Title:	Tests for Segregation Distortion in Polyploids
Version:	2.0.0
Description:	Provides tests for segregation distortion in F1 polyploid populations under different assumptions of meiosis. These tests can account for double reduction, partial preferential pairing, and genotype uncertainty through the use of genotype likelihoods. Parallelization support is provided. Details of these methods are described in Gerard et al. (2025a) <doi:10.1007/s00122-025-04816-z> and Gerard et al. (2025b) <doi:10.1101/2025.06.23.661114>. Part of this material is based upon work supported by the National Science Foundation under Grant No. 2132247. The opinions, findings, and conclusions or recommendations expressed are those of the author and do not necessarily reflect the views of the National Science Foundation.
License:	GPL (≥ 3)
BugReports:	https://github.com/dcgerard/segtest/issues
URL:	https://dcgerard.github.io/segtest/
Encoding:	UTF-8
RoxygenNote:	7.3.2
Biarch:	true
Depends:	R (≥ 3.5)
Imports:	doFuture, doRNG, foreach, future, iterators, minqa, nloptr, Rcpp, updog
Suggests:	knitr, polymapR, rmarkdown, testthat (≥ 3.0.0)
Config/testthat/edition:	3
VignetteBuilder:	knitr
LinkingTo:	Rcpp, RcppArmadillo
LazyData:	true
NeedsCompilation:	yes
Packaged:	2025-06-30 13:45:58 UTC; dgerard
Author:	David Gerard [aut, cre], Mira Thakkar [aut], Guilherme da Silva Pereira [ctb], NSF DBI 2132247 [fnd] (https://www.nsf.gov/awardsearch/showAward?AWD_ID=2132247)
Maintainer:	David Gerard <gerard.1787@gmail.com>
Repository:	CRAN
Date/Publication:	2025-06-30 18:40:02 UTC

segtest: Tests for Segregation Distortion in Polyploids

Description

Provides tests for segregation distortion in F1 polyploid populations under different assumptions of meiosis. These tests can account for double reduction, partial preferential pairing, and genotype uncertainty through the use of genotype likelihoods. Parallelization support is provided. Details of these methods are described in Gerard et al. (2025a) doi:10.1007/s00122-025-04816-z and Gerard et al. (2025b) doi:10.1101/2025.06.23.661114. Part of this material is based upon work supported by the National Science Foundation under Grant No. 2132247. The opinions, findings, and conclusions or recommendations expressed are those of the author and do not necessarily reflect the views of the National Science Foundation.

Author(s)

Maintainer: David Gerard gerard.1787@gmail.com (ORCID)

Authors:

• Mira Thakkar chrtmira@gmail.com

Other contributors:

• Guilherme da Silva Pereira g.pereira@ufv.br (ORCID) [contributor]

• NSF DBI 2132247 (https://www.nsf.gov/awardsearch/showAward?AWD_ID=2132247) [funder]

See Also

Useful links:

• https://dcgerard.github.io/segtest/

• Report bugs at https://github.com/dcgerard/segtest/issues

Bounds on the distortion at simplex loci caused by double reduction.

Description

The frequency of (nullplex, simplex, duplex) gametes is (.5 + beta, .5 - 2 * beta, beta). This function returns the upper bound on beta under two models.

Usage

beta_bounds(ploidy, model = c("ces", "prcs"))

Arguments

Details

Returns the upper bound on the probability of a gamete with a genotype of 2 when the parent has a genotype of 1. This is based on two models. The upper bound from complete equational separation is higher than the upper bound from the pure random chromatid segregation. See Huang et al (2019) for a description of these models.

Value

The upper bound on beta.

Author(s)

David Gerard

References

• Huang, K., Wang, T., Dunn, D. W., Zhang, P., Cao, X., Liu, R., & Li, B. (2019). Genotypic frequencies at equilibrium for polysomic inheritance under double-reduction. G3: Genes, Genomes, Genetics, 9(5), 1693-1706. doi:10.1534/g3.119.400132

Examples

beta_bounds(4)
beta_bounds(6)
beta_bounds(8)
beta_bounds(10)

Chi Square test when genotypes are known

Description

This chi-squared test is run under the assumption of no double reduction and no preferential pairing.

Usage

chisq_g(x, g1, g2)

chisq_g4(x, g1, g2)

Arguments

Value

A list containing the chi-squared statistic, degrees of freedom, and p-value.

Functions

• chisq_g4(): Alias for chisq_g, for backwards compatibility.

Author(s)

Mira Thakkar and David Gerard

Examples

x <- c(1, 2, 4, 3, 0)
g1 <- 2
g2 <- 2
chisq_g(x, g1, g2)

x <- c(10, 25, 10, 0, 0)
g1 <- 1
g2 <- 1
chisq_g(x, g1, g2)

Chi-Sq for GL

Description

Calculates the MLE genotype and runs a chi-squared test assuming no double reduction and no preferential pairing.

Usage

chisq_gl(gl, g1, g2)

chisq_gl4(gl, g1, g2)

Arguments

Value

A list containing the chi-squared statistic, degrees of freedom, and p-value.

Functions

• chisq_gl4(): Alias for chisq_gl, for backwards compatibility.

Author(s)

Mira Thakkar and David Gerard

Examples

## null sim
set.seed(1)
g1 <- 2
g2 <- 2
gl <- simf1gl(n = 25, g1 = g1, g2 = g2, alpha = 0, xi2 = 1/3)
chisq_gl(gl = gl, g1 = g1, g2 = g2)

Upper bounds on double reduction rates.

Description

Provides the upper bounds on the double reduction rates based on the formulas in Huang et al. (2019). There are two upper bounds provided. The upper bound from complete equational separation is higher than the upper bound from the pure random chromatid segregation.

Usage

drbounds(ploidy, model = c("ces", "prcs"))

Arguments

Value

A vector of length floor(ploidy / 4) containing the upper bounds on the rates of double reduction. The ithe element is the upper bound on the probability that there are i pairs of identical by double reduction alleles in a gamete.

Author(s)

David Gerard

References

• Haldane, J. B. S. (1930). Theoretical genetics of autopolyploids. Journal of genetics, 22, 359-372. doi:10.1007/BF02984197

• Huang, K., Wang, T., Dunn, D. W., Zhang, P., Cao, X., Liu, R., & Li, B. (2019). Genotypic frequencies at equilibrium for polysomic inheritance under double-reduction. G3: Genes, Genomes, Genetics, 9(5), 1693-1706. doi:10.1534/g3.119.400132

• Mather, K. (1935). Reductional and equational separation of the chromosomes in bivalents and multivalents. Journal of genetics, 30, 53-78. doi:10.1007/BF02982205

Examples

drbounds(4)
drbounds(6)
drbounds(8)
drbounds(10)

EM algorithm from Li (2011)

Description

EM algorithm to estimate prior genotype probabilities from genotype likelihoods.

