Package 'ricalc'

Title: Calculations for Recombinant Inbred Lines
Description: Calculate two- and three-locus probabilities in multiple-strain recombinant inbred lines, and simulate such lines. Broman (2005) <doi:10.1534/genetics.104.035212>.
Authors: Karl W Broman [aut, cre]
Maintainer: Karl W Broman <[email protected]>
License: GPL-3
Version: 0.56-2
Built: 2026-05-09 20:42:37 UTC
Source: https://github.com/kbroman/ricalc

Help Index

Overview of R/ricalc package

Description

A brief introduction to the contents of the R/ricalc package.

Stuff for the gamma model

  • coinc.gam: Calculate the three-point coincidence function for the gamma model.

  • mf.gam: Map function for the gamma model.

  • imf.gam: Inverse of map function for the gamma model.

Data

  • mouseL: Estimated genetic lengths of mouse chromosomes.

  • threept.AI: Three-point haplotype probabilities for 8-way RIL, autosome, under interference.

  • threept.ANI: Three-point haplotype probabilities for 8-way RIL, autosome, with no interference.

  • threept.XI: Three-point haplotype probabilities for 8-way RIL, X chromosome, under interference.

  • threept.XNI: Three-point haplotype probabilities for 8-way RIL, X chromosome, with no interference.

Symbolic data

  • fulltm: Generation-to-generation transition matrices for 2- and 4-way RIL by selfing and by sibling mating (in symbolic notation...lists of lists of character strings).

  • mtm: Transition matrices for meiosis, again in symbols...lists of lists of character strings).

Counting and enumerating parental types

  • lookup: Lookup tables for parental types in the generation of multiple-strain RIL, representing the

  • get.start: Symbolic notation for the starting state in the generation of multiple-strain RIL.

  • count.absorb: Count the absorbing states in multiple-strain RIL.

Calculations and simulations

  • sim.ri: Simulate multiple-strain RIL.

  • get.ril.coinc: Numerical calculation of the 3-point coincidence-type quantity for 2- and 4-way RIL.

  • get.ril.prob: Numerical calculation of haplotype probabilities on 2- or 4-way RIL chromosomes.

  • get.full.tm: Calculate the generation-to-generation transition matrix for the formation of RIL.

  • get.full.tm.symbolic: Calculate the generation-to-generation transition matrix for the formation of RIL, in symbolic form.

  • convert.full.tm: Convert a sparse version of a transition matrix into a full matrix.

Author(s)

Karl W Broman, [email protected]

References

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

Teuscher, F. and Broman, K. W. (2007) Haplotype probabilities for multiple-strain recombinant inbred lines. Genetics 175, 1267–1274.

Three-point coincidence under the gamma renewal model

Description

Calculates the three-point coincidence under the gamma renewal model, under the assumption that the two defined intervals have the same recombination fraction.

Usage

coinc.gam(r, nu=1, tol=1e-12)

Arguments

r

Recombination fraction for each interval (can be a vector).
nu

Interference parameter (nu = m+1 in the chi-square model; nu=0 is NI).
tol

Tolerance for doing numerical integration.

Details

Uses the functions mf.gam and imf.gam.

Value

Vector of three-point coincidences, of same length as the input r.

Author(s)

Karl W Broman, [email protected]

References

Zhao, H. and Speed, T. P. (1996) On genetic map functions. Genetics 142, 1369–1377.

Broman, K. W., Rowe, L. B., Churchill, G. A. and Paigen, K. (2002) Crossover interference in the mouse. Genetics 160, 1123–1131.

See Also

mf.gam, imf.gam

Examples

coinc.gam(seq(0.01,0.49,by=0.01), 11.3)

Convert sparse version of transition matrix to full form

Description

Convert a sparse version of a transition matrix (with only the non-zero elements) into a full matrix.

Usage

convert.full.tm(full.tm)

Arguments

full.tm

A list whose elements are the rows of the matrix, each being a vector with just the non-zero elements of the matrix.

Value

A full matrix version of the input.

Author(s)

Karl W Broman, [email protected]

See Also

get.full.tm, get.full.tm.symbolic

Convert simulated pedigree data to genotypes at markers

Description

Convert data generated by sim.ped to a matrix of genotypes.

Usage

convert2gen(xodat, map)

Arguments

xodat

Allele information with continuous crossover locations, as generated by sim.ped.
map

A vector of marker locations, in cM.

