Description Usage Arguments Details Author(s) Examples

Conduct West-Wu (Q) permutation tests.

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`highobj` |
object of class |

`n.perm` |
number of permutations |

`lod.thrs` |
vector of LOD thresholds |

`alpha.levels` |
vector of significance levels |

`x,object` |
object of class |

`...` |
ignored |

`verbose` |
verbose output if |

Perform permutation tests to assess the statistical significance of the
hotspots detected using the West-Wu `Q`

-method permutations. The
`ww.perm`

function implements the `Q`

-method's permutation
scheme (see the Method's section of Chaibub Neto et a. 2012, for
details). The `n.perm`

parameter specifies the number of
simulations. Here we set it to 100 in order to save time. In practice,
we recommend at least 1,000 permutations. The function's output is a
matrix with 100 rows representing the permutations, and 10 columns
representing the QTL mapping thresholds. Each entry `ij`

, represents the
maximum number of significant linkages across the entire genome detected
at permutation `i`

, using the LOD threshold `j`

. The
`ww.summary`

function computes the Q-method's hotspot size
permutation thresholds, that is, the `1-alpha`

quantiles for each
one of the QTL mapping LOD thrsholds in `lod.thrs`

. For instance,
the entry at row 10 and column 1 of the `Q.1.thr`

matrix tells us
that the 99% percentile of the permutation distribution of genome wide
maximum hotspot size based on a QTL mapping threshold of 2.11 is
27.00. In other words, any hotspot greater than 27 is considered
statistically significant at a 0.01 significance level when QTL mapping
is done using a 2.11 LOD threshold.
In general, we are often interested in using the same error rates for
the QTL mapping and hotspot analysis. That is, if we adopt a QTL mapping
threshold that controls GWER at a 1% level (in our case, 3.11) we will
also want to consider `alpha = 0.01`

for the hotspot analysis,
leading to a hotspot threshold of 12.00. Therefore, we are usually more
interested in the diagonal of `Q.1.thr`

. We adopted a GWER of 5%,
and the corresponding `Q`

-method's permutation threshold is
18. According to this threshold, all hotspots are significant.

Elias Chaibub Neto and Brian S Yandell

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