Usage

em_li(B, itermax = 100L, eps = 1e-05)

Arguments

Value

A vector of log prior probabilities for each genotype.

Author(s)

David Gerard

References

• Li, H. (2011). A statistical framework for SNP calling, mutation discovery, association mapping and population genetical parameter estimation from sequencing data. Bioinformatics, 27(21), 2987-2993. doi:10.1093/bioinformatics/btr509

Examples

# Simulate some data
set.seed(1)
gl <- simgl(nvec = c(3, 2, 4, 1, 2))
# Run em
lprob <- em_li(B = gl)
# Exponentiate to get probabilities
prob <- exp(c(lprob))
prob

Gamete frequencies under a generalized model

Description

Returns the gamete frequencies for autopolyploids, allopolyploids, and segmental allopolyploids, accounting for the effects of double reduction and partial preferential pairing.

Usage

gamfreq(
  g,
  ploidy,
  gamma = NULL,
  alpha = NULL,
  beta = NULL,
  type = c("mix", "polysomic"),
  add_dr = TRUE
)

Arguments

Value

The vector of gamete frequencies. Element i is the probability a gamete has genotype i - 1.

Models

If type = "polysomic", then the gamete frequencies correspond to those of Huang et al (2019). Those formulas are for general multiallelic loci, so see also Appendix G of Gerard (2022) for special case of biallelic loci. The relevant parameter is alpha, a vector of length floor(ploidy / 4), where alpha[[i]] is the probability that there are i pairs of double reduced alleles in a gamete. The theoretical upper bound on alpha is given in drbounds().

If type = "mix" and add_dr = FALSE, then the gamete frequencies correspond to the pairing configuration model of Gerard et al (2018). This model states that the gamete frequencies are a convex combination of the disomic inheritance frequencies. The weights of this convex combination are provided in the gamma parameter. The total number of disomic segregation patterns is given by n_pp_mix(). The order of these segregation patterns used is the order in seg.

The model for type = "mix" and add_dr = TRUE is the same as for type = "mix" and add_dr = FALSE except at parental simplex loci. At such loci, there are no effects of preferential pairing, and so the option add_dr = TRUE allows for the effects of double reduction at simplex loci. The relevant parameter here is beta. The first three gamete frequencies at simplex loci are c(0.5 + beta, 0.5 - 2 * beta, beta), and the rest are 0. The upper bound on beta for two different models are given by beta_bounds().

Author(s)

David Gerard

References

• Gerard, D. (2023). Double reduction estimation and equilibrium tests in natural autopolyploid populations. Biometrics, 79(3), 2143-2156. doi:10.1111/biom.13722

• Gerard, D., Ferrão, L. F. V., Garcia, A. A. F., & Stephens, M. (2018). Genotyping polyploids from messy sequencing data. Genetics, 210(3), 789-807. doi:10.1534/genetics.118.301468

• Huang, K., Wang, T., Dunn, D. W., Zhang, P., Cao, X., Liu, R., & Li, B. (2019). Genotypic frequencies at equilibrium for polysomic inheritance under double-reduction. G3: Genes, Genomes, Genetics, 9(5), 1693-1706. doi:10.1534/g3.119.400132

Examples

## Various duplex models
gamfreq(g = 2, ploidy = 4, gamma = c(0, 1), type = "mix")
gamfreq(g = 2, ploidy = 4, gamma = c(1, 0), type = "mix")
gamfreq(g = 2, ploidy = 4, gamma = c(0.5, 0.5), type = "mix")
gamfreq(g = 2, ploidy = 4, alpha = 0, type = "polysomic")
gamfreq(g = 2, ploidy = 4, alpha = 1/6, type = "polysomic")

## Various simplex models
gamfreq(g = 1, ploidy = 4, beta = 1/24, gamma = 1, type = "mix", add_dr = TRUE)
gamfreq(g = 1, ploidy = 4, alpha = 1/6, type = "polysomic")
gamfreq(g = 1, ploidy = 4, gamma = 1, type = "mix", add_dr = FALSE)
gamfreq(g = 1, ploidy = 4, alpha = 0, type = "polysomic")

Converts genotype counts to genotype vectors.

Description

Converts genotype counts to genotype vectors.

Usage

gcount_to_gvec(gcount)

Arguments

Value

A vector of length sum(gcount), containing gcount[1] copies of 0, gcount[2] copies of 1, gcount[3] copies of 2, etc.

Author(s)

David Gerard

See Also

gvec_to_gcount()

Examples

gcount <- c(1, 2, 3, 0, 5)
gcount_to_gvec(gcount = gcount)

Genotype frequencies of an F1 population under a generalized model.

Description

Genotype frequencies of an F1 population under a generalized model.

Usage

gf_freq(
  p1_g,
  p1_ploidy,
  p1_gamma = NULL,
  p1_alpha = NULL,
  p1_beta = NULL,
  p1_type = c("mix", "polysomic"),
  p1_add_dr = TRUE,
  p2_g,
  p2_ploidy,
  p2_gamma = NULL,
  p2_alpha = NULL,
  p2_beta = NULL,
  p2_type = c("mix", "polysomic"),
  p2_add_dr = TRUE,
  pi = 0,
  nudge = sqrt(.Machine$double.eps)
)

Arguments

Value

A vector of genotype frequencies. Element i is the probability and offspring has genotype i - 1.

Author(s)

David Gerard

See Also

gamfreq().

Examples

q <- gf_freq(
  p1_g = 2,
  p1_ploidy = 4,
  p1_gamma = c(0.1, 0.9),
  p1_type = "mix",
  p2_g = 2,
  p2_ploidy = 6,
  p2_alpha = 0.1,
  p2_type = "polysomic",
  pi = 0.05)

Inverse function of gcount_to_gvec().

Description

Inverse function of gcount_to_gvec().

Usage

gvec_to_gcount(gvec, ploidy = 4)

Arguments

Value

A vector of counts. Element k is the number of individuals with genotype k-1.

Author(s)

David Gerard

See Also

gcount_to_gvec()

Examples

gvec <- c(1, 2, 3, 2, 3, 1, 4, 0, 1, 0, 0, 1, 0, 0)
gvec_to_gcount(gvec = gvec)

Tests if the two parameter model is valid

Description

There is a dependence on the bounds of two-parameter model. This function returns TRUE if those bounds are satisfied and FALSE otherwise.