Details

The marker locations (map) must be sorted and should span a length that is less then what was used to generated xodat.

If there are just two possible alleles (1 and 2) in xodat, the genotypes are coded as 1, 2, and 3, for genotypes 11, 12 and 22. Otherwise, they are converted to binary codes. For example, with possible alleles 1, 2, and 3, an individual with genotype a,b will be given the value 2(a−1)+2(b−1)2^(a-1) + 2^(b-1).

Value

The output is a matrix with length(xodat) rows and length(map) columns. Genotype codes are described in Details.

Author(s)

Karl W Broman, [email protected]

See Also

sim.ped, genAILped

Examples

ailped <- genAILped(ngen=2, npairs=2, sibship.size=2)
aildat <- sim.ped(ailped, 100)
map <- seq(0, 100, by=10)
names(map) <- paste("M", 1:length(map), sep="")
ailgen <- convert2gen(aildat, map)

Count absorbing states

Description

Determine the absorbing states of the Markov chain for the generation of recombinant inbred lines.

Usage

count.absorb(n.strains=c("2","4"),type=c("selfing","sibmating"),
         chrtype=c("A","X"),n.loci=c("2","3"))

Arguments

n.strains

Number of parental strains.
type

Method for mating.
chrtype

Indicates autosome or X chromosome (when type=sibmating only).
n.loci

Number of loci.

Value

A vector whose names indicate the minimal set of absorbing states, and whose elements are the number of the full states corresponding to each.

Author(s)

Karl W Broman, [email protected]

References

Haldane, J. B. S. and Waddington, C. H. (1931) Inbreeding and linkage. Genetics 16, 357–374.

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

Examples

count.absorb()

Symbolic generation-to-generation transition matrices

Description

Symbolic generation-to-generation transition matrices for the process of creating multiple strain recombinant inbred lines.

Usage

data(fulltm)

Format

A list of lists; each list contains the non-zero elements in the rows of the transition matrices.

Source

These were formed using the internal function get.full.tm.symbolic, with help from mathematica to simplify the expressions.

See Also

get.full.tm, get.full.tm.symbolic, convert.full.tm

Examples

data(fulltm)
fulltm[["2sibX2"]]["AA|BB x AA"]

Generate a pedigree matrix for AIL

Description

Generate a pedigree matrix, for use with the simulation function sim.ped, for advanced intercross lines.

Usage

genAILped(ngen=8, npairs=20, sibship.size=10)

Arguments

ngen

Number of generations of crosses.
npairs

Number of mating pairs per generation.
sibship.size

Size of sibships in the final generation.

Details

We generate equal numbers of males and females at each generation. Matings are with random male/female pairs, with no attempt to avoid matings between siblings.

Value

The output is a matrix with five columns: "id", "sex" (coded as 0=female, 1=male), "mom", "dad", and "generation".

Author(s)

Karl W Broman, [email protected]

See Also

sim.ped

Examples

ailped <- genAILped(ngen=5, npairs=5, sibship.size=2)

Calculate the transition matrix for the formation of RILs

Description

Calculate the full generation-to-generation transition matrix for the formation of RILs.

Usage

get.full.tm(r, coinc=1, n.strains=c("2","4"), type=c("selfing","sibmating"),
         chrtype=c("A","X"), n.loci=c("2","3"))

Arguments

r

Recombination fraction between markers.
coinc

The 3-point coincidence (used only when n.loci=3).
n.strains

Number of parental strains.
type

Method for mating.
chrtype

Indicates autosome or X chromosome (when type=sibmating only).
n.loci

Number of loci.

Value

The transition matrix as a list whose components are the rows of the matrix. Only the non-zero elements of each row are returned.

Author(s)

Karl W Broman, [email protected]

References

Haldane, J. B. S. and Waddington, C. H. (1931) Inbreeding and linkage. Genetics 16, 357–374.

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

See Also

get.full.tm.symbolic, fulltm, convert.full.tm

Examples

fulltm2self2 <- get.full.tm(0.1)

Calculate symbolic form of transition matrix for the formation of RILs

Description

Calculate the full generation-to-generation transition matrix for the formation of RILs, in symbolic form.

