Estimates linkage disequilibrium (LD) decay along a chromosome (M. Malosetti & J.T.N.M. Thissen).

### Options

`PRINT` = string token |
What to print (`progress` ); default `*` |
---|---|

`PLOT` = string tokens |
What to plot (`ldmatrix` , `lddecay` ); default `ldde` |

`RELATIONSHIPMODEL` = string token |
What model to use to account for genetic relatedness (`eigenanalysis` , `subpopulations` , `null` ); default `eige` |

`SCORES` = pointer |
Provides the scores of significant principal components, obtained from an eigenvalue analysis |

`SUBPOPULATIONS` = factor |
Defines groupings of genotypes into subpopulations |

`CHRANALYSE` = scalar |
Defines which chromosome to analyse, using a level of the `CHROMOSOMES` factor |

`MAX%MISSING` = scalar |
Markers with more than the specified % of missing values will be excluded from the LD calculations; default 20 |

`MAXDISTANCE` = scalar |
Defines the maximum distance between markers to show in LD plots; default 30 |

`TITLE` = text |
General title for the plots |

`YTITLE` = text |
Title for the y-axis |

`XTITLE` = text |
Title for the x-axis |

### Parameters

`MKSCORES` = pointers |
Genotype codes for each marker; must be set |
---|---|

`CHROMOSOMES=` factors |
Linkage groups for the markers; must be set |

`POSITIONS` = variates |
Positions within the linkage groups of markers; must be set |

`DISTANCES` = symmetric matrices |
Saves the distances between markers |

`R2` = symmetric matrices |
Saves the value of r^{2} between markers |

### Description

`QLDDECAY`

estimates linkage disequilibrium (LD) between pairs of markers on a chromosome. The association between two markers is assessed by a linear regression model, with one marker set as response and the second one as regressor, and LD is expressed in terms of r^{2} values.

The model to account for genetic relatedness between genotypes is specified by the `RELATIONSHIPMODEL`

option, with one of the following settings:

`eigenanalysis` |
infers the underlying genetic substructure in the population by retaining the most significant principal components from the molecular marker matrix (Patterson et al. 2006) – the scores of the significant axes are used as covariables in the regression model, which is effectively an approximation to the structuring of the genetic variance covariance matrix by a coefficient of coancestry matrix (kinship matrix); |
---|---|

`subpopulations` |
includes a factor supplied by the `SUBPOPULATIONS` option in the regression model (imposing a constant covariance between genotypes within the same subpopulation); |

`null` |
makes no correction for genetic relatedness. |

By default `RELATIONSHIPMODEL=eigenanalysis`

; the scores of the significant axes are then calculated by the `QEIGENANALYSIS`

procedure with options `STANDARDIZE=frequency`

and `SCALE=none`

. Alternatively, scores calculated elsewhere can be supplied, in a pointer, using the option `SCORES`

.

LD is estimated per chromosome. It is not calculated between markers with too many missing values. The threshold is specified by the `MAX%MISSING`

option; default 20 (i.e. 20%). While LD is calculated along the whole of the chromosome, one expects LD decay at relatively short distances. Therefore, when plotting r^{2} values versus marker distances, only pairs of markers that are closer than the value specified by the `MAXDISTANCE`

option are displayed (default 30).

The marker scores are supplied by the `MKSCORES`

parameter, in a pointer containing a factor for each marker. The corresponding map information for the markers is supplied by the `CHROMOSOMES`

and `POSITIONS`

parameters. The `CHRANALYSE`

option must be set to specify the chromosome for which the analysis is to be performed.

The parameter `MKNAMES`

can be used to supply marker names that will be used to name rows and columns of output matrices. The `DISTANCE`

parameter can save a symmetric matrix of distances between the markers, and the `R2`

parameter can save a symmetric matrix of r^{2} values between markers.

The `PRINT`

option can be set to `progress`

, to monitor the progress of the analysis.

The `PLOT`

option selects the graphs to plot, with settings:

`lddecay` |
plots the probability values for the deviance ratios, on a -log10 scale, against the marker distance, and |
---|---|

`ldmatrix` |
gives a shade plot of the LD matrix. |

By default `PLOT=lddecay`

. The `TITLE`

option can be used to provide a title for the graphs, and the `YTITLE`

and `XTITLE`

options can supply titles for the y- and x-axis, respectively.

Options: `PRINT`

, `PLOT`

, `RELATIONSHIPMODEL`

, `SCORES`

, `SUBPOPULATIONS`

, `CHRANALYSE`

, `MAX%MISSING`

, `MAXDISTANCE`

, `TITLE`

, `YTITLE`

, `XTITLE`

.

Parameters: `MKSCORES`

, `CHROMOSOMES`

, `POSITIONS`

, `DISTANCES`

, `R2`

.

### Method

`QLDDECAY`

handles any type of marker, taking the first allele as reference (if a bi-allelic marker) or the most frequent allele if a marker has multiple alleles. The procedure fits a linear regression with one marker taken as response and a second one used as regressor. To account for genetic relatedness, the model can also include extra covariables (either principal component scores, or a grouping factor). Models are fitted using `RYPARALLEL`

to perform several fits in parallel. From each fit the r^{2} value is stored as measure of LD between the markers. Plots are produced to display results according to the settings of the `PLOT`

option.

### Action with `RESTRICT`

Restrictions are not allowed.

### See also

Procedures: `QEIGENANALYSIS`

, `QMASSOCIATION`

, `QSASSOCIATION`

.

Commands for: Statistical genetics and QTL estimation.

### Example

CAPTION 'QLDDECAY example'; STYLE=meta QIMPORT [POPULATION=amp] '%GENDIR%/Examples/LD_example_geno.txt';\ MAPFILE='%GENDIR%/Examples/LD_example_map.txt';\ MKSCORES=scores; CHROMOSOMES=mkchr; POSITIONS=mkpos;\ MKNAMES=mknames " calculate LD decay with eigenanalysis " QLDDECAY [PRINT=progress; PLOT=lddecay,ldmatrix;\ RELATIONSHIPMODEL=eigenanalysis;\ CHRANALYSE=2; MAXDISTANCE=25] \ scores; CHROMOSOMES=mkchr; POSITIONS=mkpos;\ MKNAMES=mknames; DISTANCE=distance; R2=r2 PRINT r2