Calculates the expected numbers of recombinations and the recombination frequencies between markers (J. Jansen, J.T.N.M. Thissen & M.P. Boer).

### Options

`PRINT` = string tokens |
What to print (`summary` , `positions` ); default `summ` |
---|---|

`PLOT` = string token |
What to plot (`frequencies` ); default `freq` |

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

`POPULATIONTYPE` = string token |
Type of population (`F2` , `BC1` , `RIL` , `DH1` , `CP` ); must be set |

`METHOD` = string token |
Which method to use (`twopoint` , `multipoint` ); default `twop` |

`USEPENALTY` = string token |
Whether to increase the number of recombinations when `METHOD=twopoint` by 0.5 recombination per informative meiosis for each missing marker score (`yes` , `no` ); default `no` |

### Parameters

`MKSCORES` = pointers |
Marker scores for each marker; must be set |
---|---|

`CHROMOSOMES` = factors |
Factor defining the linkage groups |

`POSITIONS` = variates |
Saves the positions of the markers when `METHOD=multipoint` |

`MKNAMES` = texts |
Names of the markers; must be set |

`PARENTS` = pointers |
Marker scores of the parents; must be set |

`ORDER` = variates |
Order of the markers for `METHOD=multipoint` |

`NRECOMBINATIONS` = symmetric matrices or pointers |
Saves the number of recombinations |

`RECFREQUENCIES` = symmetric matrices or pointers |
Saves the recombination frequencies |

`PHASESWITCHES` = pointers |
Saves the phase switches for pairs of markers when `POPULATIONTYPE=CP` |

`INHERITANCEVECTORS` = pointers |
Saves the inheritance vectors when `METHOD=multipoint` |

`GENNRECOMBINATIONS` = variates |
Saves the numbers of recombinations of the genotypes when `METHOD=multipoint` |

### Description

`QRECOMBINATIONS`

calculates the expected numbers of recombinations, and the recombination frequencies between markers, from the marker scores. The marker scores of the genotypes are supplied in a pointer by the `MKSCORES`

parameter. This contains a set of factors (with levels all in the same order), each one with the data for one of the markers. The names of the markers must be supplied, in a text, using the `MKNAMES`

parameter. The marker scores of the parents must be supplied using the `PARENTS`

parameter. The `CHROMOSOMES`

parameter can be set if the markers do not belong to the same linkage group. The `POPULATIONTYPE`

option must be set to specify the type of population from which the marker scores have been obtained.

The `METHOD`

option specifies whether the numbers of recombinations are calculated by the two-point or multi-point method. The default, `METHOD=twopoint`

, must be used if the order of the markers is not available. The `USEPENALTY`

option then controls whether the number of recombinations is increased by 0.5 recombination per informative meiosis for each missing marker score. For `METHOD=multipoint`

the order of the markers must be supplied, using the `ORDER`

parameter.

The numbers of recombinations and the recombination frequencies can be saved using the `NRECOMBINATIONS`

and `RECFREQUENCIES`

parameters, respectively. These usually save a symmetric matrix. However, when `POPULATIONTYPE=CP`

, the numbers of recombinations and recombination frequencies of the maternal and paternal meiosis are estimated separately, and so they each save a pointer containing two symmetric matrices. The `PHASESWITCHES`

parameter saves the phase switches in the maternal and paternal meiosis for pairs of markers, in pointers of symmetric matrices. The value of the phase switch is set to one if the saved recombination frequency is equal to one minus the observed recombination frequency, and zero otherwise.

When `METHOD=multipoint`

the positions of the markers are calculated, and can be saved in a variate using the `POSITIONS`

parameter. The inheritance vectors and expected numbers of recombinations of the genotypes can then also be saved, using the `INHERITANCEVECTORS`

and `GENNRECOMBINATIONS`

parameters, respectively.

The `PRINT`

option controls the printed output. The default setting, `summary`

, prints the minimum, mean and maximum of the `NRECOMBINATIONS`

values. When `METHOD=multipoint`

, the `positions`

setting can be used to print the minimum, mean and maximum of the `POSITIONS`

values.

The default setting, `frequencies`

, of the `PLOT`

option plots the frequencies in a shaded diagram. The `TITLE`

option can be used to provide a title for the plot.

Options: `PRINT`

, `PLOT`

, `TITLE`

, `POPULATIONTYPE`

, `METHOD`

, `USEPENALTY`

.

Parameters: `MKSCORES`

, `CHROMOSOMES`

, `POSITIONS`

, `MKNAMES`

, `PARENTS`

, `ORDER`

, `NRECOMBINATIONS`

, `RECFREQUENCIES`

, `PHASESWITCHES`

, `INHERITANCEVECTORS`

, `GENNRECOMBINATIONS`

.

### Method

For the two-point method, `QRECOMBINATIONS`

estimates the expected numbers of recombinations and maximum likelihood estimates of the recombination frequencies of pairs of markers by the EM algorithm, using the formula

*r*_{New} = E(*R*|marker data, *r*_{Current}),

where *R* denotes the number of recombinations, and *r*_{Current} and *r*_{New} denote the current and new values of the recombination frequency. The estimation requires iteration only when `POPULATIONTYPE=F2`

or in some cases when `POPULATIONTYPE=CP`

; see Maliepaard, Jansen & van Ooijen (1997). In all other cases estimation only requires simple counting of recombinations.

For the multi-point method, `QRECOMBINATIONS`

follows essentially the same procedure for estimating the recombination frequencies between adjacent markers in a sequence of markers, using hidden Markov models (HMM); see Lander & Green (1987).

### Action with `RESTRICT`

Restrictions are not allowed.

### References

Maliepaard, C., Jansen J. & van Ooijen J.W. (1997). Linkage analysis in a full-sib family of an outbreeding plant species: overview and consequences for applications. *Genet. Res., Camb,* 70, 237-250.

Lander, E.S. & Green P. (1987). Construction of multilocus genetic linkage maps in humans. *Proc. Natl. Acad. Sci USA*, 84, 2363-2367.

### See also

Procedures: `QLINKAGEGROUPS`

, `QMAP`

.

Commands for: Statistical genetics and QTL estimation.

### Example

CAPTION 'QRECOMBINATIONS examples'; STYLE=meta QIMPORT [POPULATION=F2]\ '%GENDIR%/Examples/F2maize_geno.txt';\ MKSCORES=mkscores; MKNAMES=mknames; PARENTS=parents QRECOMBINATIONS [POPULATION=F2; METHOD=twopoint; TITLE='F2 maize']\ MKSCORES=mkscores; MKNAMES=mknames; PARENTS=parents QIMPORT [POPULATION=CP]\ '%GENDIR%/Examples/CPapple_geno.txt';\ MKSCORES=mkscores; MKNAMES=mknames; PARENTS=parents QRECOMBINATIONS [POPULATION=CP; METHOD=twopoint; TITLE='CP apple']\ MKSCORES=mkscores; MKNAMES=mknames; PARENTS=parents;\ RECFREQUENCIES=recfreq PRINT recfreq[1] PRINT recfreq[2]