Usage

get.full.tm.symbolic(n.strains=c("2","4"), type=c("selfing","sibmating"),
         chrtype=c("A","X"), n.loci=c("2","3"))

Arguments

n.strains

Number of parental strains.
type

Method for mating.
chrtype

Indicates autosome or X chromosome (when type=sibmating only).
n.loci

Number of loci.

Value

The transition matrix as a list whose components are the rows of the matrix. Only the non-zero elements of each row are returned, and they are returned as character strings.

Author(s)

Karl W Broman, [email protected]

References

Haldane, J. B. S. and Waddington, C. H. (1931) Inbreeding and linkage. Genetics 16, 357–374.

Broman, K. W., Rowe, L. B., Churchill, G. A. and Paigen, K. (2002) Crossover interference in the mouse. Genetics 160, 1123–1131.

See Also

get.full.tm, convert.full.tm

Examples

fulltm2self2 <- get.full.tm.symbolic()

Calculate 3-point coincidence on an RIL chromosome

Description

Calculate (numerically) the quantity analogous to a three-point coincidence on a 2- or 4-way RIL chromosome.

Usage

get.ril.coinc(r, coinc=1, n.strains=c("2","4"), type=c("selfing","sibmating"),
         chrtype=c("A","X"), verbose=TRUE)

Arguments

r

Recombination fraction between markers.
coinc

The 3-point coincidence (used only when n.loci=3).
n.strains

Number of parental strains.
type

Method for mating.
chrtype

Indicates autosome or X chromosome (when type=sibmating only).
verbose

If TRUE, print stuff as things progress.

Value

A single number.

Author(s)

Karl W Broman, [email protected]

References

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

See Also

get.ril.prob

Examples

get.ril.coinc(0.01)

Calculate the haplotype probabilities for an RIL chromosome

Description

Calculate (numerically) the haplotype probabilities on a 2- or 4-way RIL chromosome.

Usage

get.ril.prob(r, coinc=1, n.strains=c("2","4"), type=c("selfing","sibmating"),
         chrtype=c("A","X"), n.loci=c("2","3"), verbose=TRUE)

Arguments

r

Recombination fraction between markers.
coinc

The 3-point coincidence (used only when n.loci=3).
n.strains

Number of parental strains.
type

Method for mating.
chrtype

Indicates autosome or X chromosome (when type=sibmating only).
n.loci

Number of loci.
verbose

If TRUE, print stuff as things progress.

Value

A vector of probabilities, with absorbing states in their reduced form.

Author(s)

Karl W Broman, [email protected]

References

Haldane, J. B. S. and Waddington, C. H. (1931) Inbreeding and linkage. Genetics 16, 357–374.

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

See Also

get.ril.coinc

Determine the initial state in the generation of RILs

Description

Determine the initial state in the Markov chain to generate 2- or 4-way recombination inbred lines.

Usage

get.start(n.strains=c("2","4"),type=c("selfing","sibmating"),
         chrtype=c("A","X"),n.loci=c("2","3"))

Arguments

n.strains

Number of parental strains.
type

Method for mating.
chrtype

Indicates autosome or X chromosome (when type=sibmating only).
n.loci

Number of loci.

Value

A character string.

Author(s)

Karl W Broman, [email protected]

References

Haldane, J. B. S. and Waddington, C. H. (1931) Inbreeding and linkage. Genetics 16, 357–374.

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

See Also

count.absorb

Examples

get.start()

Inverse map function for gamma renewal model

Description

Calculates the genetic length (in cM) corresponding to a particular recombination fraction for the gamma renewal model for recombination at meiosis.

Usage

imf.gam(r, nu=1, tol=1e-12)

Arguments

r

Recombination fraction, potentially a vector.
nu

Interference parameter (nu = m+1 in the chi-square model; nu=0 is NI).
tol

Tolerance for doing numerical integration and finding root.

Details

Uses uniroot to solve the r = mf.gam(d, nu).

Value

Vector of interval lengths (in cM), of same length as the input r.

Author(s)

Karl W Broman, [email protected]

References

Zhao, H. and Speed, T. P. (1996) On genetic map functions. Genetics 142, 1369–1377.

Broman, K. W., Rowe, L. B., Churchill, G. A. and Paigen, K. (2002) Crossover interference in the mouse. Genetics 160, 1123–1131.