Usage

is_valid_2(dr, pp, drbound = 1/6)

Arguments

Value

TRUE if the model is valid, FALSE otherwise.

Author(s)

David Gerard

Examples

TOL <- 1e-6
is_valid_2(dr = 1/6, pp = 1/3, drbound = 1/6) # Valid
is_valid_2(dr = 1/6, pp = 1/3 - TOL, drbound = 1/6) # Not valid
is_valid_2(dr = 1/6, pp = 1/3 + TOL, drbound = 1/6) # Not valid

Iterator over array

Description

Iterator over array

Usage

## S3 method for class 'array'
iter(obj, by = 1, recycle = FALSE, ...)

Arguments

Value

An iterator. This is an S3 arrayiter object, used in conjunction with nextElem to iterate over one index of an array.

Author(s)

David Gerard

See Also

nextElem.arrayiter()

Examples

glist <- multidog_to_g(
  mout = ufit,
  ploidy = 4,
  type = "all_gl",
  p1 = "indigocrisp",
  p2 = "sweetcrisp")
g <- iterators::iter(glist$g, by = 3)
head(iterators::nextElem(g))
head(iterators::nextElem(g))
head(iterators::nextElem(g))

Likelihood under three parameter model when genotypes are known

Description

This is under the two parameter model.

Usage

like_gknown_2(x, alpha, xi1, xi2, g1, g2, log_p = TRUE, pen = 0)

Arguments

Value

The (log) likelihood.

Author(s)

David Gerard

Examples

x <- c(1, 4, 5, 3, 1)
alpha <- 0.01
xi1 <- 0.5
xi2 <- 0.3
g1 <- 1
g2 <- 2
like_gknown_2(
  x = x,
  alpha = alpha,
  xi1 = xi1,
  xi2 = xi2,
  g1 = g1,
  g2 = g2)

Likelihood under three parameter model when genotypes are known

Description

This is under the three parameter model.

Usage

like_gknown_3(x, tau, beta, gamma1, gamma2, g1, g2, log_p = TRUE, pen = 0)

Arguments

Value

The (log) likelihood.

Author(s)

David Gerard

Examples

x <- c(1, 4, 5, 3, 1)
tau <- 0.5
beta <- 0.1
gamma1 <- 0.5
gamma2 <- 0.3
g1 <- 1
g2 <- 2
like_gknown_3(
  x = x,
  tau = tau,
  beta = beta,
  gamma1 = gamma1,
  gamma2 = gamma2,
  g1 = g1,
  g2 = g2)

Likelihood under three parameter model when using offspring genotypes likelihoods but parent genotypes are known.

Description

This is under the two parameter model.

Usage

like_glpknown_2(gl, alpha, xi1, xi2, g1, g2, log_p = TRUE)

Arguments

Value

The (log) likelihood of the two parameter model when using genotype likelihoods.

Author(s)

David Gerard

Examples

g1 <- 1
g2 <- 0
gl <- simf1gl(
  n = 25,
  g1 = g1,
  g2 = g2,
  rd = 10,
  alpha = 0,
  xi1 = 1/3,
  xi2 = 1/3)
like_glpknown_2(
  gl = gl,
  alpha = 0.01,
  xi1 = 0.5,
  xi2 = 0.3,
  g1 = g1,
  g2 = g2,
  log_p = TRUE)

Likelihood under three parameter model when using offspring genotypes likelihoods but parent genotypes are known.

Description

This is under the three parameter model.

Usage

like_glpknown_3(gl, tau, beta, gamma1, gamma2, g1, g2, log_p = TRUE)

Arguments

Value

The (log) likelihood of the three parameter model when using genotype likelihoods.

Author(s)

David Gerard

Examples

g1 <- 1
g2 <- 0
gl <- simf1gl(
  n = 25,
  g1 = g1,
  g2 = g2,
  rd = 10,
  alpha = 0,
  xi1 = 1/3,
  xi2 = 1/3)
like_glpknown_3(
  gl = gl,
  tau = 1/2,
  beta = 1/12,
  gamma1 = 1/3,
  gamma2 = 1/3,
  g1 = g1,
  g2 = g2,
  log_p = TRUE)

Objective function for em_li()

Description

Objective function for em_li()

Usage

llike_li(B, lpivec)

Arguments

Value

The log-likelihood of a vector of genotype frequencies when using genotype likelihoods. This is from Li (2011).

Author(s)

David Gerard

References

• Li, H. (2011). A statistical framework for SNP calling, mutation discovery, association mapping and population genetical parameter estimation from sequencing data. Bioinformatics, 27(21), 2987-2993. doi:10.1093/bioinformatics/btr509

Examples

# Simulate some data
set.seed(1)
gl <- simgl(nvec = c(3, 2, 4, 1, 2))
# Log-likelihood at given log-priors
prob <- c(0.1, 0.2, 0.4, 0.2, 0.1)
lprob <- log(prob)
llike_li(B = gl, lpivec = lprob)

Likelihood ratio test for segregation distortion with known genotypes

Description

This will run a likelihood ratio test using the genotypes of an F1 population of tetraploids for the null of Mendelian segregation (accounting for double reduction and preferential pairing) against the alternative of segregation distortion. This is when the genotypes are assumed known.

Usage

lrt_men_g4(
  x,
  g1,
  g2,
  drbound = 1/6,
  pp = TRUE,
  dr = TRUE,
  alpha = 0,
  xi1 = 1/3,
  xi2 = 1/3
)

Arguments

Value

A list with the following elements

statistic

The log-likelihood ratio test statistic.

df

The degrees of freedom.

p_value

The p-value.

alpha

The estimated double reduction rate.

xi1

The estimated preferential pairing parameter of parent 1.

xi2

The estimated preferential pairing parameter of parent 2.

Impossible genotypes

Some offspring genotype combinations are impossible given the parental genotypes. If these impossible genotypes combinations show up, we return a p-value of 0, a log-likelihood ratio statistic of Infinity, and missing values for all other return items. The impossible genotypes are:

g1 = 0 && g2 = 0

Only offspring genotypes of 0 are possible.

g1 = 4 && g2 = 4

Only offspring genotypes of 4 are possible.

g1 = 0 && g2 = 4 || g1 == 4 && g2 == 0

Only offspring genotypes of 2 are possible.

g1 = 0 && g2 %in% c(1, 2, 3) || g1 = %in% c(1, 2, 3) && g2 == 0

Only offspring genotypes of 0, 1, and 2 are possible.

g1 = 4 && g2 %in% c(1, 2, 3) || g1 = %in% c(1, 2, 3) && g2 == 4

Only offspring genotypes of 2, 3, and 4 are possible.

