Description Usage Arguments Details Value Examples

Estimate by simulation various relatedness coefficients, and two-locus
versions of the same coefficients, for a given recombination rate. The
current implementation covers inbreeding coefficients, kinship coefficients,
IBD (kappa) coefficients between noninbred individuals, and condensed
identity coefficients. These functions are primarily meant as tools for
validating exact algorithms, e.g., as implemented in the `ribd`

package.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 | ```
estimateInbreeding(x, id, Nsim, Xchrom = FALSE, verbose = FALSE, ...)
estimateTwoLocusInbreeding(
x,
id,
rho = NULL,
cM = NULL,
Nsim,
Xchrom = FALSE,
verbose = FALSE,
...
)
estimateKinship(x, ids, Nsim, Xchrom = FALSE, verbose = FALSE, ...)
estimateTwoLocusKinship(
x,
ids,
rho = NULL,
cM = NULL,
Nsim,
Xchrom = FALSE,
verbose = FALSE,
...
)
estimateKappa(x, ids, Nsim, Xchrom = FALSE, verbose = FALSE, ...)
estimateTwoLocusKappa(
x,
ids,
rho = NULL,
cM = NULL,
Nsim,
Xchrom = FALSE,
verbose = FALSE,
...
)
estimateIdentity(x, ids, Nsim, Xchrom = FALSE, verbose = FALSE, ...)
estimateTwoLocusIdentity(
x,
ids,
rho = NULL,
cM = NULL,
Nsim,
Xchrom = FALSE,
verbose = FALSE,
...
)
``` |

`x` |
A pedigree in the form of a |

`id, ids` |
A vector of one or two ID labels. |

`Nsim` |
The number of simulations. |

`Xchrom` |
A logical indicating if the loci are X-linked (if TRUE) or autosomal (FALSE). |

`verbose` |
A logical. |

`...` |
Further arguments passed on to |

`rho` |
A scalar in the interval |

`cM` |
A non-negative number: the genetic distance between the two loci,
given in centiMorgans. Either |

In the following, let L1 and L2 denote two arbitrary autosomal loci with
recombination rate *ρ*, and let A and B be members of the pedigree
`x`

.

The *two-locus inbreeding coefficient* *f_2(ρ)* of A is defined as the
probability that A is autozygous at both L1 and L2 simultaneously.

The *two-locus kinship coefficient* *φ_2(ρ)* of A and B is defined
as the probability that a random gamete emitted from A, and a random gamete
emitted from B, contain IBD alleles at both L1 and L2.

The *two-locus kappa coefficient* *κ_{ij}(ρ)*, for *i,j =
0,1,2*, of noninbred A and B, is the probability that A and B share exactly
`i`

alleles IBD at L1, and exactly `j`

alleles IBD at L2.

The *two-locus identity coefficient* *Δ_{ij}*, *i,j = 1,...,9*
is defined for any (possibly inbred) A and B, as the probability that A and B
are in identity state `i`

at L1, and state `j`

at L2. This uses the
conventional ordering of the nine condensed identity states. For details, see
for instance the GitHub page of the `ribd`

package.

`estimateInbreeding()`

: a single probability.

`estimateTwoLocusInbreeding()`

: a single probability.

`estimateKappa()`

: a numeric vector of length 3, with the estimated
*κ* coefficients.

`estimateTwoLocusKappa()`

: a symmetric, numerical 3*3 matrix, with the
estimated values of *κ_{ij}*, for *i,j = 0,1,2*.

`estimateIdentity()`

: a numeric vector of length 9, with the estimated
identity coefficients.

`estimateTwoLocusIdentity()`

: a symmetric, numerical 9*9 matrix, with the
estimated values of *Δ_{ij}*, for *i,j = 1,...,9*.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | ```
############################
### Two-locus inbreeding ###
############################
x = cousinPed(0, child = TRUE)
rho = 0.25
Nsim = 10 # Increase!
estimateTwoLocusInbreeding(x, id = 5, rho = rho, Nsim = Nsim, seed = 123)
########################################
### Two-locus kappa: ###
### Grandparent vs half sib vs uncle ###
########################################
# These are indistinguishable with unlinked loci, see e.g.
# pages 182-183 in Egeland, Kling and Mostad (2016).
# In the following, each simulation approximation is followed
# by its exact counterpart.
rho = 0.25; R = .5 * (rho^2 + (1-rho)^2)
Nsim = 10 # Should be increased to at least 10000
# Grandparent/grandchild
G = linearPed(2); G.ids = c(1,5); # plot(G, hatched = G.ids)
estimateTwoLocusKappa(G, G.ids, rho = rho, Nsim = Nsim, seed = 123)[2,2]
.5*(1-rho) # exact
# Half sibs
H = halfSibPed(); H.ids = c(4,5); # plot(H, hatched = H.ids)
estimateTwoLocusKappa(H, H.ids, rho = rho, Nsim = Nsim, seed = 123)[2,2]
R # exact
# Uncle
U = cousinPed(0, removal = 1); U.ids = c(3,6); # plot(U, hatched = U.ids)
estimateTwoLocusKappa(U, U.ids, rho = rho, Nsim = Nsim, seed = 123)[2,2]
(1-rho) * R + rho/4 # exact
# Exact calculations by ribd:
# ribd::twoLocusIBD(G, G.ids, rho = rho, coefs = "k11")
# ribd::twoLocusIBD(H, H.ids, rho = rho, coefs = "k11")
# ribd::twoLocusIBD(U, U.ids, rho = rho, coefs = "k11")
##########################
### Two-locus Jacquard ###
##########################
x = fullSibMating(1)
rho = 0.25
Nsim = 10 # (increase to at least 10000)
estimateTwoLocusIdentity(x, ids = 5:6, rho = rho, Nsim = Nsim, seed = 123)
# Exact by ribd:
# ribd::twoLocusIdentity(x, ids = 5:6, rho = rho)
``` |

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