IBDtriangle: IBD triangle plot

Description

The IBD triangle is typically used to visualize the pairwise relatedness of non-inbred individuals. Various annotations are available, including points marking the most common relationships, contour lines for the kinship coefficients, and shading of the unattainable region.

Usage

IBDtriangle(
  relationships = c("UN", "PO", "MZ", "S", "H,U,G", "FC", "SC", "DFC", "Q"),
  kinship.lines = numeric(),
  shading = "lightgray",
  pch = 16,
  cex_points = 1.2,
  cex_text = 1,
  axes = FALSE
)

Arguments

relationships

A character vector indicating relationships points to be included in the plot. By default all of the following are included: UN=unrelated; PO=parent/offspring; MZ=monozygotic twins; S=full siblings; H=half siblings; U=uncle/niece and similar; G=grandparent/grandchild; FC=first cousins; SC=second cousins; DFC=double first cousins; Q=quadruple first half cousins.

kinship.lines

A numeric vector. (See Details.)

shading

The shading colour for the unattainable region.

pch

Symbol used for the relationship points (see par).

cex_points

A single numeric controlling the symbol size for the relationship points.

cex_text

A single numeric controlling the font size for the relationship labels.

axes

Draw surrounding axis box?

Details

For any pair of non-inbred individuals A and B, their genetic relationship can be summarized by the IBD coefficients $(\kappa_0, \kappa_1, \kappa_2)$, where $$\kappa_i = P(A and B share i alleles IBD at random autosomal locus).$$ Since $\kappa_0+\kappa_1+\kappa_2=1$, any relationship corresponds to a point in the triangle in the $(\kappa_0, \kappa_2)$-plane defined by $\kappa_0 \ge 0, \kappa_2 \ge 0, \kappa_0 + \kappa_2 \le 1$. The choice of $\kappa_0$ and $\kappa_2$ as the axis variables is done for reasons of symmetry and is not significant (other authors have used different views of the triangle).

As shown in (Thompson, 1976) points in the subset of the triangle defined by $4\kappa_0\kappa_2 > \kappa_1^2$ is unattainable for pairwise relationships. By default this region in shaded in a 'lightgray' colour.

The IBD coefficients are linearly related to the kinship coefficient $\phi$ by the formula $$\phi = 0.25\kappa_1 + 0.5\kappa_2.$$ By indicating values for $\phi$ in the kinship.lines argument, the corresponding contour lines are shown as dashed lines in the triangle plot.

References

E. A. Thompson (1975). The estimation of pairwise relationships. Annals of Human Genetics 39.

E. A. Thompson (1976). A restriction on the space of genetic relationships. Annals of Human Genetics 40.

Examples

Run this code

# NOT RUN {
IBDtriangle()
IBDtriangle(kinship=c(0.25, 0.125), shading=NULL, cex_text=0.8)

# }