Unidentified parameters

When g1 = 2 or g2 = 2 (or both), the model is not identified and those estimates (alpha, xi1, and xi2) are meaningless. Do NOT interpret them.

The estimate of alpha (double reduction rate) IS identified as long as at least one parent is simplex, and no parent is duplex. However, the estimates of the double reduction rate have extremely high variance.

Author(s)

David Gerard

Examples

set.seed(100)
gf <- offspring_gf_2(alpha = 1/12, xi1 = 0.2, xi2 = 0.6, p1 = 1, p2 = 0)
x <- offspring_geno(gf = gf, n = 100)
lrt_men_g4(x = x, g1 = 1, g2 = 0)

Likelihood ratio test using genotype likelihoods.

Description

This will run a likelihood ratio test using the genotypes of an F1 population of tetraploids for the null of Mendelian segregation (accounting for double reduction and preferential pairing) against the alternative of segregation distortion. This is when genotype uncertainty is accounted for through genotype likelihoods.

Usage

lrt_men_gl4(
  gl,
  g1 = NULL,
  g2 = NULL,
  drbound = 1/6,
  pp = TRUE,
  dr = TRUE,
  alpha = 0,
  xi1 = 1/3,
  xi2 = 1/3
)

Arguments

Value

A list with the following elements

statistic

The log-likelihood ratio test statistic.

df

The degrees of freedom.

p_value

The p-value.

alpha

The estimated double reduction rate.

xi1

The estimated preferential pairing parameter of parent 1.

xi2

The estimated preferential pairing parameter of parent 2.

Unidentified parameters

When g1 = 2 or g2 = 2 (or both), the model is not identified and those estimates (alpha, xi1, and xi2) are meaningless. Do NOT interpret them.

The estimate of alpha (double reduction rate) IS identified as long as at least one parent is simplex, and no parent is duplex. However, the estimates of the double reduction rate have extremely high variance.

Author(s)

David Gerard

Examples

## null simulation
set.seed(1)
g1 <- 2
g2 <- 2
gl <- simf1gl(n = 25, g1 = g1, g2 = g2, alpha = 1/12, xi2 = 1/2)

## LRT when parent genotypes are known.
lrt_men_gl4(gl = gl, g1 = g1, g2 = g2)

## LRT when parent genotypes are not known
lrt_men_gl4(gl = gl)

## Alternative simulation
gl <- simgl(nvec = rep(5, 5))
lrt_men_gl4(gl = gl, g1 = g1, g2 = g2)

Parallelized likelihood ratio test for segregation distortion.

Description

Uses the future package to implement parallelization support for the likelihood ratio tests for segregation distortion. This function only works for tetraploids, and cannot account for outliers. For higher ploidies and more functionality, see seg_multi().

Usage

multi_lrt(
  g,
  p1,
  p2,
  drbound = 1/6,
  pp = TRUE,
  dr = TRUE,
  alpha = 0,
  xi1 = 1/3,
  xi2 = 1/3,
  nullprop = FALSE
)

Arguments

Value

A data frame with the following elements:

statistic

The likelihood ratio test statistic

p_value

The p-value of the likelihood ratio test.

df

The degrees of freedom of the test.

alpha

The MLE of the double reduction rate. Do not use for real work.

xi1

The MLE of the first parent's partial preferential pairing parameter. Do not use for real work.

xi2

The MLE of the second parent's partial preferential pairing parameter. Do not use for real work.

p1

(Estimate of) the first parent's genotype.

p2

(Estimate of) the second parent's genotype.

snp

The name of the SNP.

Parallel Computation

The multi_lrt() function supports parallel computing. It does so through the future package.

You first specify the evaluation plan with plan() from the future package. On a local machine, this is typically just future::plan(future::multisession, workers = nc) where nc is the number of workers you want. You can find the maximum number of possible workers with availableCores(). You then run multi_lrt(), then shut down the workers with future::plan(future::sequential).

Author(s)

David Gerard

See Also

• lrt_men_g4() Single locus LRT for segregation distortion when genotypes are known.

• lrt_men_gl4() Single locus LRT for segregation distortion when using genotype likelihoods.

Examples

## Assuming genotypes are known (typically a bad idea)
glist <- multidog_to_g(
  mout = ufit,
  ploidy = 4,
  type = "all_g",
  p1 = "indigocrisp",
  p2 = "sweetcrisp")
p1_1 <- glist$p1
p2_1 <- glist$p2
g_1 <- glist$g
multi_lrt(g = g_1, p1 = p1_1, p2 = p2_1)

## Using genotype likelihoods (typically a good idea)
glist <- multidog_to_g(
  mout = ufit,
  ploidy = 4,
  type = "all_gl",
  p1 = "indigocrisp",
  p2 = "sweetcrisp")
p1_2 <- glist$p1
p2_2 <- glist$p2
g_2 <- glist$g
multi_lrt(g = g_2, p1 = p1_2, p2 = p2_2)

## Offspring genotype likelihoods and parent genotypes known
multi_lrt(g = g_2, p1 = p1_1, p2 = p2_1)

## Offspring genotype likelihoods and no information on parent genotypes
multi_lrt(g = g_2, p1 = NULL, p2 = NULL)

## Parallel computing is supported through the future package
# future::plan(future::multisession, workers = 2)
# multi_lrt(g = g_2, p1 = p1_2, p2 = p2_2)
# future::plan(future::sequential)

Converts multidog output to a format usable for seg_multi() and multi_lrt()

Description

Converts multidog output to a format usable for seg_multi() and multi_lrt()

Usage

multidog_to_g(
  mout,
  ploidy,
  type = c("off_gl", "all_gl", "off_g", "all_g"),
  p1 = NULL,
  p2 = NULL
)

Arguments

Value

A list with the following elements

g

Either a matrix of counts, where the columns index the genotype and the rows index the loci (type = "all_g" or type = "off_g"). Or an array of genotype (natural) log-likelihoods where the rows index the loci, the columns index the individuals, and the slices index the genotypes (type = "all_gl" or type = "off_gl").

p1

Either a vector of known parental genotypes (type = "off_gl", type = "all_g" or type = "off_g"). Or a matrix of genotype (natural) log-likelihoods where the rows index the loci and the columns index the genotypes (type = "all_gl").

p2

Either a vector of known parental genotypes (type = "off_gl", type = "all_g" or type = "off_g"). Or a matrix of genotype (natural) log-likelihoods where the rows index the loci and the columns index the genotypes (type = "all_gl"). This will be NULL if you (i) used "s1" or "s1pp" models in updog and used either type = "off_g" or type = "off_gl" or (ii) used type = "all_g" or type = "all_gl" and only specified p1 but not p2.

