The R package `qtlpoly`

(v. 0.2.4) (Pereira et al. 2020) is an under development
software to map multiple quantitative trait loci (QTL) in full-sib
families of outcrossing autopolyploid species. It is based on the
following random-effect model:

\[\boldsymbol{y} = \boldsymbol{1}\mu + \sum_{q=1}^Q \boldsymbol{g}_q + \boldsymbol{e}\]

where the vector of phenotypic values from a specific trait \(\boldsymbol{y}\) is a function of the fixed intercept \(\mu\), the \(q = 1, \dots, Q\) random QTL effects \(\boldsymbol{g}_q \sim \mathcal{N}(\boldsymbol{0}, \boldsymbol{G}_q\sigma^2_q)\), and the random environmental error \(\boldsymbol{e} \sim \mathcal{N}(\boldsymbol{0}, \boldsymbol{I}\sigma^2)\). \(\boldsymbol{G}_q\) is the additive relationship matrix between full-sibs derived from the genotype conditional probabilities of QTL \(q\). See model details in Pereira et al. (2020).

Variance components associated with putative QTL (\(\sigma^2_q\)) are tested using score
statistics, as proposed in Qu, Guennel, and
Marshall (2013). Final models are fitted using residual maximum
likelihood (REML) from the R package `sommer`

(v. 4.1) (Covarrubias-Pazaran 2016). Plots for
visualizing the results are based on `ggplot2`

(v. 3.1.0)
(Wickham 2016).

This tutorial used R version 4.2.2 Patched (2022-11-10 r83330) running on Ubuntu 20.04 LTS (64-bit).

`qtlpoly`

package and data`qtlpoly`

package is available in its stable version on CRAN and an
under-development version at GitHub. You can
install the stable version from CRAN by running:

`> install.packages("qtlpoly")`

To use the development version, please run the following commands to
install `qtlpoly`

and all of its dependencies:

```
> ## install.packages('devtools')
> devtools::install_github("gabrielgesteira/qtlpoly")
```

Then, use the function `library()`

â€“ or
`require()`

â€“ to load the package:

`> library(qtlpoly)`

`qtlpoly`

includes preloaded datasets that are simpler, so
one can run the functions along with this tutorial using a regular
personal computer (with 4 cores and 6 GB of RAM, minimum). For real data
analyses, one may need to run an R script in a cluster with more cores
and RAM. In general, the computational needs depend on ploidy level,
population size, and the number of markers.

The dataset used in this tutorial was based on a full-sib family
(\(N = 156\)) from a biparental potato
population. You can view the maps with `mappoly`

after
installing it:

```
> ## install.packages('mappoly')
> library(mappoly)
## Warning in fun(libname, pkgname): couldn't connect to display ":0"
## =====================================================
## MAPpoly Package [Version 0.3.22022-12-02 08:00:02 UTC]
## More information: https://github.com/mmollina/MAPpoly
## =====================================================
> plot_map_list(maps4x)
```

`> plot(maps4x[[1]])`