lrt_men_g4: 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
)

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.

Arguments

x: A vector of genotype counts. x[i] is the number of offspring with genotype i-1.
g1: The genotype of parent 1.
g2: The genotype of parent 2.
drbound: The maximum rate of double reduction. A default of 1/6 is provided, which is the rate under the complete equational segregation model of meiosis.
pp: A logical. Should we account for preferential pairing (TRUE) or not (FALSE)?
dr: A logical. Should we account for double reduction (TRUE) or not (FALSE)?
alpha: If dr = FALSE, this is the known rate of double reduction.
xi1: If pp = FALSE, this is the known preferential pairing parameter of parent 1.
xi2: If pp = FALSE, this is the known 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

David Gerard

Examples

Run this code

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)

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