Author(s)

David Gerard

Examples

multidog_to_g(
  mout = ufit,
  ploidy = 4,
  type = "all_g",
  p1 = "indigocrisp",
  p2 = "sweetcrisp")
multidog_to_g(
  mout = ufit,
  ploidy = 4,
  type = "all_gl",
  p1 = "indigocrisp",
  p2 = "sweetcrisp")
multidog_to_g(mout = ufit2, ploidy = 4, type = "off_g")
multidog_to_g(mout = ufit2, ploidy = 4, type = "off_gl")
multidog_to_g(mout = ufit3, ploidy = 4, type = "off_g")
multidog_to_g(mout = ufit3, ploidy = 4, type = "off_gl")

Number of mixture components

Description

The number of disomic inheritance patterns for a given ploidy and a given parental dosage. See also seg for the list of all possible disomic inheritance patterns for even ploidies up to 20.

Usage

n_pp_mix(g, ploidy)

Arguments

Value

The number of mixture components.

Examples

n_pp_mix(g = 0, ploidy = 4)
n_pp_mix(g = 1, ploidy = 4)
n_pp_mix(g = 2, ploidy = 4)
n_pp_mix(g = 3, ploidy = 4)
n_pp_mix(g = 4, ploidy = 4)

n_pp_mix(g = 0, ploidy = 6)
n_pp_mix(g = 1, ploidy = 6)
n_pp_mix(g = 2, ploidy = 6)
n_pp_mix(g = 3, ploidy = 6)
n_pp_mix(g = 4, ploidy = 6)
n_pp_mix(g = 5, ploidy = 6)
n_pp_mix(g = 6, ploidy = 6)

Next element in an array

Description

This is applied to an arrayiter object to obtain the next sub-array along one of the dimensions.

Usage

## S3 method for class 'arrayiter'
nextElem(obj, ...)

Arguments

Value

The next sub-array.

Author(s)

David Gerard

See Also

iter.array()

Examples

glist <- multidog_to_g(
  mout = ufit,
  ploidy = 4,
  type = "all_gl",
  p1 = "indigocrisp",
  p2 = "sweetcrisp")
g <- iterators::iter(glist$g, by = 3)
head(iterators::nextElem(g))
head(iterators::nextElem(g))
head(iterators::nextElem(g))

Simulates genotypes given genotype frequencies.

Description

Takes as input the offspring genotype frequencies and a sample size and returns simulated genotypes.

Usage

offspring_geno(gf, n)

Arguments

Value

Simulated genotypes

Author(s)

Mira Thakkar

Examples

set.seed(1)
gf <- offspring_gf_2(alpha = 1/6, xi1 = 1/3, xi2 = 1/3, p1 = 2, p2 = 3)
offspring_geno(gf = gf, n = 10)

Calculates offspring genotype frequencies under the two-parameter model.

Description

Calculates offspring genotype frequencies under the two-parameter model.

Usage

offspring_gf_2(alpha, xi1, xi2 = xi1, p1, p2)

Arguments

Value

Offspring genotype frequencies

Author(s)

Mira Thakkar

Examples

alpha <- 1/6
xi1 <- 1/3
xi2 <- 1/3
p1 <- 2
p2 <- 3
offspring_gf_2(alpha = alpha, xi1 = xi1, xi2 = xi2, p1 = p1, p2 = p2)

Calculates offspring genotype frequencies under the three-parameter model.

Description

Calculates offspring genotype frequencies under the three-parameter model.

Usage

offspring_gf_3(tau, beta, gamma1, gamma2 = gamma1, p1, p2)

Arguments

Value

Offspring genotype frequencies

Author(s)

David Gerard

Examples

offspring_gf_3(
  tau = 1/2,
  beta = 1/6,
  gamma1 = 1/3,
  gamma2 = 1/3,
  p1 = 1,
  p2 = 2)

Jointly tests for segregation distortion and number of incompatible genotypes

Description

This is experimental. I haven't tested it out in lots of scenarios yet.

Usage

otest_g(
  x,
  g1,
  g2,
  pbad = 0.03,
  drbound = 1/6,
  pp = TRUE,
  dr = TRUE,
  alpha = 0,
  xi1 = 1/3,
  xi2 = 1/3
)

Arguments

Details

Here, we test if the compatible genotypes are consistent with F1 populations and separately test that the number of incompatible genotypes isn't too large (less than 3 percent by default). This is the strategy the polymapR software uses. But we use a Bonferroni correction to combine these tests (minimum of two times the p-values), while they just multiply the p-values together. So our approach accounts for double reduction and preferential pairing, while also controlling the family-wise error rate.

Value

A list with the following elements

statistic

The log-likelihood ratio test statistic.

df

The degrees of freedom.

p_value

The Bonferroni corrected p-value.

p_lrt

The p-value of the LRT.

p_binom

The p-value of the one-sided binomial test.

alpha

The estimated double reduction rate.

xi1

The estimated preferential pairing parameter of parent 1.

xi2

The estimated preferential pairing parameter of parent 2.

Author(s)

David Gerard

Examples

# Run a test where genotypes 0, 1, and 2 are possible
x <- c(10, 10, 4, 0, 5)
otest_g(x = x, g1 = 1, g2 = 0)

# polymapR's multiplication and the Bonferroni differ
df <- expand.grid(p1 = seq(0, 1, length.out = 20), p2 = seq(0, 1, length.out = 20))
df$polymapr <- NA
df$bonferroni <- NA
for (i in seq_len(nrow(df))) {
  df$polymapr[[i]] <- df$p1[[i]] * df$p2[[i]]
  df$bonferroni[[i]] <- 2 * min(c(df$p1[[i]], df$p2[[i]], 0.5))
}
graphics::plot(df$polymapr, df$bonferroni)

Generate genotype likelihoods from offspring genotypes.

Description

Takes as input (i) the parent genotypes, (ii) the offspring genotype frequency, (iii) sequencing error rate, (iv) read depth, (v) bias, and (vi) overdispersion. It returns genotype likelihoods.

Usage

po_gl(
  genovec,
  ploidy,
  p1_geno = NULL,
  p2_geno = NULL,
  rd = 10,
  seq = 0.01,
  bias = 1,
  od = 0.01
)

Arguments

Value

Genotype likelihoods

Author(s)

Mira Thakkar

Examples

set.seed(1)
po_gl(genovec = c(1, 2, 1, 1, 3), p1_geno = 2, p2_geno = 2, ploidy = 4)

Run segregation distortion tests as implemented in the polymapR package.

