunt-niece                    AN            0.5   0.5    0     
#>  7 Double first cousins          DFC           0.562 0.375  0.0625
#>  8 Half aunt-niece               HAN           0.75  0.25   0     
#>  9 First cousins                 FC            0.75  0.25   0     
#> 10 Half first cousins            HFC           0.875 0.125  0     
#> 11 Double half first cousins     DHFC          0.766 0.219  0.0156
#> 12 Second cousins                SC            0.938 0.0625 0     
#> 13 Half second cousins           HSC           0.969 0.0312 0     
#> 14 Unrelated                     U             1     0      0

And now we will show a series pedigrees that depict the relationships, (except for monozygous twins and unrelated, which don’t yield interesting pedigrees) alongside the IBD coefficient values. In these pedigrees, the nodes corresponding to members of the pair are shaded (gray) and are labeled 1 and 2.

The members of each pair are labelled 1 and 2 in these pedigree definitions. CKMRsim now uses these same pedigrees with its internal Rcpp linked-marker simulator by default. The older Mendel-based backend is still available for legacy comparisons, and these pedigrees retain the non-founder convention that made the Mendel output parsing straightforward.

Parent-offspring

$\kappa_0 = 0 ~~~~~~~\kappa_1 = 1 ~~~~~~~\kappa_2 = 0$

PO: Parent-offspring

Full siblings

$\kappa_0 = 0.25 ~~~~~~~\kappa_1 = 0.5 ~~~~~~~\kappa_2 = 0.25$

FS: Full siblings

Half siblings

$\kappa_0 = 0.5 ~~~~~~~\kappa_1 = 0.5 ~~~~~~~\kappa_2 = 0$

HS: Half siblings

Grandparent-grandchild

$\kappa_0 = 0.5 ~~~~~~~\kappa_1 = 0.5 ~~~~~~~\kappa_2 = 0$

GP: Grandparent-grandchild

Aunt-niece

$\kappa_0 = 0.5 ~~~~~~~\kappa_1 = 0.5 ~~~~~~~\kappa_2 = 0$

AN: Aunt-niece

Double first cousins

$\kappa_0 = 0.5625 ~~~~~~~\kappa_1 = 0.375 ~~~~~~~\kappa_2 = 0.0625$

DFC: Double first cousins

Half aunt-niece

$\kappa_0 = 0.75 ~~~~~~~\kappa_1 = 0.25 ~~~~~~~\kappa_2 = 0$

HAN: Half aunt-niece

First cousins

$\kappa_0 = 0.75 ~~~~~~~\kappa_1 = 0.25 ~~~~~~~\kappa_2 = 0$

FC: First cousins

Half first cousins

$\kappa_0 = 0.875 ~~~~~~~\kappa_1 = 0.125 ~~~~~~~\kappa_2 = 0$

HFC: Half first cousins

Double half first cousins

$\kappa_0 = 0.765625 ~~~~~~~\kappa_1 = 0.21875 ~~~~~~~\kappa_2 = 0.015625$

DHFC: Double half first cousins

Second cousins

$\kappa_0 = 0.9375 ~~~~~~~\kappa_1 = 0.0625 ~~~~~~~\kappa_2 = 0$

SC: Second cousins

Half second cousins

$\kappa_0 = 0.96875 ~~~~~~~\kappa_1 = 0.03125 ~~~~~~~\kappa_2 = 0$

HSC: Half second cousins