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Gamete frequencies under a generalized model

Source: R/higher_freq.R
gamfreq.Rd

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

g

Parent genotype.

ploidy

Parent ploidy. Should be even, and between 2 and 20 (inclusive). Let me know if you need the ploidy to be higher. I can update the package really easily.

gamma

The mixture proportions for the pairing configurations. The proportions are in the same order the configurations in seg. See Gerard et al (2018) for details on pairing configurations.

alpha

The double reduction rate(s) (if using). Defaults to 0's.

beta

The double reduction adjustment for simplex markers if type = "mix" and add_dr = TRUE. Assumed to be 0 by default.

type

Either "mix", meaning a mixture model of pairing configurations, or "polysomic" for polysomic inheritance.

add_dr

A logical. If type = "polysomic", then the double double reduction rate ("alpha") will be used no matter the value of add_dr, so set alpha = 0 if you don't want it. But if type = "mix" then we will incorporate double reduction only in simplex markers (where it matters the most, and where preferential pairing does not operate).

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().

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

Author

David Gerard

Examples

## Various duplex models
gamfreq(g = 2, ploidy = 4, gamma = c(0, 1), type = "mix")
#> [1] 0 1 0
gamfreq(g = 2, ploidy = 4, gamma = c(1, 0), type = "mix")
#> [1] 0.25 0.50 0.25
gamfreq(g = 2, ploidy = 4, gamma = c(0.5, 0.5), type = "mix")
#> [1] 0.125 0.750 0.125
gamfreq(g = 2, ploidy = 4, alpha = 0, type = "polysomic")
#> [1] 0.1666667 0.6666667 0.1666667
gamfreq(g = 2, ploidy = 4, alpha = 1/6, type = "polysomic")
#> [1] 0.2222222 0.5555556 0.2222222

## Various simplex models
gamfreq(g = 1, ploidy = 4, beta = 1/24, gamma = 1, type = "mix", add_dr = TRUE)
#> [1] 0.54166667 0.41666667 0.04166667
gamfreq(g = 1, ploidy = 4, alpha = 1/6, type = "polysomic")
#> [1] 0.54166667 0.41666667 0.04166667
gamfreq(g = 1, ploidy = 4, gamma = 1, type = "mix", add_dr = FALSE)
#> [1] 0.5 0.5 0.0
gamfreq(g = 1, ploidy = 4, alpha = 0, type = "polysomic")
#> [1] 0.5 0.5 0.0