IBDtriangle: IBD triangle plot

In forrel: Forensic Pedigree Analysis and Relatedness Inference

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"),
  kinshipLines = numeric(),
  shading = "lightgray",
  pch = 16,
  cex_points = 1.2,
  cex_text = 1.2,
  axes = FALSE,
  xlim = c(0, 1),
  ylim = c(0, 1),
  xlab = expression(kappa[0]),
  ylab = expression(kappa[2]),
  cex_lab = cex_text,
  mar = c(3.1, 3.1, 1, 1),
  xpd = TRUE,
  keep.par = TRUE
)

Arguments

relationships	A character vector indicating relationships points to be included in the plot. See Details for a list of valid entries.
kinshipLines	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 number controlling the symbol size for the relationship points.
cex_text	A number controlling the font size for the relationship labels.
axes	A logical: Draw surrounding axis box?
xlim, ylim, mar, xpd	Graphical parameters; see par().
xlab, ylab	Axis labels
cex_lab	A number controlling the font size for the axis labels.
keep.par	A logical. If TRUE, the graphical parameters are not reset after plotting, which may be useful for adding additional annotation.

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 by Thompson (1976), points in the subset of the triangle defined by 4\kappa_0\kappa_2 > \kappa_1^2 are unattainable for pairwise relationships. By default this region is shaded in light grey colour, but this can be modified with the shading argument.

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 kinshipLines argument, the corresponding contour lines are shown as dashed lines in the triangle plot.

The following abbreviations are valid entries in the relationships argument:

• UN = unrelated

• PO = parent/offspring

• MZ = monozygotic twins

• S = full siblings

• H,U,G = half sibling/avuncular (uncle)/grandparent

• FC = first cousins

• SC = second cousins

• DFC = double first cousins

• Q = quadruple first half cousins

Value

None

Author(s)

Magnus Dehli Vigeland

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.

See Also

ibdEstimate()

Examples

opar = par(no.readonly = TRUE) # store graphical parameters

IBDtriangle()
IBDtriangle(kinshipLines = c(0.25, 0.125), shading = NULL, cex_text = 0.8)

par(opar) # reset graphical parameters

forrel documentation built on Nov. 19, 2023, 5:14 p.m.