The pedmut package is part of the ped suite ecosystem for pedigree analysis in R. Its aim is to provide a framework for modelling mutations in pedigree computations.
Although pedmut is self-contained, its main purpose is to be imported by other ped suite packages, like pedprobr (marker probabilities and pedigree likelihoods), forrel (forensic pedigree analysis) and dvir.
For the theoretical background of mutation models and their properties (stationarity, reversibility, lumpability), I recommend Chapter 5 of Pedigree analysis in R, and the references therein.
# The easiest way to get `pedmut` is to install the entire `ped suite`:
install.packages("pedsuite")
# Alternatively, you can install just `pedmut`:
install.packages("pedmut")
# If you need the latest development version, install it from GitHub:
# install.packages("devtools")
devtools::install_github("magnusdv/pedmut")
The examples below require the packages pedtools and pedprobr in
addition to pedmut. The first two are core members of the ped suite
and can be loaded collectively with library(pedsuite)
.
library(pedsuite)
library(pedmut)
The figure below shows a father and son who are homozygous for different alleles. We assume that the locus is an autosomal marker with two alleles, labelled 1 and 2.
# Create pedigree
x = nuclearPed(father = "fa", mother = "mo", child = "boy")
# Add marker
x = addMarker(x, fa = "1/1", boy = "2/2")
# Plot with genotypes
plot(x, marker = 1)
The data clearly constitutes a Mendelian error, and gives a likelihood of 0 without mutation modelling:
likelihood(x, marker = 1)
#> [1] 0
The following code sets a simple mutation model and recomputes the pedigree likelihood.
x2 = setMutationModel(x, marker = 1, model = "equal", rate = 0.1)
likelihood(x2, marker = 1)
#> [1] 0.0125
Under the mutation model, the combination of genotypes is no longer
impossible, yielding a non-zero likelihood. To see details about the
mutation model, we can use the mutmod()
accessor:
mutmod(x2, marker = 1)
#> Unisex mutation matrix:
#> 1 2
#> 1 0.9 0.1
#> 2 0.1 0.9
#>
#> Model: equal
#> Rate: 0.1
#> Frequencies: 0.5, 0.5
#>
#> Stationary: Yes
#> Reversible: Yes
#> Lumpable: Always
A mutation matrix in pedmut is a stochastic matrix, with each row summing to 1, where the rows and columns are named with allele labels.
Two central functions of package are mutationMatrix()
and
mutationModel()
. The first constructs a single mutation matrix
according to various model specifications. The second produces what is
typically required in applications, namely a list of two mutation
matrices, named “male” and “female”.
The mutation models currently implemented in pedmut are:
equal
: All mutations equally likely; probability 1-rate
of no
mutation. Parameters: rate
.
proportional
: Mutation probabilities are proportional to the target
allele frequencies. Parameters: rate
, afreq
.
random
: This produces a matrix of random numbers, each row
normalised to have sum 1. Parameters: seed
.
custom
: Allows any valid mutation matrix to be provided by the user.
Parameters: matrix
.
onestep
: Applicable if all alleles are integers. Mutations are
allowed only to the nearest integer neighbour. Parameters: rate
.
stepwise
: For this model alleles must be integers or decimal numbers
with a single decimal, such as ‘17.1’, indicating a microvariant.
Mutation rates depend on whether transitions are within the same group
or not, i.e., between integer alleles and microvariants in the latter
case. Mutations also depend on the size of the mutation as modelled by
the parameter range
, the relative probability of mutating n+1 steps
versus mutating n steps. Parameters: rate
, rate2
, range
.
trivial
: Diagonal mutation matrix with 1 on the diagonal.
Parameters: None.
Several properties of mutation models are of interest (both theoretical and practical) for likelihood computations. The pedmut package provides utility functions for quickly checking these:
isStationary(M, afreq)
: Checks if afreq
is a right eigenvector of
the mutation matrix M
. Stationary models have the desirable property
that allele frequencies don’t change across generations.
isReversible(M, afreq)
: Checks if M
together with afreq
form a
reversible Markov chain, i.e., that they satisfy the detailed
balance criterion.
isLumpable(M, lump)
: Checks if M
allows clustering (“lumping”) of
a given subset of alleles. This implements the necessary and
sufficient condition of strong lumpability of Kemeny and Snell
(Finite Markov Chains, 1976).
alwaysLumpable(M)
: Checks if M
allows lumping of any allele
subset.
An equal
model with rate 0.1:
mutationMatrix("equal", rate = 0.1, alleles = c("a", "b", "c"))
#> a b c
#> a 0.90 0.05 0.05
#> b 0.05 0.90 0.05
#> c 0.05 0.05 0.90
#>
#> Model: equal
#> Rate: 0.1
#>
#> Lumpable: Always
Next, a proportional
model with rate 0.1. Note that this model depends
on the allele frequencies.
mutationMatrix("prop", rate = 0.1, alleles = c("a", "b", "c"), afreq = c(0.7, 0.2, 0.1))
#> a b c
#> a 0.93478261 0.04347826 0.02173913
#> b 0.15217391 0.82608696 0.02173913
#> c 0.15217391 0.04347826 0.80434783
#>
#> Model: proportional
#> Rate: 0.1
#> Frequencies: 0.7, 0.2, 0.1
#>
#> Stationary: Yes
#> Reversible: Yes
#> Lumpable: Always
To illustrate the stepwise
model, we recreate the mutation matrix in
Section 2.1.3 of Simonsson and Mostad (FSI:Genetics, 2015). This is done
as follows:
mutationMatrix(model = "stepwise", alleles = c("16", "17", "18", "16.1", "17.1"),
rate = 0.003, rate2 = 0.001, range = 0.5)
#> 16 17 18 16.1 17.1
#> 16 0.9960000000 0.0020000000 0.0010000000 0.0005000000 0.0005000000
#> 17 0.0015000000 0.9960000000 0.0015000000 0.0005000000 0.0005000000
#> 18 0.0010000000 0.0020000000 0.9960000000 0.0005000000 0.0005000000
#> 16.1 0.0003333333 0.0003333333 0.0003333333 0.9960000000 0.0030000000
#> 17.1 0.0003333333 0.0003333333 0.0003333333 0.0030000000 0.9960000000
#>
#> Model: stepwise
#> Rate: 0.003
#> Rate2: 0.001
#> Range: 0.5
#>
#> Lumpable: Not always
A simpler version of the stepwise
model above, is the onestep
model,
in which only the immediate neighbouring integers are reachable by
mutation. This model is only applicable when all alleles are integers.
mutationMatrix(model = "onestep", alleles = c("16", "17", "18"), rate = 0.04)
#> 16 17 18
#> 16 0.96 0.04 0.00
#> 17 0.02 0.96 0.02
#> 18 0.00 0.04 0.96
#>
#> Model: onestep
#> Rate: 0.04
#>
#> Lumpable: Not always
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