Description

The polymapR package tests for segregation distortion by iterating through all possible forms of disomic or polysomic inheritance from either parent, tests for concordance of the offspring genotypes using a chi-squared test, and returns the largest p-value. It sometimes chooses a different p-value based on other heuristics. They also sometimes return NA. When type = "segtest", we only look at patterns of the given parent genotypes, choosing the largest p-value. When type = "polymapR", we return what they use via their heuristics.

Usage

polymapr_test(x, g1 = NULL, g2 = NULL, type = c("segtest", "polymapR"))

Arguments

Value

A list with the following elements:

p_value

The p-value of the test.

bestfit

The genotype frequencies of the best fit model.

frq_invalid

The frequency of invalid genotypes.

p_invalid

The p-value of the invalid proportion.

Author(s)

David Gerard

See Also

checkF1().

Examples

g1 <- 0
g2 <- 1
x <- c(4, 16, 0, 0, 0)
polymapr_test(x = x, g1 = g1, g2 = g2, type = "segtest")
polymapr_test(x = x, g1 = g1, g2 = g2, type = "polymapR")

Tetraploid gamete frequencies of gametes when one parent's genotype is known

Description

This is under the two parameter model.

Usage

pvec_tet_2(alpha, xi, ell)

Arguments

Value

The gamete genotype frequencies

Author(s)

Mira Thakkar and David Gerard

Examples

alpha <- 1/6
xi <- 1/3
pvec_tet_2(alpha = alpha, xi = xi, ell = 0)
pvec_tet_2(alpha = alpha, xi = xi, ell = 1)
pvec_tet_2(alpha = alpha, xi = xi, ell = 2)
pvec_tet_2(alpha = alpha, xi = xi, ell = 3)
pvec_tet_2(alpha = alpha, xi = xi, ell = 4)

Tetraploid gamete frequencies of gametes when one parent's genotype is known

Description

This is under the three parameter model.

Usage

pvec_tet_3(tau, beta, gamma, ell)

Arguments

Value

The gamete genotype frequencies

Author(s)

David Gerard

Examples

pvec_tet_3(tau = 0.5, beta = 0.1, gamma = 0.5, ell = 2)

Disomic and polysomic segregation patterns

Description

Gamete frequencies for all possible disomic and polysomic segregation patterns for even ploidies 2 through 20. If you need higher ploidy levels, let me know and I'll update it (it's very easy).

Usage

seg

Format

A data frame with the following columns

ploidy

The ploidy of the parent.

g

The genotype of the parent.

m

The pairing configuration given disomic inheritance. See Gerard et al (2018).

p

The gamete frequencies. Element p[[i]] is the probability a gamete will have dosage i-1.

mode

Whether the inheritance pattern that leads to these gamete frequencies is "disomic", "polysomic", or "both".

Author(s)

David Gerard

References

• Gerard, D., Ferrão, L. F. V., Garcia, A. A. F., & Stephens, M. (2018). Genotyping polyploids from messy sequencing data. Genetics, 210(3), 789-807. doi:10.1534/genetics.118.301468

Test for segregation distortion in a polyploid F1 population.

Description

Provides tests for segregation distortion for an F1 population of polyploids under various models of meiosis. You can use this test for autopolyploids that exhibit full polysomic inheritance, allopolyploids that exhibit full disomic inheritance, or segmental allopolyploids that exhibit partial preferential pairing. Double reduction is (optionally) fully accounted for in tetraploids, and (optionally) partially accounted for (only at simplex loci) for higher ploidies. Some maximum proportion of outliers can be specified (default at 3%), and so this method can accommodate moderate levels of double reduction at non-simplex loci. Offspring genotypes can either be known, or genotype uncertainty can be represented through genotype likelihoods. Parent data may or may not be provided, at your option. Parents can have different (even) ploidies, at your option. Details of the methods may be found in Gerard et al. (2025).

Usage

seg_lrt(
  x,
  p1_ploidy,
  p2_ploidy = p1_ploidy,
  p1 = NULL,
  p2 = NULL,
  model = c("seg", "auto", "auto_dr", "allo", "allo_pp", "auto_allo"),
  outlier = TRUE,
  ret_out = FALSE,
  ob = 0.03,
  db = c("ces", "prcs"),
  ntry = 3,
  opt = c("bobyqa", "L-BFGS-B"),
  optg = c("NLOPT_GN_MLSL_LDS", "NLOPT_GN_ESCH", "NLOPT_GN_CRS2_LM", "NLOPT_GN_ISRES"),
  df_tol = 0.001,
  chisq = FALSE
)

Arguments

Value

A list with some or all of the following elements

stat

The test statistic.

df

The degrees of freedom of the test.

p_value

The p-value of the test.

null_bic

The null model's BIC.

outprob

Outlier probabilities. Only returned in ret_out = TRUE.

• If using genotype counts, element i is the probability that an individual with genotype i-1 is an outlier. So the return vector has length ploidy plus 1.

• If using genotype log-likelihoods, element i is the probability that individual i is an outlier. So the return vector has the same length as the number of individuals.

These outlier probabilities are only valid if the null of no segregation is true.

null

A list with estimates and information on the null model.

l0_pp

Maximized likelihood under the null plus the parent log-likelihoods.

l0

Maximized likelihood under using estimated parent genotypes are known parent genotypes.

q0

Estimated genotype frequencies under the null.

df0

Estimated number of parameters under the null.

gam

A list of three lists with estimates of the model parameters. The third list contains the elements outlier (which is TRUE if outliers were modeled) and pi (the estimated outlier proportion). The first two lists contain information on each parent with the following elements:

ploidy

The ploidy of the parent.

g

The (estimated) genotype of the parent.

alpha

The estimated double reduction rate(s). alpha[i] is the estimated probability that a gamete has i copies of identical by double reduction alleles.

beta

Double reduction's effect on simplex loci when type = "mix" and add_dr = TRUE.

gamma

The mixing proportions for the pairing configurations. The order is the same as in seg.

type

Either "mix" or "polysomic"

add_dr

Did we model double reduction at simplex loci when using type = "mix" (TRUE) or not (FALSE)?

alt

A list with estimates and information on the alternative model.

l1

The maximized likelihood under the alternative.

q1

The estimated genotype frequencies under the alternative.

df1

The estimated number of parameters under the alternative.