See Also

mf.gam, coinc.gam

Examples

imf.gam(seq(0,0.49,by=0.01), 11.3)

Look-up tables for multi-locus parental types

Description

Look-up tables for multi-locus parental types in the generation of 2-way or 4-way recombinant inbred lines by selfing, sibling mating with the X chromosome, or sibling mating with an autosome, and for cases of two or three loci. The tables connect all possible parental types to the prototypical versions after collapsing according to various symmetries.

Usage

data(lookup)

Format

A list of vectors, each corresponding to a different set of conditions (for example, 2-way selfing at 3 points). Each vector has names corresponding to all possible parental types and with entries being the corresponding prototypes after collapsing according to various symmetries.

Source

These were formed using the internal function gtypes.

References

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

Examples

data(lookup)
length(lookup[["2self3"]])
length(unique(lookup[["2self3"]]))

Map function for gamma renewal model

Description

Calculates the recombination fraction corresponding to a particular cM interval length for the gamma renewal model for recombination at meiosis.

Usage

mf.gam(d, nu=1, tol=1e-12)

Arguments

d

Interval length (in cM), potentially a vector.
nu

Interference parameter (nu = m+1 in the chi-square model; nu=0 is NI).
tol

Tolerance for doing numerical integration.

Details

Uses the function integrate to do numerical integration.

Value

Vector of recombination fractions, of same length as the input d.

Author(s)

Karl W Broman, [email protected]

References

Zhao, H. and Speed, T. P. (1996) On genetic map functions. Genetics 142, 1369–1377.

Broman, K. W., Rowe, L. B., Churchill, G. A. and Paigen, K. (2002) Crossover interference in the mouse. Genetics 160, 1123–1131.

See Also

imf.gam, coinc.gam

Examples

mf.gam(0:25, 11.3)

Estimated genetic lengths of mouse chromosomes

Description

Estimated genetic lengths (in cM) of mouse chromosomes.

Usage

data(mouseL)

Format

An vector of length 20, each element being the length (in cM) of the corresponding chromosome.

Source

Mouse Genome Informatics, http://www.informatics.jax.org/mgihome/other/mouse_facts1.shtml

See Also

sim.ri

Examples

data(mouseL)
ri <- sim.ri(mouseL, type="selfing", n.str="8")

Symbolic transition matrices for meiosis

Description

Transition matrices for meiosis: the probabilities of the possible haplotypes for a meiotic product from a given parental type. These are symbolic versions.

Usage

data(mtm)

Format

A list of lists. Each list corresponds to a different condition (for example, 2 alleles for the X chromosome at 3 points). Each list contains a set of vectors, one for each possible parental type, containing a vector of character strings specifying the probabilities of each possible meiotic haplotype.

Source

These were formed using the internal functions write.meiosis.tm.symbolic and read.meiosis.tm.symbolic, using mathematica to simplify the expressions.

Examples

data(mtm)
sapply(mtm[["2A3"]],length)

Installed version of R/ricalc

Description

Print the version number of the currently installed version of R/ricalc.

Usage

ricalcversion()

Value

A character string with the version number of the currently installed version of R/ricalc.

Author(s)

Karl W Broman, [email protected]

Examples

ricalcversion()

Simulate a general pedigree

Description

Simulates alleles for a general pedigree, using the chi-square model for interference at meiosis.

Usage

sim.ped(pedigree, L, sexsp=1, xchr=FALSE, m=10, obligate.chiasma=FALSE)

Arguments

pedigree

A matrix with rows corresponding to individuals and columns being individual identifiers ("id"), sex (0/1 or F/M), mom, and dad. Parents must precede their offspring.
L

Length of chromosome in cM.
sexsp

Female:male recombination rate (must be > 0)
xchr

If TRUE, simulate the X chromosome.
m

The interference parameter (a non-negative integer). m=0 corresponds to no interference; m>0 corresponds to positive crossover interference.
obligate.chiasma

Indicates whether there is an obligate chiasma on the four-strand bundle.

Details

Meiosis is simulated by the chi-square model (see Zhao et al. 1995), with the possibility of requiring an obligate chiasma on the four-strand bundle at meiosis.

The pedigree matrix must have columns named "id", "sex", "mom"/"dam" and "dad"/"sire". Other columns are ignored. Founders should have 0 in the mom and dad columns; others should have the identifiers for the mom and dad. Each individual must have either both parents in the matrix or neither.

