gl.grm.network: Represents a genomic relationship matrix (GRM) as a network

In dartR.captive: Analysing 'SNP' Data to Support Captive Breeding

Represents a genomic relationship matrix (GRM) as a network

Description

This script takes a G matrix generated by gl.grm and represents the relationship among the specimens as a network diagram. In order to use this script, a decision is required on a threshold for relatedness to be represented as link in the network, and on the layout used to create the diagram.

Usage

gl.grm.network(
  G,
  x,
  method = "fr",
  node.size = 8,
  node.label = TRUE,
  node.label.size = 2,
  node.label.color = "black",
  node.shape = NULL,
  link.color = NULL,
  link.size = 2,
  relatedness_factor = 0.125,
  title = "Network based on a genomic relationship matrix",
  palette_discrete = gl.select.colors(x, library = "brewer", palette = "PuOr", ncolors =
    nPop(x), verbose = 0),
  plot.dir = NULL,
  plot.file = NULL,
  verbose = NULL
)

Arguments

G	A genomic relationship matrix (GRM) generated by gl.grm [required].
x	A genlight object from which the G matrix was generated [required].
method	One of 'fr', 'kk', 'gh' or 'mds' [default 'fr'].
node.size	Size of the symbols for the network nodes [default 8].
node.label	TRUE to display node labels [default TRUE].
node.label.size	Size of the node labels [default 3].
node.label.color	Color of the text of the node labels [default 'black'].
node.shape	Optionally provide a vector of nPop shapes (run gl.select.shapes() for shape options) [default NULL].
link.color	Colors for links [default gl.select.colors].
link.size	Size of the links [default 2].
relatedness_factor	Factor of relatedness [default 0.125].
title	Title for the plot [default 'Network based on genomic relationship matrix'].
palette_discrete	A discrete set of colors with as many colors as there are populations in the dataset [default NULL].
plot.dir	Directory to save the plot RDS files [default as specified by the global working directory or tempdir()]
plot.file	Name for the RDS binary file to save (base name only, exclude extension) [default NULL]
verbose	Verbosity: 0, silent or fatal errors; 1, begin and end; 2, progress log ; 3, progress and results summary; 5, full report [default 2 or as specified using gl.set.verbosity].

Details

The gl.grm.network function creates a network diagram that represents genetic relationships among individuals in a dataset using a Genomic Relationship Matrix (GRM). The GRM is generated by the gl.grm function, which utilizes the A.mat function from the rrBLUP package. This method follows the approach developed by Endelman and Jannink (2012).

The GRM quantifies the additive genetic relationships between individuals based on genome-wide SNP data. It provides an estimate of the actual genetic similarity — known as realized relatedness— between individuals by measuring how much of their genome they share identical by descent (IBD).

Two alleles are Identical by State (IBS) if they are the same in state, regardless of whether they come from a common ancestor. Two alleles are Identical by Descent (IBD) if they are inherited from a common ancestor. While IBS does not necessarily imply IBD, using high-density SNP data improves the estimation of IBD probabilities from IBS measures.

The off-Diagonal elements of the GRM represent twice the kinship coefficient between pairs of individuals. The kinship coefficient is the probability that a randomly selected allele from each individual at the same locus is IBD. Diagonal elements represent one plus twice the inbreeding coefficient of each individual. The inbreeding coefficient is the probability that both alleles at a random locus within an individual are IBD.

Choosing meaningful thresholds to represent relationships between individuals can be challenging because kinship and inbreeding coefficients re relative measures. To standardize the GRM and facilitate interpretation, the function adjusts the matrix through the following steps:

1. Centering Inbreeding Coefficients: Subtract 1 from the mean of the diagonal elements to calculate the average inbreeding coefficient. This centers the inbreeding coefficients around zero, providing a reference point relative to the population's average inbreeding level.

2. Calculating Kinship Coefficients: Divide the off-diagonal elements by 2 to obtain the kinship coefficients. This conversion reflects the probability of sharing alleles IBD between pairs of individuals.

3. Centering Kinship Coefficients: Subtract the adjusted mean inbreeding coefficient (from step 1) from each kinship coefficient (from step 2). This centers the kinship coefficients relative to the population average, allowing for meaningful comparisons.

This adjustment method aligns with the approach used by Goudet et al. (2018), enabling the relationships to be interpreted in the context of the overall genetic relatedness within the population.

Below is a table modified from Speed & Balding (2015) showing kinship values, and their confidence intervals (CI), for different relationships that could be used to guide the choosing of the relatedness threshold in the function.

|Relationship|Kinship|95 |Identical twins/clones/same individual | 0.5 | - |

|Sibling/Parent-Offspring | 0.25 | (0.204, 0.296)|

|Half-sibling | 0.125 | (0.092, 0.158)|

|First cousin | 0.062 | (0.038, 0.089)|

|Half-cousin | 0.031 | (0.012, 0.055)|

|Second cousin | 0.016 | (0.004, 0.031)|

|Half-second cousin | 0.008 | (0.001, 0.020)|

|Third cousin | 0.004 | (0.000, 0.012)|

|Unrelated | 0 | - |

Four layout options are implemented in this function:

• 'fr' Fruchterman-Reingold layout layout_with_fr (package igraph)

• 'kk' Kamada-Kawai layout layout_with_kk (package igraph)

• 'gh' Graphopt layout layout_with_graphopt (package igraph)

• 'mds' Multidimensional scaling layout layout_with_mds (package igraph)

Value

A network plot showing relatedness between individuals

Author(s)

Custodian: Arthur Georges – Post to https://groups.google.com/d/forum/dartr

References

• Endelman, J. B. , Jannink, J.-L. (2012). Shrinkage estimation of the realized relationship matrix. G3: Genes, Genomics, Genetics 2, 1405.

• Goudet, J., Kay, T., & Weir, B. S. (2018). How to estimate kinship. Molecular Ecology, 27(20), 4121-4135.

• Speed, D., & Balding, D. J. (2015). Relatedness in the post-genomic era: is it still useful?. Nature Reviews Genetics, 16(1), 33-44.

See Also

gl.grm

Other inbreeding functions: gl.grm()

Examples

if (requireNamespace("igraph", quietly = TRUE) & requireNamespace("rrBLUP",
  quietly = TRUE
) & requireNamespace("fields", quietly = TRUE)) {
  t1 <- possums.gl
  # filtering on call rate
  t1 <- gl.filter.callrate(t1)
  t1 <- gl.subsample.loc(t1, n = 100)
  # relatedness matrix
  res <- gl.grm(t1, plotheatmap = FALSE)
  # relatedness network
  res2 <- gl.grm.network(res, t1, relatedness_factor = 0.125)
}

dartR.captive documentation built on April 3, 2025, 7:34 p.m.