Null Model

The gamete frequencies under the null model can be calculated via gamfreq(). The genotype frequencies, which are just a discrete linear convolution (convolve()) of the gamete frequencies, can be calculated via gf_freq().

The null model's gamete frequencies for true autopolyploids (model = "auto") or true allopolyploids (model = "allo") are given in the seg data frame that comes with this package. I only made that data frame go up to ploidy 20, but let me know if you need it for higher ploidies.

The polyRAD folks test for full autopolyploid and full allopolyploid, so I included that as an option (model = "auto_allo").

We can account for arbitrary levels of double reduction in autopolyploids (model = "auto_dr") using the gamete frequencies from Huang et al (2019).

The null model for segmental allopolyploids (model = "allo_pp") is the mixture model of the possible allopolyploid gamete frequencies. The autopolyploid model (without double reduction) is a subset of this mixture model.

In the above mixture model, we can account for double reduction for simplex loci (model = "seg") by just slightly reducing the number of simplex gametes and increasing the number of duplex and nullplex gametes. That is, the frequencies for (nullplex, simplex, duplex) gametes go from (0.5, 0.5, 0) to (0.5 + b, 0.5 - 2 * b, b).

model = "seg" is the most general, so it is the default. But you should use other models if you have more information on your species. E.g. if you know you have an autopolyploid, use either model = "auto" or model = "auto_dr".

Unidentified Parameters

Do NOT interpret the estimated parameters in the null$gam list. These parameters are weakly identified (I had to do some fancy spectral methods to account for this in the null distribution of the tests). Even though they are technically identified, you would need a massive data set to be able to estimate them accurately.

Author(s)

David Gerard

References

• Byrd, R. H., Lu, P., Nocedal, J., & Zhu, C. (1995). A limited memory algorithm for bound constrained optimization. SIAM Journal on scientific computing, 16(5), 1190-1208. doi:10.1137/0916069

• da Silva Santos, C. H., Goncalves, M. S., & Hernandez-Figueroa, H. E. (2010). Designing novel photonic devices by bio-inspired computing. IEEE Photonics Technology Letters, 22(15), 1177-1179. doi:10.1109/LPT.2010.2051222

• Gerard, D, Ambrosano, GB, Pereira, GdS, & Garcia, AAF (2025). Tests for segregation distortion in higher ploidy F1 populations. bioRxiv, p. 1-20. doi:10.1101/2025.06.23.661114

• Huang, K., Wang, T., Dunn, D. W., Zhang, P., Cao, X., Liu, R., & Li, B. (2019). Genotypic frequencies at equilibrium for polysomic inheritance under double-reduction. G3: Genes, Genomes, Genetics, 9(5), 1693-1706. doi:10.1534/g3.119.400132

• Johnson S (2008). The NLopt nonlinear-optimization package. https://github.com/stevengj/nlopt.

• Kaelo, P., & Ali, M. M. (2006). Some variants of the controlled random search algorithm for global optimization. Journal of optimization theory and applications, 130, 253-264. doi:10.1007/s10957-006-9101-0

• Kucherenko, S., & Sytsko, Y. (2005). Application of deterministic low-discrepancy sequences in global optimization. Computational Optimization and Applications, 30, 297-318. doi:10.1007/s10589-005-4615-1

• Powell, M. J. D. (2009), The BOBYQA algorithm for bound constrained optimization without derivatives, Report No. DAMTP 2009/NA06, Centre for Mathematical Sciences, University of Cambridge, UK.

• Runarsson, T. P., & Yao, X. (2005). Search biases in constrained evolutionary optimization. IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews), 35(2), 233-243. doi:10.1109/TSMCC.2004.841906

Examples

set.seed(1)
p1_ploidy <- 4
p1 <- 1
p2_ploidy <- 8
p2 <- 4
q <- gf_freq(
  p1_g = p1,
  p1_ploidy = p1_ploidy,
  p1_gamma = 1,
  p1_type = "mix",
  p2_g = p2,
  p2_ploidy = p2_ploidy,
  p2_gamma= c(0.2, 0.2, 0.6),
  p2_type = "mix",
  pi = 0.01)
nvec <- c(stats::rmultinom(n = 1, size = 200, prob = q))
gl <- simgl(nvec = nvec)
seg_lrt(x = nvec, p1_ploidy = p1_ploidy, p2_ploidy = p2_ploidy, p1 = p1, p2 = p2)$p_value
seg_lrt(x = gl, p1_ploidy = p1_ploidy, p2_ploidy = p2_ploidy, p1 = p1, p2 = p2)$p_value

Parallelized likelihood ratio test for segregation distortion for arbitrary (even) ploidies.

Description

Uses the future package to implement parallelization support for the likelihood ratio tests for segregation distortion. Details of this test are provided in the seg_lrt() function's documentation. See Gerard et al. (2025) for details of the methods.

Usage

seg_multi(
  g,
  p1_ploidy,
  p2_ploidy = p1_ploidy,
  p1 = NULL,
  p2 = NULL,
  model = c("seg", "auto", "auto_dr", "allo", "allo_pp", "auto_allo"),
  outlier = TRUE,
  ret_out = FALSE,
  ob = 0.03,
  db = c("ces", "prcs"),
  ntry = 3,
  df_tol = 0.001
)

Arguments

Value

A data frame with the following elements:

statistic

The likelihood ratio test statistic

p_value

The p-value of the likelihood ratio test.

df

The (estimated) degrees of freedom of the test.

null_bic

The BIC of the null model (no segregation distortion).

df0

The (estimated) number of parameters under null.

df1

The (estimated) number of parameters under the alternative.

p1

The (estimated) genotype of parent 1.

p2

The (estimated) genotype of parent 2.

q0

The MLE of the genotype frequencies under the null.

q1

The MLE of the genotype frequencies under the alternative.

outprob

Outlier probabilities. Only returned in ret_out = TRUE.

• If using genotype counts, element i is the probability that an individual with genotype i-1 is an outlier. So the return vector has length ploidy plus 1.

• If using genotype log-likelihoods, element i is the probability that individual i is an outlier. So the return vector has the same length as the number of individuals.

These outlier probabilities are only valid if the null of no segregation is true.

Note that since this data frame contains the list-columns q0 and q1, you cannot use write.csv() to save it. You have to either remove those columns first or use something like saveRDS()

Parallel Computation

The seg_multi() function supports parallel computing. It does so through the future package.