Value

The output is a list with length equal to the number of rows in pedigree. Each component is itself a list with two components, the maternal and paternal chromosomes. These are matrices with two rows: The first row consists of the locations of exchanges (0 and L are included); the second row contains the allele (coded 1, 2, ..., no. founders) in the interval to the left.

Author(s)

Karl W Broman, [email protected]

References

Zhao, H., Speed, T. P. and McPeek, M. S. (1995) Statistical analysis of crossover interference using the chi-square model. Genetics 139, 1045–1056.

See Also

sim.ri, genAILped, convert2gen

Examples

ailped <- genAILped(ngen=5, npairs=5, sibship.size=2)
aildat <- sim.ped(ailped, 100)

Simulate a recombinant inbred line

Description

Simulates alleles for a multiple-strain RI line, using the chi-square model for interference at meiosis, performing inbreeding by selfing or sibling mating, until complete fixation has occurred.

Usage

sim.ri(L, sexsp=1, type=c("selfing","sibmating"),
       n.strains=c("2","4","8"),
       xchr=FALSE, m=10, obligate.chiasma=FALSE)

Arguments

L

Length of chromosome(s) in cM; either a vector or a single number.
sexsp

Female:male recombination rate (must be > 0)
type

Indicates whether the inbreeding is by selfing or by sibling mating.
n.strains

Number of initial parental strains.
xchr

If length(L)==1 and type="sibmating", this indicates to simulate the X chromosome. If length(L) > 1, the chromosomes named "X" or "x" are taken to be the X chromosome and all others are assumed to be autosomes.
m

The interference parameter (a non-negative integer). m=0 corresponds to no interference; m>0 corresponds to positive crossover interference.
obligate.chiasma

Indicates whether there is an obligate chiasma on the four-strand bundle.

Details

Meiosis is simulated by the chi-square model (see Zhao et al. 1995), with the possibility of requiring an obligate chiasma on the four-strand bundle at meiosis.

Inbreeding is performed until complete fixation. Of course, we assume no mutation and no selection.

Value

If length(L)==1, the output is a two-row matrix whose first row consists of the locations of exchanges along the recombinant inbred chromosome (0 and L are included). The second row contains the allele (coded 1, 2, ..., 8) in the interval to the left. Attributes "prop.het" and "num.het" are included which contain the proportion of the genome that is not yet fixed and the number of segments of such heterozygosity, respectively, after each generation of inbreeding. The attribute "nubreak" gives the number of unique breakpoints at each generation.

If length(L)>1, the output is a list of length length(L), with each component being a two-row matrix, as above. The overall list also has attributes "prop.het" and "num.het", specifying the proportion of the entire genome that has not yet been fixed and the number of segments of such heterozygosity, respectively, after each generation of inbreeding.

Author(s)

Karl W Broman, [email protected]

References

Haldane, J. B. S. and Waddington, C. H. (1931) Inbreeding and linkage. Genetics 16, 357–374.

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

Broman, K. W., Rowe, L. B., Churchill, G. A. and Paigen, K. (2002) Crossover interference in the mouse. Genetics 160, 1123–1131.

Zhao, H., Speed, T. P. and McPeek, M. S. (1995) Statistical analysis of crossover interference using the chi-square model. Genetics 139, 1045–1056.

See Also

sim.ri

Examples

data(mouseL)
ri <- sim.ri(mouseL, type="selfing", n.str="8")

Three-point probabilities for four-way RILs by sibling mating

Description

Three-point haplotype probabilities for four-way recombinant inbred lines formed by sibling mating. A and X indicate autosome and the X chromosome. I and NI indicate strong crossover interference (gamma model with ν=11.3\nu=11.3) and no interference.

Usage

data(threept.AI)
data(threept.ANI)
data(threept.XI)
data(threept.XNI)

Format

Each is matrix; the first two columns indicate the recombination fraction between markers (at meiosis) and the three-point coincidence (at meiosis). The remaining columns are the haplotype probabilities for the fixed RIL chromosome. These are for the reduced set of states, taking account of many symmetries.

Use count.absorb to get the numbers of full states in each reduced state.

Source

These were calculated using perl programs included with this package.

References

Haldane, J. B. S. and Waddington, C. H. (1931) Inbreeding and linkage. Genetics 16, 357–374.

Broman, K. W. (2005) The genomes of recombinant inbred lines. Genetics 169, 1133–1146.

See Also

get.ril.prob

Examples

data(threept.AI)
  plot(threept.AI[,c(1,3)])