You first specify the evaluation plan with plan() from the future package. On a local machine, this is typically just future::plan(future::multisession, workers = nc) where nc is the number of workers you want. You can find the maximum number of possible workers with availableCores(). You then run seg_multi(), then shut down the workers with future::plan(future::sequential). The pseudo code is

  future::plan(future::multisession, workers = nc)
  seg_multi()
  future::plan(future::sequential)

Null Model

The gamete frequencies under the null model can be calculated via gamfreq(). The genotype frequencies, which are just a discrete linear convolution (convolve()) of the gamete frequencies, can be calculated via gf_freq().

The null model's gamete frequencies for true autopolyploids (model = "auto") or true allopolyploids (model = "allo") are given in the seg data frame that comes with this package. I only made that data frame go up to ploidy 20, but let me know if you need it for higher ploidies.

The polyRAD folks test for full autopolyploid and full allopolyploid, so I included that as an option (model = "auto_allo").

We can account for arbitrary levels of double reduction in autopolyploids (model = "auto_dr") using the gamete frequencies from Huang et al (2019).

The null model for segmental allopolyploids (model = "allo_pp") is the mixture model of the possible allopolyploid gamete frequencies. The autopolyploid model (without double reduction) is a subset of this mixture model.

In the above mixture model, we can account for double reduction for simplex loci (model = "seg") by just slightly reducing the number of simplex gametes and increasing the number of duplex and nullplex gametes. That is, the frequencies for (nullplex, simplex, duplex) gametes go from (0.5, 0.5, 0) to (0.5 + b, 0.5 - 2 * b, b).

model = "seg" is the most general, so it is the default. But you should use other models if you have more information on your species. E.g. if you know you have an autopolyploid, use either model = "auto" or model = "auto_dr".

Unidentified Parameters

Do NOT interpret the estimated parameters in the null$gam list. These parameters are weakly identified (I had to do some fancy spectral methods to account for this in the null distribution of the tests). Even though they are technically identified, you would need a massive data set to be able to estimate them accurately.

Author(s)

David Gerard

References

• Gerard, D, Ambrosano, GB, Pereira, GdS, & Garcia, AAF (2025). Tests for segregation distortion in higher ploidy F1 populations. bioRxiv, p. 1-20. doi:10.1101/2025.06.23.661114

See Also

• seg_lrt() Single locus LRT for segregation distortion.

• gamfreq() Gamete frequencies under various models of meiosis

• gf_freq() F1 genotype frequencies under various models of meiosis.

• multidog_to_g() Converts the output of updog::multidog() into something that you can input into seg_multi().

Examples

## Assuming genotypes are known (typically a bad idea)
glist <- multidog_to_g(
  mout = ufit,
  ploidy = 4,
  type = "all_g",
  p1 = "indigocrisp",
  p2 = "sweetcrisp")
p1_1 <- glist$p1
p2_1 <- glist$p2
g_1 <- glist$g
s1 <- seg_multi(
  g = g_1,
  p1_ploidy = 4,
  p2_ploidy = 4,
  p1 = p1_1,
  p2 = p2_1)
s1[, c("snp", "p_value")]

## Put NULL if you have absolutely no information on the parents
s2 <- seg_multi(g = g_1, p1_ploidy = 4, p2_ploidy = 4, p1 = NULL, p2 = NULL)
s2[, c("snp", "p_value")]

## Using genotype likelihoods (typically a good idea)
## Also demonstrate parallelization through future package.
glist <- multidog_to_g(
  mout = ufit,
  ploidy = 4,
  type = "all_gl",
  p1 = "indigocrisp",
  p2 = "sweetcrisp")
p1_2 <- glist$p1
p2_2 <- glist$p2
g_2 <- glist$g

# future::plan(future::multisession, workers = 2)
# s3 <- seg_multi(
#   g = g_2,
#   p1_ploidy = 4,
#   p2_ploidy = 4,
#   p1 = p1_2,
#   p2 = p2_2,
#   ret_out = TRUE)
# future::plan(future::sequential)
# s3[, c("snp", "p_value")]

## Outlier probabilities are returned if `ret_out = TRUE`
# graphics::plot(s3$outprob[[6]], ylim = c(0, 1))

Simulate genotype counts from F1 individuals

Description

Simulate genotype counts from F1 individuals

Usage

simf1g(n, g1, g2, alpha = 0, xi1 = 1/3, xi2 = 1/3)

Arguments

Value

A vector of counts, where element i is the number of simulated individuals with genotype i-1.

Author(s)

David Gerard

Examples

set.seed(1)
simf1g(n = 10, g1 = 1, g2 = 2)

Simulate genotype likelihoods of F1 individuals.

Description

Simulate genotype likelihoods of F1 individuals.

Usage

simf1gl(n, g1, g2, rd = 10, alpha = 0, xi1 = 1/3, xi2 = 1/3)

Arguments

Value

The matrix of offspring genotype log-likelihoods.

Author(s)

David Gerard

Examples

set.seed(1)
simf1gl(n = 10, g1 = 1, g2 = 2)

Simulate genotype (log) likelihoods from genotype counts

Description

Provide a vector of genotype counts and this will return a matrix of genotype log-likelihoods.

Usage

simgl(nvec, rd = 10, seq = 0.01, bias = 1, od = 0.01)

Arguments

Value

A matrix of genotype log-likelihoods. The rows index the individuals and the columns index the genotypes. This is natural log (base e).

Author(s)

David Gerard

Examples

set.seed(1)
simgl(nvec = c(1, 2, 1, 1, 3))

Convert from three parameters to two parameters

Description

Convert from three parameters to two parameters

Usage

three_to_two(tau, beta, gamma)

Arguments

Value

A vector of length two. The first is the double reduction rate (alpha), and the second is the preferential pairing parameter (xi).

Author(s)

David Gerard

Examples

three_to_two(tau = 0.1, beta = 1/6, gamma = 1/4)

Genotype data from Cappai et al. (2020)

Description

A subset of data from Cappai et al. (2020), fit using multidog(). This just contains a random set of 10 loci.

Usage

ufit

ufit2

ufit3

Format

An object of type multidog output from multidog().

ufit

Uses the model = "norm" option.

ufit2

Uses the model = "f1pp" option.

ufit3

Uses the model = "f1" option.

An object of class multidog of length 2.

An object of class multidog of length 2.

Source

doi:10.5281/zenodo.13715703

References

• Cappai, F., Amadeu, R. R., Benevenuto, J., Cullen, R., Garcia, A., Grossman, A., Ferrão, L., & Munoz, P. (2020). High-resolution linkage map and QTL analyses of fruit firmness in autotetraploid blueberry. Frontiers in plant science, 11, 562171. doi:10.3389/fpls.2020.562171.